claims depot shelf
The Hierarchy Problem
Formal claims (Lean)
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Within the implicit regularization scheme, quadratic divergences are parametrized as $I_{\rm quad}(m^2)=b(c_2\Lambda^2+(1+c_1)m^2+m^2\ln(\Lambda^2/m^2))$, where $c_2$ is the coefficient that would break scale symmetry through a hard $\Lambda^2$ term. The paper's central discovery is that the regulator $R_n(x)=L_n(x)e^{-x}$ with $n>0$ has $\int_0^\infty R_n(x)\,dx=0$ because it is a total derivativ
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The paper's central result concerns the Goldberger-Wise mechanism, the standard way of pinning the interbrane distance in the Randall-Sundrum model. The authors compute the effective mass squared of the radion — the field that sets that distance — from small perturbations in the presence of brane-localized matter. They find that matter with positive trace T of the energy-momentum tensor makes the
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The paper's central result concerns the Goldberger-Wise mechanism, the standard way of pinning the interbrane distance in the Randall-Sundrum model. The authors compute the effective mass squared of the radion — the field that sets that distance — from small perturbations in the presence of brane-localized matter. They find that matter with positive trace T of the energy-momentum tensor makes the
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Once the scalar self-energy is completely renormalized, the physical mass function m^{2}(q^{2}) itself runs as q^{2}. Evaluated in units of the scale at which it is probed, it remains O(1) at every energy; at the GUT scale the Standard Model content alone yields m^{2}(M_GUT^{2})/M_GUT^{2} o +0.86. Matching an order-one GUT boundary condition therefore produces an electroweak-scale pole mass throug
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On the paper's own terms, the central discovery is that UV/IR mixing via classicalization forces a little hierarchy m << Λ* and, once a potential or Yukawa coupling is present, forces a chameleon screening layer to envelop the Vainshtein core. In the quadratic-potential case the classicalon radius saturates at the Compton wavelength, so a classicalon with N >> 1 weakly interacting constituents nev
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The central discovery is a complete inventory of which scalars in the SO(10) Yukawa sector can actually destabilise the proton. Of the sixty B−L-charged scalars in $10_H$, $120_H$, $\overline{126}_H$, and $16_H$, only the colour triplets $T(3,1,1/3)$, $T(3,1,4/3)$, and $T(3,3,1/3)$ (with conjugates) have both the diquark and leptoquark vertices needed for tree-level dimension-six decay, and only $
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The central claim is that in theories where the strong-gravity scale $M_f$ lies far below the Planck mass $M_P$, the memory-burden effect suppresses black hole evaporation much more effectively than in the canonical Planck-scale picture. The suppression is parameterized by $\mathrm{d}M/\mathrm{d}t = S^{-k}\,\mathrm{d}M/\mathrm{d}t|_{\mathrm{SC}}$, with the entropy $S$ enlarged by extra dimensions
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The central discovery claim is that the strong CP, hierarchy, and cosmological constant problems can be solved together in type IIA flux compactification on $T^6/(\mathbb{Z}_2\times\mathbb{Z}_2)$. The strong CP part works by identifying the axion potential of the four-form-coupled mechanism with the flux-induced potential of the orientifold: the flux constraint $b_{ij} b_j = h_i$ forces $X=0$ in t
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On the paper's own terms, the central claim is that replacing metric gravity by Einstein-Cartan gravity changes the status of Weyl symmetry. In metric gravity a local scale (Weyl) invariance is destroyed by the Weyl anomaly, and a local Weyl-invariant action is essentially the Weyl-squared theory with ghosts. In the EC formulation the vector part of the torsion, $v_\mu$, transforms as a Weyl gauge
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On the paper's own terms, the hierarchy problem is the absence of a physical mechanism for electroweak symmetry breaking, not a numerical instability of $\mu^2$. The radiative-correction formula $\mu^2 = \mu^2_{\mathrm{bare}} - \frac{3y_t^2}{8\pi^2}\Lambda^2 + \cdots$ records that any heavier particles coupled to the Higgs shift its mass term by amounts of order their mass squared; dimensional reg
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The same composite dynamics alleviates the Standard Model naturalness problem while explaining the halo structure problems.
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The inflaton scale is the geometric mean of the pre-inflation energy scale^(1/4) and the quasi-de Sitter inflation energy scale^(1/4): M_I = sqrt(rho_tilde^(1/4) * rho_inf^(1/4)).
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The Higgs mass scale is the geometric mean of the dark energy scale and the inflaton scale: M*_Higgs = sqrt(M_Lambda * M_I).
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On the paper's own terms, the central claim is that the hierarchy problem should be reframed as the Loerarchy Problem—producing the electroweak scale with no visible structure—and that the New Trail solves it by invoking the physical breakdown of effective field theory. The detailed mechanism is UV/IR mixing in noncommutative field theory: spacetime noncommutativity entangles ultraviolet and infra
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The paper's central claim is that 'strong UV/IR duality'—the one-loop transmutation of UV divergences into infrared poles—holds in noncommutative Yukawa theory, contrary to an earlier analysis that kept only one of the two inequivalent interaction orderings. Once CPT invariance is imposed, the two Yukawa couplings are equal, nonplanar diagrams contribute already at one loop, and the scalar two-poi
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The central claim, stated on the paper's own terms, is that the observed Higgs vacuum is singular in the vacuum landscape: there are infinitely many vacua with Higgs VEVs infinitesimally close to $\Phi_*\sim 100$ GeV, so the vacuum entropy $S_V=\ln n_V$ diverges. This happens because the Higgs VEV acts as a feedback control on the scanning: the charge $Q(\Phi)$ of a 2-brane sourcing the 4-form fie
Stated claims
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The paper establishes that after the Higgs discovery, the electroweak beacon — the theoretical guarantee that something new must appear near the TeV scale — has gone out. It makes the case that the Higgs boson, precisely because it is a light fundamental scalar without symmetry protection, is both a puzzle (the naturalness problem) and a tool (a portal to sectors that would otherwise be invisible). The central prescription is that the field should now operate under a paradigm of exploration rather than discovery: measure precisely what can be measured, keep a broad experimental base, encourage unconventional theory, and honestly communicate that the value of fundamental science does not depend on a promised discovery.
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A first-order stochastic dominance monotonicity assumption currently underpins the only general reductions for learning stochastic online optimization, but it fails in natural problems where observations change future feasibility, resource use, or reference points: in the full-information secretary problem a stochastically larger later value makes waiting more attractive, and in overbooking more arrivals save refunds but risk overflow costs. The paper's central discovery is that the assumption can be dropped entirely: replace every expectation in the dynamic program of the optimal policy by its supremum over a confidence set of distributions, provided the resulting optimistic continuation value, as a function $z \mapsto \bar{g}_v(z, x_{\mathrm{obs}(u)})$ of the coordinate revealed on the edge $(u,v)$, has superlevel sets that are unions of at most $s_i$ intervals (Assumption 3.1). Under this level-set condition, Theorem 3.2 gives $R_T = \tilde{O}(\sqrt{ST})$ with $S=\sum_i \min\{s_i,k_i\}$, with no FSD monotonicity and no knowledge of $s_i$, $k_i$, or the supports; for constant $s_i$ the rate is $\tilde{O}(\sqrt{nT})$ even for continuous distributions, and Corollary 3.3 gives $\tilde{O}(\sqrt{nkT})$ without any level-set condition, improving the prior bound $\tilde{O}(n(\sqrt{kT}+k))$ even in the monotone regime. Theorem 3.6 proves the matching lower bound $\Omega(\min\{T,\sqrt{ST}\})$ with $k_i = 2s_i + 1$, valid even under full feedback. The paper verifies the level-set condition with small constants ($s_i = 1$ or $2$) for five applications and, for scheduling and overbooking where the full continuation value can oscillate badly, proves a decomposition theorem (Theorem 3.7) that bounds the immediate and residual parts separately.
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The central discovery is that a single gauged chiral U(1)_χ symmetry, with charges chosen to forbid dimension-5 operators in both the clockwork and Nelson-Barr sectors while cancelling anomalies with additional vector-like quarks, resolves the quality problems that plagued earlier Nelson-Barr relaxion constructions. This raises the Nelson-Barr quality ceiling from f ≲ $10^{8}$ GeV to f ≲ $10^{13}$ GeV, and for the benchmark couplings studied the phenomenological ceiling for the scale of CP violation becomes f_pheno_max ~ 4×$10^{11}$ GeV, about eight times larger than in the original NBR model. The charge assignment (Table 1) also allows a type-I seesaw for neutrino masses and, provided the right-handed-neutrino masses and reheating temperature satisfy the Davidson–Ibarra bound, thermal leptogenesis can explain the baryon asymmetry.
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The central discovery is that single-Queen n-Hive is EXPTIME-complete, established by a reduction from unbounded two-player Constraint Logic that uses only Grasshoppers to represent reversible edge orientations and the One Hive rule to enforce vertex inflow constraints. A scaling factor s = Θ(N³) ensures that the punishment route (O(N²s) moves) is strictly shorter than the royal traversal (Ω(s²) moves) that a player must complete after reversing their target edge. The construction works even when all pieces are pre-placed and requires only Queens, Beetles, and Grasshoppers if Mosquitoes are removed, making it the first application of unbounded two-player Constraint Logic to prove EXPTIME-completeness for a natural problem.
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The authors show that the profile function $F(E)$ of an accelerated UD detector, when coupled to a bulk scalar field whose KK tower propagates in the effective $(3+1)$-dimensional brane, encodes the compactification geometry through the spacing of KK masses. For flat ADD extra dimensions, where $m_n = n/R$, the mode spacing shrinks as $R$ grows, so $F(E)$ increases smoothly with $E$ and eventually forms a continuum. For warped RS extra dimensions, where $m_n = x_n k e^{-kR_y\pi}$ with $x_n$ roots of a Bessel equation, the spacing approaches a constant $\sim 6.4$ TeV at large $n$, so $F(E)$ retains a discrete, staircase structure even at high energies. Moreover, $F(R_y)$ in RS rises dramatically within a tiny window of $R_y$ because the mass thresholds depend logarithmically on $x_n$, whereas $F(R)$ in ADD rises gradually. This qualitative contrast is robust against increasing the number of extra dimensions (studied for $d=2$ in both models). The main result is that a single measurement of the detector's response as a function of $E$ or $R$ can tell whether the extra dimension is flat or warped, without prior knowledge of the compactification scale.
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For any ε > 0 and any directed cycle, there is a one-way one-round anonymous quantum algorithm that assigns each node a color from q = 2·$10^{4}$ colors so that the probability a given edge is monochromatic is at most ε; the round count stays 1 while the number of qubits grows with ε. A classical 3-round color-reduction procedure takes the 20,000-color output down to 3 colors, and further classical reductions turn the 3-coloring oracle into O(1)-round quantum-LOCAL algorithms for every LCL problem whose classical round complexity is O(log* n), including maximal independent set and maximal matching in bounded-degree graphs. The paper thereby claims the first natural problems with an asymptotic distributed quantum advantage in the LOCAL model and a full resolution of the quantum-LOCAL landscape in the O(log* n) region.
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The central discovery is that a deformed exterior derivative $\tilde{d}$, defined on the deformed coframe $\widetilde{dx}^i = (1-\theta(x))dx^i$ where $\theta = \ln\varphi^2$ arises from spin-structure deformations, is nilpotent of order three: $\tilde{d}^3 = 0$ but $\tilde{d}^2 \neq 0$. This property causes the de Rham cohomology to split into two generalized cohomology groups, $H^k_{(1)}(\tilde{d}) = \ker\tilde{d}|_{\Omega^k}/\operatorname{im}\tilde{d}^2|_{\Omega^{k-2}}$ and $H^k_{(2)}(\tilde{d}) = \ker\tilde{d}^2|_{\Omega^k}/\operatorname{im}\tilde{d}|_{\Omega^{k-1}}$, both distinct from ordinary de Rham cohomology. Theorem III.1 establishes that the Poincaré lemma fails in both sectors: a concrete two-dimensional counterexample ($\theta=x$, $\omega=y\,dx$) satisfies $\tilde{d}^2\omega=0$ but is not $\tilde{d}$-ecact. On the physical side, when $\theta$ is taken constant, the metric transforms as $\tilde{\eta}_{ij} = (1-\theta)^{-2}\eta_{ij}$, leading to a rescaled Higgs vacuum expectation value $v = (1-\theta)^{-1}v_0$. Choosing $1-\theta \sim 10^{15}$ reproduces the observed Planck-TeV hierarchy.
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The paper claims that the absence of matter-enhanced active–sterile transitions in 10.7 years of high-energy muon-neutrino data places strong neutrino-based constraints on low-scale gravity. In the ADD framework, where the right-handed neutrino propagates in a bulk with $d$ compact extra dimensions and appears as a Kaluza-Klein tower of sterile modes, the limit on the largest radius is $R \lesssim 0.17\,\mu\mathrm{m}$ at 90% confidence level, and the result holds for both normal and inverted mass ordering with essentially no dependence on the lightest neutrino mass $m_0$. In the many-species framework, where permutation symmetry leaves one heavy state per flavor with mixing $\sin^2 2\theta \simeq 4/N$, the data exclude copy numbers below $N \gtrsim \mathcal{O}(400)$ for the values of the mass factor $\mu$ that place the resonances inside the sample's energy window. The best-fit points in both models are consistent with the null hypothesis at significance well below $3\sigma$, and a small closed contour appearing at $m_0 = 0.1$ eV corresponds to the mild-deficit region already reported in the eV sterile search, not to evidence for a signal. Over much of the parameter space the limits are competitive with or stronger than existing neutrino-oscillation bounds, and in other regions they probe previously unexplored territory.
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Within the implicit regularization scheme, quadratic divergences are parametrized as $I_{\rm quad}(m^2)=b(c_2\Lambda^2+(1+c_1)m^2+m^2\ln(\Lambda^2/m^2))$, where $c_2$ is the coefficient that would break scale symmetry through a hard $\Lambda^2$ term. The paper's central discovery is that the regulator $R_n(x)=L_n(x)e^{-x}$ with $n>0$ has $\int_0^\infty R_n(x)\,dx=0$ because it is a total derivative in the radial variable; consequently $c_2=0$ and the hard term disappears. This is proved by identifying $R_n$ with the Rodrigues formula for Laguerre polynomials. The same condition also makes the quadratic surface term $\upsilon_2$ vanish, so the regulator is compatible with the gauge Ward identity in the Higgs sector. As a result, the one-loop correction to the Higgs mass is free of a hard quadratic divergence, and the trace anomaly $\Theta^\mu_\mu$ contains no $c_2\Lambda^2\Phi^\dagger\Phi$ term, going to zero as $m\to 0$ and $\beta\to 0$.
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The paper's central claim is that the N-naturalness tower of neutrinos, in its Majorana realization, produces observable enhancements in the effective Majorana mass m_ββ and distortions in reactor neutrino oscillations. Using a global fit, the authors find that with current GERDA data combined with Daya Bay, all non-fine-tuned scenarios with r=1 up to N=10^4 are excluded at 90% confidence level, in both normal and inverted mass ordering. This rules out the benchmark scenario in which N=10^4 sectors with a cutoff around 10 TeV solve the hierarchy problem without additional fine-tuning while preserving gauge coupling unification. For projected JUNO+TAO data, the exclusion extends to N<500 for
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We formalize a k-level instruction hierarchy problem and instantiate it for k=5, yielding ten pairwise priority relations that a compliant model must enforce. We then introduce Gravity-Weighted DPO (GW-DPO), a preference-optimization objective whose per-sample offset scales with the structural distance between conflicting levels under a linear or bilateral schedule, the latter weighting severity by both the privilege gap and the privilege of the victim level. Combined with hierarchy-specific delimiter tokens and Instructional Segment Embeddings, GW-DPO with the bilateral schedule Pareto-improves over standard DPO and the linear variant on Llama-3.1-8B-Instruct, raising macro pairwise priorit
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Electroweak symmetry breaking may arise from emergent nonlocal Källén-Lehmann spectral densities in Hamiltonians with multiscalar interactions. The nonlocality scale Λ_NL emerges naturally from the exponentially increasing degeneracy of mass eigenstates in the Higgs two-point function at scales p² ≥ Λ²_NL. Following renormalization of the nonlocal Higgs propagator, analytic expressions for non-perturbative scattering amplitudes show exponential suppression for energies above Λ_NL. The real part of the Higgs self-energy is suppressed at p² ∼ −Λ²_NL, providing a solution to the hierarchy problem. Such nonlocal scalar sectors can be constrained at the LHC by a simultaneous global fit to exclusi
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The paper's central result concerns the Goldberger-Wise mechanism, the standard way of pinning the interbrane distance in the Randall-Sundrum model. The authors compute the effective mass squared of the radion — the field that sets that distance — from small perturbations in the presence of brane-localized matter. They find that matter with positive trace T of the energy-momentum tensor makes the radion's effective mass squared negative at the stabilized minimum, so the radion runs to a different minimum: for one concrete choice of parameters the stabilized interbrane separation lands at kr_cT ≈ 17×10⁻⁵ instead of ≈ 36, five orders of magnitude off the value that exponentiates the weak scale
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The synergy of scaling and non-overlapping global symmetries leads to Renormalisation Group Invariants (RGIs) among the parameters of potentials with multiple scalars, with scale-invariant field directions instrumental in identifying and constructing RGIs for bilinear field operators to all loops.
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We show that the natural problems of computing optimal controller placements or game values in this defender-attacker model are NP-complete or ΣP2-complete, depending on whether players move sequentially or simultaneously and whether they employ pure or mixed strategies. These hardness results apply to the problems of deciding if the defender can guarantee a score of at least a given threshold. For graphs that are interval graphs or have bounded treewidth, the problems admit polynomial-time solutions.
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By anchoring the brick wall to the local energy cutoff of boundary modes, the resulting blueshifted normal modes for BTZ are shown to be qualitatively identical to conventional brick-wall modes in the relevant spectrum. Exact evaluation of the partition function then identifies a little hierarchy problem: non-exact J-degeneracy makes the area-law prefactor subleading, resolvable by a trans-Planckian shift or by incorporating radial horizon degrees of freedom.
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Once the scalar self-energy is completely renormalized, the physical mass function m^{2}(q^{2}) itself runs as q^{2}. Evaluated in units of the scale at which it is probed, it remains O(1) at every energy; at the GUT scale the Standard Model content alone yields m^{2}(M_GUT^{2})/M_GUT^{2} o +0.86. Matching an order-one GUT boundary condition therefore produces an electroweak-scale pole mass through ordinary SM running, with no residual cancellation among huge numbers and no protective symmetry required.
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Beyond solving the hierarchy problem, classically conformal (CC) theories naturally accommodate dark matter (DM). In this work, we explore the CC SU(2)_X gauge theory with a triplet dark scalar, uncovering two distinct DM scenarios: weakly interacting massive particle (WIMP) and supercooled DM. The production mechanisms are strongly influenced by the CC model's unique first-order phase transition evolution history, which differs significantly from those in non-conformal models. We obtain the viable parameter space for each scenario and investigate the current constraints and future sensitivities at experiments, demonstrating that gravitational wave signals from the phase transition provide a
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Fine-tuning is quantified by the non-zero eigenvalues of the rescaled fine-tuning matrix F_ij obtained from the Fisher information matrix. This matrix encodes the sensitivity of observables to parameters through information divergences and, by Chentsov's theorem, supplies the physically natural metric on parameter space. When observables outnumber parameters, F_ij is the pullback of the Euclidean metric from observable space to the manifold of admissible predictions; large eigenvalues then correspond to stretched directions and indicate fine-tuning. The construction reproduces the Barbieri-Giudice measure in the single-parameter limit and extends it to correlated multi-parameter cases, as is
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Our main results are efficient algorithms that yield a simple O(log n)-approximation as well as a more involved O(log n/log log n)-approximation. We show that rooted instances can be solved exactly. We further show APX-hardness for general instances on star graphs. For paths, we prove strong NP-hardness and outline a PTAS. Moreover, we show that computing an optimal solution is in FPT or XP for several natural problem parameters.
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There are no weak scale triggers in the SMEFT up to dimension six that can solve the hierarchy problem far above the weak scale. Our arguments can be used to show that the same is true at dimension eight. Weak scale triggers are local operators sensitive to the Higgs mass squared and they are needed in a large number of qualitatively different cosmological solutions to the hierarchy problem. These solutions have little in common besides the use of a trigger operator. Focusing on the signatures of the three already-known trigger operators can lead to discovering or excluding this class of solutions to the hierarchy problem.
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On the paper's own terms, the central discovery is that UV/IR mixing via classicalization forces a little hierarchy m << Λ* and, once a potential or Yukawa coupling is present, forces a chameleon screening layer to envelop the Vainshtein core. In the quadratic-potential case the classicalon radius saturates at the Compton wavelength, so a classicalon with N >> 1 weakly interacting constituents never forms unless the mass is well below the interaction scale. A quartic potential or a direct Yukawa coupling would otherwise inject large radiative corrections into the core; the paper shows that a tanh-flattened potential and a conformal factor e^{-(φ/Λ)²} suppress these terms exponentially inside
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We give a natural problem over input quantum oracles U which cannot be solved with exponentially many black-box queries to U and U dagger, but which can be solved with constant many queries to U and U star, or U and U transpose.
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Let $L$ be a decidable parameterized problem. The paper defines a $\mathrm{P}^{\mathrm{NP}}$-kernel as a polynomial-time algorithm with oracle access to an NP-complete problem that maps $(x,r)$ to an equivalent $(x',r')$ with $|x'|+r' \le f(r)$, and a polynomial $\mathrm{P}^{\mathrm{NP}}$-kernel when $f(r)=r^{O(1)}$. Its central discovery is the exact correspondence $L \in \mathrm{FPT}^{\mathrm{NP}}$ if and only if $L$ admits a $\mathrm{P}^{\mathrm{NP}}$-kernel, matching the classical theorem that decidable FPT equals kernelizable. Since many natural problems above NP, such as problems hard for the second level of the polynomial hierarchy or PSPACE-hard problems, are in $\mathrm{FPT}^{\mathr
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The authors establish that the goofy symmetry — realized as $H \to iH$, $H^\dagger \to iH^\dagger$, together with $\partial_\mu \to -i \partial_\mu$, $A_\mu \to -i A_\mu$, and fermion phase factors $\sqrt{i}$ (with opposite sign for right-handed singlets) — leaves the Standard Model Lagrangian invariant provided the term $m_H^2 |H|^2$ is absent. The Higgs mass term is the unique Standard Model operator that flips sign under this transformation, so its absence is protected against radiative corrections. The paper then shows that a nonzero Higgs mass and electroweak symmetry breaking can arise spontaneously: either through the operator $|H|^8$ with a negative quartic, which gives $\kappa_{hhh}/\kappa^{\rm SM}_{hhh}=3$ and $\lambda_{hhhh}/\lambda^{\rm SM}_{hhhh}=17$, or through a portal coupling to a complex scalar singlet that acquires a vacuum expectation value and breaks goofy symmetry. In the singlet case the singlet's $Z_2$-odd component is stable and serves as a dark matter candidate, and vector-like quarks get masses only from spontaneous goofy breaking.
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The central discovery is a complete inventory of which scalars in the SO(10) Yukawa sector can actually destabilise the proton. Of the sixty B−L-charged scalars in $10_H$, $120_H$, $\overline{126}_H$, and $16_H$, only the colour triplets $T(3,1,1/3)$, $T(3,1,4/3)$, and $T(3,3,1/3)$ (with conjugates) have both the diquark and leptoquark vertices needed for tree-level dimension-six decay, and only $\Theta(3,1,2/3)$, $\Delta(3,2,1/6)$, and $\Omega(3,2,7/6)$ mediate the dimension-seven $\Delta(B-L)=2$ modes. In a realistic minimal SO(10) model built from $10_H$ and $\overline{126}_H$, the proton then decays preferentially into second-generation mesons: $p\to K^+\nu$ dominates when the antitriplet is lighter, $p\to\mu^+K^0$ when the triplet is lighter, while $p\to e^+\pi^0$ is suppressed by the hierarchical Yukawa texture. This is the opposite of gauge-boson-mediated decay, which favours $p\to e^+\pi^0$ and $p\to\nu\pi^+$. The same machinery constrains the coloured sextets via meson-antimeson oscillation, neutron-antineutron oscillation, and baryogenesis, and shows that one-loop scalar corrections can repair the minimal SU(5) relation $Y_d=Y_e^T$.
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The paper's central claim is that experimental context strongly determines pursuitworthiness, and it identifies the conditions under which experiment encourages the pursuit of ugly models: the absence of new physics discoveries combined with the absence of a new higher-energy experiment. That context makes two desiderata dominant in high-energy physics today. Radical novelty means a genuinely new class of theoretical solutions that lets physicists approach problems with new tools and insights, rather than merely new predictions from an old framework. Immediate testability means clear predictions at achievable energies and sensitivities, testable with existing facilities or small, cost-effective amendments. Because pursuit is a decision about where to allocate work before decisive evidence exists, these two desiderata can outweigh the traditional virtues and can even override minimal criteria such as consistency and empirical adequacy. The four case studies are presented as representative: the singlino-like neutralino of the next-to-minimal supersymmetric model is ad hoc and confined to a tiny surviving region of parameter space but can be probed with existing LHC data; the relaxion is a radically new solution to the Higgs naturalness problem that is not technically natural and needs roughly $10^{33}$ e-foldings; repulsive gravity is baroque, proposes multiple dark copies of the known matter content, and conflicts with general relativity but was cheaply and decisively testable with antiprotons already produced as a by-product of LHC operations; and lepton-flavour-universality-violating models were narrow in scope and heavily fine-tuned but made direct contact with anomalous LHCb data. The normative conclusion operates at the level of the discipline: it is rational for some physicists to pursue such models as part of a division of cognitive labour, even though no individual physicist is obliged to pursue any particular one.
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The central claim is that in theories where the strong-gravity scale $M_f$ lies far below the Planck mass $M_P$, the memory-burden effect suppresses black hole evaporation much more effectively than in the canonical Planck-scale picture. The suppression is parameterized by $\mathrm{d}M/\mathrm{d}t = S^{-k}\,\mathrm{d}M/\mathrm{d}t|_{\mathrm{SC}}$, with the entropy $S$ enlarged by extra dimensions or by many particle species; the black hole leaves the semiclassical regime at a smaller remaining-mass fraction $q$ and over a narrower width $\delta$, with $q$ and $\delta$ given by Eqs. (20a,b) and their entropic scalings in Eqs. (21a,b). Consequently, large-extra-dimension scenarios could keep primordial black holes alive to the present day down to about $10^{14}$ GeV $\approx 10^{-10}$ g, i.e. $10^{-5}\,M_P$, while many-species scenarios allow survival down to about $10^5$ g only when memory burden is included.
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The central discovery claim is that the strong CP, hierarchy, and cosmological constant problems can be solved together in type IIA flux compactification on $T^6/(\mathbb{Z}_2\times\mathbb{Z}_2)$. The strong CP part works by identifying the axion potential of the four-form-coupled mechanism with the flux-induced potential of the orientifold: the flux constraint $b_{ij} b_j = h_i$ forces $X=0$ in the vacuum, so the CP-violating combination vanishes dynamically. The cosmological constant part adopts the KL downshift: a supersymmetric Minkowski vacuum is displaced to AdS by a small correction $\Delta W$, then uplifted by an anti-D6-brane contribution. After checking several power-law forms for $\Delta W$, the paper argues that the only viable form is $\Delta W = f_0 U^3$, because it avoids runaway directions, keeps the vacuum near Minkowski, and does not conflict with the swampland distance conjecture. In this case the gravitino mass is $m_{3/2} = |f_0| u^{3/2}/(2^{7/2} s^{1/2} t^{3/2})$, which is below 100 TeV when $|f_0| \lesssim 10^{-6}$ and $s \sim t \sim 100$, $u \sim 0.1$.
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On the paper's own terms, the central claim is that replacing metric gravity by Einstein-Cartan gravity changes the status of Weyl symmetry. In metric gravity a local scale (Weyl) invariance is destroyed by the Weyl anomaly, and a local Weyl-invariant action is essentially the Weyl-squared theory with ghosts. In the EC formulation the vector part of the torsion, $v_\mu$, transforms as a Weyl gauge field, making curvature invariants Weyl-covariant and allowing a Weyl-invariant, ghost-free quadratic action $S_{EC,4} = \int \det e\,(\frac{1}{f^2}F^2 + \frac{1}{\tilde f^2}\tilde F^2 + \frac{2}{f_m^2}F\tilde F)$. Coupled to the Standard Model, after gauge-fixing the Weyl symmetry, for instance by setting $\chi=M_P$, one is left with the graviton, the Standard Model fields, and one extra scalar, the field $a$, an axion-like particle. The paper's conclusions state that this ALP has all properties needed to solve the strong CP problem, and that the smallness of the cosmological constant and of the ALP, Higgs, and heavy neutral lepton masses results from tiny values of the dimensionless Lorentz gauge couplings $f,\tilde f,f_m$. The paper also claims that the EC formulation permits anomaly-free quantum Weyl-invariant theories, while acknowledging that the full quantum theory remains to be constructed.
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The Hierarchy Problem separates into the Intrinsic Hierarchy Problem (IHP), caused by Wilsonian renormalization group inducing large Λ_UV² cutoff dependence on lighter scalar masses creating fine-tuning, and the Extrinsic Hierarchy Problem (EHP), which occurs when the IR theory is augmented with generically assumed extra states and interactions in the UV, making the resulting IR effective theory appear highly fine-tuned. The EHP is analyzed as a formal paradox whose premises can be identified and violated by solutions.
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The central discovery claimed is that the little hierarchy problem can be removed by combining classical scale invariance with a custodial symmetry of the extended scalar sector. At $\mu=M_{\rm Pl}$ the potential is taken to be $V(H,\Phi)=\lambda(|H|^2+|\Phi|^2)^2$, invariant under SO(6) rotations of the six real scalar components. Below that scale, the couplings split as $\lambda_H$, $\lambda_p$, and $\lambda_\Phi$ run; dimensional transmutation gives $\Phi$ a VEV $v_\Phi$, and the electroweak scale is $\mu_{\rm EW}^2\sim(\lambda_p-\lambda_\Phi)v_\Phi^2$. Because SO(6) keeps $\lambda_p\simeq\lambda_\Phi$, this scale is custodially suppressed rather than tuned, and the physical Higgs is the pseudo-Nambu-Goldstone boson with mass $m_h^2\simeq 2[\lambda_\Phi(1+g_{12}/(2g_X))^2-\lambda_p]v_\Phi^2$; making the Higgs heavier than the custodial protection wants requires additional sources of custodial breaking. In its minimal form the model has the same number of parameters as the SM and yields predicted masses $m_{Z'}\simeq g_X v_\Phi$ in the $4$--$100$ TeV range and $m_{h_\Phi}\simeq 75$ GeV for the dilaton.
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On the paper's own terms, the hierarchy problem is the absence of a physical mechanism for electroweak symmetry breaking, not a numerical instability of $\mu^2$. The radiative-correction formula $\mu^2 = \mu^2_{\mathrm{bare}} - \frac{3y_t^2}{8\pi^2}\Lambda^2 + \cdots$ records that any heavier particles coupled to the Higgs shift its mass term by amounts of order their mass squared; dimensional regularization hides this by subtracting the massless integral $\int d^d k/(2\pi)^d\, 1/k^2 = 0$, but the paper argues that fluctuations of the $t$, $\Phi$, $W$, and $Z$ fields are physically real and must be counted. Consequently, the author asserts, a solution requires new interactions at shorter distances, and without it the major open questions of particle physics — fermion masses and flavor, baryogenesis, neutrino masses, dark matter — have no unique path. The paper further claims that the little hierarchy problem, the gap between the measured Higgs mass and the masses of particles required by dynamical models, is the component most likely to be solved next, with three candidate mechanisms: competing forces, two-stage symmetry breaking, and supersoft Dirac gauginos.
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The central claim is that the large hierarchy between the electroweak scale and the scale of ultraviolet completion can be generated from just two ingredients: classical scale invariance and an SO(6) custodial symmetry of the scalar potential at the Planck scale. The potential $V=\lambda(|H|^2+|\Phi|^2)^2$ is symmetric under rotations between the SM Higgs doublet $H$ and a complex singlet $\Phi$, and neither field has a tree-level mass. Quantum corrections drive the couplings so that the potential develops a flat direction, and the Coleman-Weinberg mechanism spontaneously breaks both scale and custodial symmetry at an intermediate scale, SO(6) $\to$ SO(5). Four of the five resulting Goldstone bosons are eaten, while the fifth is the physical Higgs, whose small mass is fixed by the amount of custodial symmetry violation: $m_h^2 \approx 2(\lambda_\Phi-\lambda_p)v_\Phi^2$ in the limit of small kinetic mixing and new Yukawas. Because the top Yukawa and electroweak gauge couplings break the custodial symmetry only in subleading order, the Higgs mass is protected without introducing top partners. The paper demonstrates stability of this picture under variations of high-scale boundary conditions and under new sources of custodial symmetry violation, and constructs minimal, neutrino-portal, and dark-matter realizations.
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The paper's load-bearing claim is that the inverse limit operator f maps to f^∞, defined as the infinite compositional product realized by an infinite loop, is a well-behaved operation on Weihrauch degrees, and that WKL is a fixed point: Theorem 1 and Corollary 27 state C_{2^N}^∞ ≡_{sW} C_{2^N}, C_{N^N}^∞ ≡_{sW} C_{N^N}, and WKL^∞ ≡_{sW} WKL, so the class of non-deterministically computable problems is closed under inverse limits. The paper additionally claims CN <_W lim ≡_W C_N^∞ <_W lim^∞ and that, in general, f^∞ is strictly stronger than the parallelized diamond operator bf^⋄, while equivalent for most natural problems and for single-valued problems.
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Section 4 claims that flavour-deconstructed gauge interactions can be combined with a composite Higgs to better accommodate the tuning in the Higgs mass: 'Enforcing a left-right symmetry to eliminate a divergent contribution, the Higgs mass is [Eq. (3)]' and 'this allows for the top partner to be heavier (MT > 2 TeV), affording better compatibility with direct searches than is possible with the usual minimal CH model.' The abstract states that the resulting framework 'better accommodates the requisite tuning in the Higgs mass.' If correct, TeV-scale U(2)-aligned new physics can solve both the hierarchy problem and the flavour puzzle, with explicit signatures at HL-LHC and FCC-ee.
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The paper's central claim is that the mass of a self-interacting dark matter Dirac fermion can be generated by the same composite dynamics that produces the Higgs, in a minimal $\mathrm{Sp}(4)$ gauge-fermion theory with two fermion sectors. The $Q$-sector fermions form the composite Higgs doublet, the $\Lambda$-sector fermions form a light complex scalar mediator, and a four-fermion interaction gives the mediator a vacuum expectation value that becomes the dark matter mass. The resulting dark matter self-scatters through Yukawa exchange with a transfer cross section that declines with collision velocity, matching the pattern inferred from dwarf galaxies, low-surface-brightness galaxies, and clusters. The paper argues that the model simultaneously addresses the small-scale structure problems of cold dark matter and the naturalness problem of the Standard Model Higgs, and that its parameter space survives the combined constraints from relic abundance, BBN, CMB, and direct and indirect searches.
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On the paper's own terms, the discovery claim is stated in Section 3.5: in all Pion-like Higgs scenarios we expect modified Higgs couplings to show up at some level. More broadly, the lectures maintain that the hierarchy problem is crisp: just as the charged-pion mass splitting demands a cutoff near 750 MeV unless it is fine-tuned, the measured Higgs mass demands new physics near the TeV scale unless the Standard Model is fine-tuned. Because no symmetry is restored when the Higgs mass goes to zero, the smallness must be explained either by a protecting symmetry, by dynamics that selects a critical point, or by accepting the mass as an input parameter. The paper's contribution is to lay out the theoretical menu and to show how each option connects to specific observables—modified couplings, vector and coloured resonances, exotic Higgs decays, and cosmological signatures.
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The central claim is that the effective Higgs mass is a seesaw, geometric-mean combination of the dark energy scale and the inflaton scale, rather than an independent Standard Model parameter. With the local dark energy density fixing $M_{\Lambda}\approx2.345\times10^{-12}$ GeV and the measured Higgs mass $m_{\mathrm{Higgs}}\approx125.20$ GeV, Eq. (10) requires $M_{I}\approx6.69\times10^{15}$ GeV. The paper argues that the Planck scale cannot serve as the inflaton scale, because it would make the inflation energy density too high and violate the tensor-to-scalar bound; instead it identifies $M_{I}$ as the geometric mean of the pre-inflation energy scale $\tilde{\rho}^{1/4}$ and the quasi-de Sitter inflation scale $\rho_{\mathrm{inf}}^{1/4}$. Combining a quantum-gravity Hagedorn temperature (the maximum temperature of a thermal state, set here by the reduced Planck mass) with a locality factor of one half and a horizon cloning-fidelity factor of one sixth gives $\tilde{\rho}^{1/4}=3.73\times10^{16}$ GeV and hence $\rho_{\mathrm{inf}}^{1/4}\approx1.2\times10^{15}$ GeV, which the paper takes to match the initial conditions of unified holographic constant-roll inflation.
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The paper's central claim is that the vacuum metastability bound of the Standard Model — the upper limit on the Higgs bilinear set by the scale where the effective quartic turns negative — can be drastically lowered by a light axion-like particle mixing with the Higgs. In the Standard Model this bound is $m_{\rm crit}^2 \sim (10^{10}\,\mathrm{GeV})^2$, far above the observed value; the axion shifts the effective quartic to $\tilde\lambda_{\rm eff}=\lambda_{\rm eff}-\frac12 A'^2/m_S^2$, so the instability scale $\mu_I$ (where $\tilde\lambda_{\rm eff}=0$) drops from $\sim 10^{11}$ GeV to the TeV scale. Solving the stationary conditions in the two-field potential then gives the critical bilinear of Eq. (3.11), $m_{\rm crit}^2 = -\frac12 \beta_\lambda|_{\mu_I} e^{-3/2}\mu_I^2 + \frac12 A'^2 v^2/m_S^2$, in which the first term is the Standard Model result evaluated at the new, much lower $\mu_I$ and the second term is the axion shift; together they place $m_{\rm crit}^2$ near the weak scale. The outcome is a predictively large region of ALP parameter space — $M_S$ from a few MeV to about 20 GeV with $\sin\theta$ between $10^{-4}$ and $10^{-1}$ — where the ratio $m_H^2/m_{\rm crit}^2$ lies within two orders of magnitude of unity, meaning the smallness of the Higgs mass is no longer accidental if a cosmological criticality mechanism selects the near-critical vacuum.
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The survey's central assertion is that sparse MoE has become the standard mechanism for decoupling model capacity from per-token computation in transformer language models, and that the resulting literature is legible along three axes. On the algorithm axis it traces gating from Shazeer et al.'s differentiable top-$k$ router with auxiliary load-balancing losses through token-choice variants (top-1 in Switch Transformer, expert capacity and random secondary routing in GShard, batch prioritized routing, hash and domain-mapped non-trainable routers, BASE's linear-assignment balancing, expert-choice routing that inverts the direction of selection) and through dense and soft alternatives that merge tokens or merge expert weights to keep the whole computation differentiable. It records the design space of experts themselves: FFN experts as the default, attention experts in Mixture of Attention Heads, shared always-on experts as in DeepSpeed-MoE and DeepSeekMoE, and LoRA or adapter experts in the parameter-efficient MoE line. On the system axis it describes expert parallelism as an extension of data parallelism and catalogues the computation, All-to-All communication, and memory-hierarchy problems that sparsity creates, along with the frameworks that attack them. On the application axis it collects evidence that the same conditional-computation idea carries over to vision, recommendation, and multimodal models. The claim that would matter most if it holds is the taxonomy's sufficiency: that a reader can place any given MoE contribution on this map and find the neighbouring work.
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The paper's claim is that the mirror twin Higgs model, built to solve the Higgs hierarchy problem, also explains the nanohertz stochastic gravitational-wave background. In this model the twin sector is colder than ours by a ratio $epsilon = T_{rm twin}/T_{rm SM}$ and its QCD confinement scale is larger by the one-loop running of Eq. 1, so the dark QCD transition happens at a higher temperature than the Standard Model one. Taking the transition as first order, with the two viable flavour assignments $N_f = 0$ (twin top and bottom only) and $N_f = 4$ (two extra massless flavours), the authors compute the combined bubble-collision and sound-wave spectrum and fit it to the NANOGrav 15-year, EPTA DR2full and PPTA DR3 data. The fits favour strong transitions (large $alpha_*$) with slow nucleation rates ($beta/H_*$ near the percolation floor of 3), and require a non-zero $epsilon$ of order 0.1 to 0.2, meaning the twin sector cannot be arbitrarily cold. Translating the fitted $epsilon$ and $alpha_*$ into extra relativistic degrees of freedom through Eq. 8 gives $Delta N_{rm eff}$ between about 0.2 and 0.5, which is exactly the interval where the authors' earlier cosmological fit found the model relieves both the $H_0$ and $S_8$ tensions. The paper presents this overlap as a single parameter region answering three anomalies at once.
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The paper's central claim is that naturalness has abundant past validation as a discovery heuristic and that this validation survives the LHC's non-observation of supersymmetry and compositeness. The author separates three things that are often conflated: technical naturalness, meaning a small parameter is not destabilised by physics at intermediate scales; 't Hooft naturalness, meaning a symmetry is restored when the parameter is taken to zero; and the broader pragmatic use of naturalness to estimate the scale at which a more complete theory must enter. On this reading, the quadratic divergence in the Higgs mass calculation is not itself a problem, since the Standard Model in isolation simply has a measured parameter, but it is a reliable proxy for the size of finite contributions from whatever completes the theory in the ultraviolet. The same logic that fixed the scale of the rho meson and predicted the charm mass therefore still points at new physics within reach of the electroweak scale, even though the specific candidates Nature chose not to use have been excluded. The paper closes with a table mapping solution types across the three problems, continuous symmetries, discrete symmetries, relaxation, anthropic selection, and ultraviolet/infrared mixing, arguing that the problems are more productively thought about together than in isolation.
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The paper's central claim is that hierarchical axion couplings are simultaneously the most experimentally accessible and the most theoretically natural corner of axion model space. Quantitatively, for a fixed axion mass the detectable coupling obeys $g_{aX} ∼ 3×10^{-12} R_X (m_a/ eV)^{1/4} GeV^{-1}$ for ALP dark matter and $g_{aX} ∼ 10^{-13} R_X (m_a/μeV) GeV^{-1}$ for the QCD axion, with $R_X$ built from ratios like $c_γ/N_{DW}$ and $c_q/N_{DW}$; pushing $R_X$ up by $10^2$ or $10^4$ moves the predicted coupling straight into the reach of resonant cavities, CASPEr-type spin precession, and storage-ring probes. The same logic supplies the relaxion, where solving the weak-scale hierarchy problem is traded for a technically natural hierarchy $N_{br}/N_{DW} ≳ Λ_H^4/v^4$ between the barrier and rolling couplings, and the trans-Planckian excursion problem, where the weak gravity conjecture forces the instanton coupling $g_{aWGC}$ to exceed $g_{aΛ}$ by up to two orders of magnitude. The review then argues that these hierarchies need not be put in by hand: with $N_H$ heavy and $N_L$ light axions, the light-axion coupling vector is an integer vector orthogonal to $N_H$ charge vectors, and when $N_H ≫ N_L$ it is exponentially hard for it to stay short, so $|n̂_a| ∼ |q̂|^{N_H/N_L}$ follows from order-one inputs. The analysis assumes a clean separation between the heavy and light potential scales, $Λ_A ≫ Λ_a$, and the authors note in footnote 4 that if all potential terms have comparable size the resulting landscape structure can differ substantially.
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On the paper's own terms, the central claim is that the hierarchy problem should be reframed as the Loerarchy Problem—producing the electroweak scale with no visible structure—and that the New Trail solves it by invoking the physical breakdown of effective field theory. The detailed mechanism is UV/IR mixing in noncommutative field theory: spacetime noncommutativity entangles ultraviolet and infrared modes, so quantum-gravitational UV effects can set an infrared scale such as the Higgs mass. The thesis shows this concretely in real scalar φ4 theory, Yukawa theory, and a softly broken Wess–Zumino model, where ultraviolet divergences generate infrared dynamics. This is a proposed mechanism, supported by explicit calculations of the scale-generation effect, rather than a complete model of the Standard Model.
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The paper's central claim is that the relaxion is generically stabilized at a special place in field space, close to the inflection point of the periodic backreaction potential, and that this single fact reorganizes its low-energy phenomenology. Because the Higgs vacuum expectation value changes only incrementally from one period to the next, by a fractional amount of order $|delta^2 = (|mu_b/|Lambda)^2$, the backreaction amplitude can barely overshoot the rolling slope. The first minimum therefore appears within $|Delta|theta |sim |delta$ of the inflection point, and the relaxion mass becomes $m_|varphi^2 |simeq |delta |Lambda_{br}^4/f^2$ instead of the naive $|Lambda_{br}^4/f^2$, with the barrier height suppressed by $|delta^3$. The mixing angle, by contrast, keeps its naive size, $|sin|theta_{h|varphi} |simeq |Lambda_{br}^2/(f v_{EW})$. Combining this with the requirement that relaxation actually succeed, the authors derive a maximum mixing angle of roughly $(m_|varphi/v_{EW})^{2/3}$ for relaxion masses above an eV, with two further regimes at lower mass set by the cosmological constraint and by requiring a sub-Planckian decay constant, plus a mass-dependent lower edge and a floor near $10^{-44}$. The physical reading is that the relaxion itself is relaxed, so its mass and its couplings need not obey the relation that radiative stability would demand.
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The central claim is that a de Sitter black hole's fate depends sharply on the ratio $m^2/(qE)$ of the charged carrier, and that the fast-discharge regime is incompatible with de Sitter behaving as a thermal system. In the slow regime the flow on the $(M,Q)$ plane stays inside the region bounded by extremal and charged Nariai solutions — the authors' shark fin — and every solution reaches empty de Sitter, consistent with the thermal picture. In the fast regime the black hole loses its charge while keeping its mass, which puts it at a neutral point heavier than the neutral Nariai solution; from there the two-sphere shrinks and the spacetime ends in a crunch, with the authors checking via singularity theorems that the crunch does not depend on the chosen initial surface or on the Nariai approximation. Demanding that this never happens yields $m^2 > q g M_P H$ for every charged particle, a bound that survives the $M_P o infty$ limit and therefore forbids decoupling gravity at fixed $H$ and $g$. The authors are explicit that this is a candidate constraint rather than a derived theorem, since they have no stringy examples to test it against.
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The paper's central claim is that 'strong UV/IR duality'—the one-loop transmutation of UV divergences into infrared poles—holds in noncommutative Yukawa theory, contrary to an earlier analysis that kept only one of the two inequivalent interaction orderings. Once CPT invariance is imposed, the two Yukawa couplings are equal, nonplanar diagrams contribute already at one loop, and the scalar two-point function acquires a pole of the form $-2g_1g_2/(\pi^2 p\circ p)$ in the infrared, with sign opposite to the pole found in real $\phi^4$ theory. The paper states that this opposite sign makes the pole accessible in Euclidean signature, clearly signaling a tachyonic instability, and that in the Lorentzian theory with timelike noncommutativity the pole is accessible in the s-channel. The pole position depends on the boost of the scattering frame, so the corresponding resonance is smeared rather than sharp. The same mechanism is shown to disappear in the softly-broken Wess-Zumino model when both scalar and fermion are below the cutoff, and to reappear when the fermion is heavier than the cutoff.
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The paper's central claim is that in a $D=2n$ Starobinsky model with an added term $\lambda R^m/(mM^{2m-2})$, the leading shifts in the spectral index and tensor-to-scalar ratio are $\delta n_s = -\frac{4\lambda n(m-1)^2(m-n)}{m(n-1)^2(2n-1)(m+n-2)}\left(\frac{2n}{2n-1}N_e\right)^{\frac{m-n}{n-1}}$ and $\delta r = -\frac{32\lambda n^2(m-1)(m-n)}{m(n-1)^2(2n-1)(m+n-2)}\left(\frac{2n}{2n-1}N_e\right)^{\frac{m-n}{n-1}-1}$, up to higher order in slow-roll parameters. For $m>n$ the $N_e$-dependent factor is much smaller than one when $N_e\simeq 50$–$60$, and the prefactors fall roughly as $n^{-2}$, so the same value of $\lambda$ moves the predictions less as $D$ grows. Numerical evaluation in $D=10$ confirms the trend: the CMB-allowed range of $\lambda$ is orders of magnitude wider than in $D=4$ for the same $m$ and $N_e$. The paper concludes that the observational predictions of $D>4$ Starobinsky-like models are less sensitive to higher-curvature terms, which eases the hierarchy problem in constructing such models.
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The central claim, stated on the paper's own terms, is that the observed Higgs vacuum is singular in the vacuum landscape: there are infinitely many vacua with Higgs VEVs infinitesimally close to $\Phi_*\sim 100$ GeV, so the vacuum entropy $S_V=\ln n_V$ diverges. This happens because the Higgs VEV acts as a feedback control on the scanning: the charge $Q(\Phi)$ of a 2-brane sourcing the 4-form field strength $F$ vanishes at $\Phi_*$, making the jumps $\Delta F=Q(\Phi)$ shrink to zero as the VEV approaches the attractor. Crossing the brane an infinite number of times is then required to reach $\Phi_*$, which is exactly what eternal inflation supplies. Consequently, the Universe is driven to the critical VEV with unit probability, and no stabilizing new physics need appear below the cutoff, which may be as high as the Planck mass. The paper adds that this is compatible with Wilsonian decoupling because the massless graviton, through eternal inflation, is the agent that realizes the maximal-entropy vacuum over arbitrarily long time scales.
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Partial compositeness generically produces lepton flavour universality violation, enabling both a simple model and the minimal fundamental partial compositeness model to account for the anomalies in rare B-meson decays while the latter also solves the naturalness problem of the Standard Model.
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The paper's central claim is that the $mu$ problem needs restating for the LHC era: the requirement is no longer $|mu|$ of order the soft breaking scale but $|mu|$ of order $100$-$300$ GeV while $m_{soft}$ sits at several TeV, a little hierarchy that any viable solution must accommodate. Reviewing twenty mechanisms grouped into supergravity/string constructions, extended-MSSM singlet models, extra local $U(1)'$ models, and Peccei-Quinn/axion models, the authors find that nearly all of them can host this hierarchy, usually by tuning a dimensionless coupling. What separates them is gravity safety: global symmetries such as Peccei-Quinn are expected to be spoiled by Planck-suppressed operators, so the authors apply the Kamionkowski-March-Russell criterion, which demands that every symmetry-violating operator in the scalar potential be suppressed by at least eight powers of $1/m_P$. Screening the candidates against the anomaly-free discrete R-symmetries $Z_N^R$ ($N = 4, 6, 8, 12, 24$) that are consistent with grand unification, they report that the radiative Peccei-Quinn models (MSY, CCK, SPM) and the $Z_{22}$ discrete-gauge model fail under every entry, while the hybrid constructions based on $Z_{24}^R$ pass, and $Z_4^R$ is singled out as the simplest symmetry that forbids $mu$, forbids proton-decay operators, and leaves R-parity exact.
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The central claim is that the phenomenology of the triplet extension is set by the $1/f$ effective operators, not by the renormalizable Lagrangian. Because the renormalizable trilinear coupling that would let the triplet decay is bounded by the $rho$ parameter to give a triplet vacuum expectation value below about a GeV, the decays are instead dominated by operators of the form $q_L( H Phi) q_R / f$, giving widths that scale as $(c/f)^2$ and produce $t$- and $b$-rich final states. From that starting point the authors derive current and projected LHC exclusions in the $(m_Phi, c/f)$ plane from three existing search strategies — gluon-fusion single production of the neutral component into $bb$, associated production $pp to phi^pm t b$ with $phi^pm to tb$, and rare top decays $t to phi^pm b$ — and show that a wide region of small $c/f$ remains untouched by all of them. They then fill that gap with a dedicated simulation of $pp to phi^pm phi^0 to tb(bt), bb$, a channel whose cross section is fixed by electroweak couplings alone, finding significances from 2.7 to 7.3 at 3 ab$^{-1}$ for triplet masses between 185 and 340 GeV. In parallel, the paper computes the finite-temperature effective potential and finds a region of the scalar potential, not yet excluded by the measured $h to gamma gamma$ rate, where the transition is strongly first order and the resulting gravitational wave signal falls inside the LISA sensitivity band.
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The paper's central claim is that the lifetime frontier is a distinct and consequential part of the search program for physics beyond the Standard Model, not a niche corner of it. The argument runs in three steps. First, long lifetimes are generic: a particle is long-lived whenever its decay is forbidden by an approximate symmetry, suppressed by a high mass scale, or squeezed by limited phase space, and each of these conditions arises naturally in models built to address the hierarchy problem, dark matter, and neutrino masses. Second, these particles produce signatures that ordinary prompt reconstruction handles poorly — a charged LLP far heavier than a proton moves slowly, so it deposits anomalously large ionization energy and arrives late at the outer detectors; a neutral LLP that decays inside the tracker leaves a displaced vertex or a track that simply stops; a particle that comes to rest in dense material can decay during an unfilled bunch crossing, when no collision background exists. Third, because these signatures are so unusual, the searches built around them have backgrounds that are frequently well below one event, so sensitivity grows roughly linearly with integrated luminosity rather than with its square root, which makes LLP searches unusually valuable at high-luminosity machines. The review backs this with a volume-acceptance calculation for a generic LHC-like detector, showing that for pair-produced 2 TeV gluinos the inner tracker gives the best reach across a wide span of lifetimes, and that only at lifetimes beyond roughly 100 ns does the muon system take over.
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The central claim is that the freeze-in production history of a feebly interacting dark fermion is modified, in a structured and readable way, by the thermal history of a two-step phase transition. Concretely, the authors solve a coupled set of Boltzmann equations for the dark fermion $N$, the hidden scalar $h$ and the dark fermion $N$ in which the field-dependent masses $m_ h(T)$, $m_ h(T)$ and the vacuum expectation values $v_h(T)$, $v_ h(T)$ are supplied by the finite-temperature potential. As the temperature falls, the one-to-two channels $h_ h(T)$ close whenever $|m_ h(T)-m_N| < m_ h(T) < m_ h(T)+m_N$ and reopen outside that window, producing a sequence of dips in $dY_ h/dz$; the second-order transition then raises $m_ h(T)$ again through the nonzero $v_ h(T)$, and the first-order transition produces a final discontinuity. The authors present benchmarks in which the abundance computed with the phase transition differs substantially from the one computed without it, particularly when the one-to-two channel is kinematically forbidden at zero temperature. They also compute the nucleation temperature from the bounce action, estimate the entropy injection at percent level, and show that the same benchmark couplings give gravitational wave spectra in the band covered by LISA, ALIA, BBO and DECIGO.
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The paper's claim is that the relaxion sector, with no new ingredient beyond what the hierarchy-problem solution already requires, reproduces the observed dark matter relic density. The mechanism is a dynamical version of axion misalignment: after reheating at a temperature above the electroweak crossover the backreaction potential $V_{br} = -mu^2 |H|^2 cos(varphi/f)$ is switched off, the relaxion rolls under its linear slope, and it is left at $Delta phi/f simeq m_0^2/(20 H^2)$ away from the minimum that will re-form. The relic abundance then follows from the standard misalignment formula, $Omega_phi h^2 approx 3 (Delta theta)^2 (sqrt{m_phi f}/1,mathrm{GeV})^4 (100,mathrm{GeV}/T_{rm os})^3$, with $T_{rm os} simeq min[T_{rm ra}, sqrt{m_phi M_{rm Pl}}]$. Requiring that the relaxion be retrapped by the barrier gives the viable window $5times 10^{-11},Lambda_{rm TeV}^{8/11}(M_{rm Pl}/f)^{20/11} lesssim m_phi/mathrm{eV} lesssim 10^{-8},Lambda_{rm TeV}^{-4/7}(T_{rm ra}/150,mathrm{GeV})^{20/7}$, and also turns into a new exclusion: a region of relaxion parameter space would overclose the universe. For heavier relaxion, where Hubble friction alone cannot stop the field, the authors add a coupling $(r_X/4f)varphi X_{mu nu}tilde X^{mu nu}$ to a dark photon; the resulting tachyonic particle production drains the field's kinetic energy, the velocity asymptotes to $dot theta simeq r_xi H$, and the total excursion becomes only logarithmic in the model parameters, $Delta phi/f simeq r_xi[1/2 + ln(H_{rm pp}/H_{rm ra})]$, which can be chosen to be $mathcal{O}(delta)$ and therefore small enough to be trapped.
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The paper's central claim is that a two-doublet scalar potential of the form $V = m^2(|H|^2-|H_H|^2) + (g_X^2/2)(|H_H|^2-|H|^2-f_X^2)^2$ has a classical vacuum manifold that is a hyperbola, $|H_H|^2-|H|^2=f^2$, and that this potential possesses an accidental $U(2,2)$ symmetry which the one-loop top-sector corrections inherit. The top quark contributes $+(N_c/16π^2)λ_t^2 Λ^2 |H|^2$; the Hyperbolic stops, being scalars, contribute with the opposite sign, so the cutoff-sensitive piece is proportional to $(|H_H|^2-|H|^2)$ and cancels from the light Higgs mass. The authors emphasize that $U(2,2)$ is not a symmetry of the full theory — the kinetic terms break it — so this is an accidental infrared protection rather than an exact one, and the SM-like Higgs emerges as the massless mixture $h_{SM}=h cos θ + h_H sin θ$ with $tan θ = v/v_H$. They then build an explicit completion in five-dimensional supersymmetry with a $Z_2$ exchange symmetry, Scherk-Schwarz boundary conditions that leave fermionic zero modes in the visible sector and bosonic zero modes in the Hyperbolic sector, and a new $U(1)_X$ gauge symmetry whose non-decoupling D-term supplies the $U(2,2)$-symmetric quartic.
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The central claim is that a non-linearly realized discrete symmetry does the work usually assigned to supersymmetry, compositeness, or an extra dimension. Take a periodic scalar $��$ of period $2πf$ whose exact shift symmetry is broken only by a spurion $ϵ$, and $N$ copies of the particles it couples to, permuted cyclically by $Z_N$. Because the scalar's potential must be $2πf/N$ periodic, it is a sum $V(φ) ∝ ∑_{k=0}^{N-1} F(φ/f + 2πk/N)$; that sum is a Riemann approximation to $N/2π ∫_0^{2π} F(θ) dθ$, which carries no $φ$ dependence at all. The residual $φ$-dependent piece is bounded by the convergence rate of the sum: for a function that is $2m+1$ times differentiable the bound falls only as a power of $N$, but for an analytic function it falls as $4πM/(e^{Na}-1)$, exponentially in $N$ with $a$ set by the distance from the real axis to the nearest singularity. Applied to an axion coupled to $N$ copies of QCD with $θ_k = 2πk/N$, the axion mass is suppressed by at least $2^{-N/2}$, with a numerical fit agreeing with that exponential scaling; applied to $N = 3$ or $4$ copies of the Standard Model Higgs with $φ$ as the modulus of the Higgs mass squared, it yields one Higgs roughly a factor of ten lighter than its natural value, because the potential is sensitive to the phase transition where a Higgs mass crosses zero.
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The central claim is that the clockwork/linear dilaton (CW/LD) theory is a calculable and distinctive alternative to the standard extra-dimensional benchmarks, and that its most characteristic prediction — a mass gap followed by a narrowly spaced graviton tower — can be searched for directly by Fourier-transforming the diphoton and dielectron invariant mass spectra. Because the Kaluza-Klein masses satisfy $m_n^2 = k^2 + n^2/R^2$, the spectrum is periodic in $k^2 + n^2/R^2$'s square root with period $1/R$; the authors define a power spectrum $P(T)$ in their eq. (3.5) and show, after adding the ATLAS spin-2 diphoton background, fitting and subtracting a smooth non-oscillating curve, and generating Poisson-fluctuated pseudo-experiments, that the peak at $T = 1/R$ survives. The resulting expected limit is reported as competitive with high-mass continuum searches, single-resonance bump hunts, and dijet angular analyses, with $M_5$ typically required to exceed roughly 6 TeV. A second new result is that decays of a heavy KK graviton into pairs of lighter ones are not negligible: they can dominate at large mode number, they prefer $n$ approximately equal to the sum of the two daughter mode numbers, and they make cascades, high-multiplicity final states, and displaced decays part of the same phenomenology.
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The central claim is that the naturalness problem in adversarial example generation is a search-space problem. Instead of minimizing a distance in input space, the authors search in the latent space $z$ of a generative model trained on unlabeled data, defining the adversary as $x^* = G_ heta(z^*)$ where $z^* = nd{argmin}_{ilde{z}} | ilde{z} - I_gamma(x) |$ subject to $f(G_ heta( ilde{z})) eq f(x)$, with $I_gamma$ an inverter trained to reconstruct inputs through the generator and to keep the latent space close to a Gaussian. Because every candidate is decoded through the generator, every candidate is by construction a sample the generator considers plausible, which is what makes the adversaries legible in MNIST digits, in LSUN church-versus-tower images, and in SNLI hypotheses. The authors then turn the machinery into an evaluation tool: the latent distance $Delta z = |z^* - z'|$ needed to flip a classifier is offered as a measure of how much semantic change that classifier demands, and they report that this quantity rises with test accuracy for random forests versus LeNet on MNIST, for embedding, LSTM, and TreeLSTM entailment models, and across 80 varied MNIST classifiers, all without access to gradients or labels.
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The central claim is that the relaxion and the inflaton can be one and the same field, provided a dissipation channel survives past the end of inflation. The authors couple the relaxion to an Abelian gauge field through a $c_? (4f) F ?F$ term; the time-dependent background makes one polarization of the gauge field tachyonic, and the resulting backreaction term $(c_?/f)?E?B?$ balances the slope of the rolling potential. This balance holds the field's velocity roughly constant, so the relaxion does not run away after the Hubble friction of inflation is gone, and it can be caught by the periodic wiggle potential at the point where the Higgs vacuum expectation value is 246 GeV. Because the relaxion is the inflaton, the potential energy available is of order the cutoff scale rather than being constrained by a separate inflationary sector, which is what lets the cutoff reach close to the Planck scale. The same exponential gauge-field production yields a reheat mechanism: the photons have huge occupation numbers at very low momentum, form a coherent electric field, and drive Schwinger pair production of electrons and positrons, which thermalize. The authors show that the Standard Model photon version is not viable — the pairs heat the plasma to $T$ of order $m_e$, the Debye mass $m_D$ suppresses the tachyonic growth by a factor of order $H^4/m_D^4$, and both the friction and the reheat temperature fail. Introducing a massless dark photon with a small kinetic mixing $?$ to the visible photon restores both, and the paper maps out the window in $?$ where pair production is fast enough while the dark photon stays out of thermal equilibrium. The authors acknowledge that the minimal model does not generate the observed curvature perturbations and that a curvaton or similar ingredient is needed.
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The central claim is eq. (10): with $A^{UV}_{y} > 0$ above the Planck scale and $A^{IR}_{y} = -2$ below it, the physical scalar mass divided by the Planck mass is $m_{ph}/M = (k_X/M)^{A^{UV}_{y}/A^{IR}_{y}}$, which for $A^{UV}_{y} = 0.5$ gives $10^{-16}$ from an initial $y(k_X)$ of order one. The authors describe the flow of the dimensionless mass parameter as first decreasing towards the critical surface in the ultraviolet and then increasing in the infrared, and they argue that the sensitivity of the final mass to the initial parameter is order one, so no fine-tuning is involved. The mechanism requires a gravity-induced anomalous dimension large enough to make the scalar mass term irrelevant at the ultraviolet fixed point. The paper reports that the scalar-gravity system without fermions gives $A^{UV}_{y} approx -0.117$, which does not work, while a six-coupling Higgs-Yukawa-gravity truncation gives $A^{UV}_{y} approx 0.5$, which does.
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The paper establishes that the minimal mirror Twin Higgs is ruled out by its own twin radiation — the twin photon alone forces $Delta N_{rm eff}$ well above the Planck limit for every neutrino mass spectrum the authors try — and then shows two ways to dilute the twin sector while respecting the softly broken $Z_2$. The first and most developed is a real scalar $X$ that is a total gauge singlet and couples symmetrically to both Higgs doublets through $lambda_x X (X + x)(|H_A|^2 + |H_B|^2)$. Because $X$ communicates with fermions and gauge bosons only through mixing with the two Higgs mass eigenstates, and because the mixing into the twin doublet is suppressed by $v_A/f$, the branching ratio into the twin sector scales as $(v/f)^2$ for $m_X < f$. A symmetric coupling therefore produces an asymmetric reheating. If $X$ dominates the energy density and decays below the $sim 2$ GeV decoupling temperature, the twin plasma ends up cooler than the Standard Model plasma by a factor set by the branching ratio, and the twin contribution to $Delta N_{rm eff}$ is pushed below the observational bound. The second scenario, Twinflation, twins a $phi^2$ chaotic inflation sector so that a heavier twinflaton drives a first inflationary epoch that reheats mostly the twin sector, which is then diluted by a second epoch of ordinary inflation that reheats the Standard Model to below decoupling. In both cases the dilution mechanism is not a patch bolted onto the model but a consequence of the same hierarchy that makes the model natural.
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The central claim is that exponential suppression of couplings is a structural property of a lattice with asymmetric nearest-neighbour mixing, not a property of any particular field. The mass matrix $M^2_=m^2$ tridiagonal with entries $1$, $1+q^2$, and $-q$ has one zero eigenvalue and $N$ eigenvalues $m^2(q^2+1-2qcos(kpi/(N+1)))$, and the zero-mode components fall as $O_{j0}propto q^{-j}$. Coupling an external sector at site $N$ therefore generates an effective scale $f_0=fq^N/N_0$ from a fundamental scale $f$ with no small parameter anywhere. The authors extend this to a chiral chain for fermions, to $N+1$ $U(1)$ factors Higgsed by scalars of charge $(1,-q)$ for vectors, and to $N+1$ copies of linearised gravity with Pauli-Fierz mixings for gravitons, in each case finding the same spectrum of $N$ heavy gears plus one protected massless state. The continuum limit is claimed to be forced: requiring site-independent masses and a finite $q^N$ as $Ntoinfty$ fixes the metric to $e^{4k|y|/3}(dx^2+dy^2)$, which the authors identify as the linear dilaton background dual to Little String Theory, and which yields $M_P^2=(M_5^3/k)(e^{2kpi R}-1)$ with gear interaction scales $Lambda_napprox M_5^{3/2}/k^{1/2}$.
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Assuming the relaxion's initial energy is dissipated by Hubble friction during inflation, the authors derive the region of $(m_phi, f)$ compatible with a given acceptable number of e-foldings $N_e$ and a Higgs mass cutoff $M$. Requiring $N_e < 10^{24}$ forces the barrier potential to come from new physics near the weak scale rather than from QCD, which in turn bounds $M$ below roughly 10 TeV and ties the relaxion mass to the barrier amplitude through $m_phi ~ Lambda_b^2/f$. Overlaying the observational constraints, they find that most of the parameter space with $m_phi > 100$ eV or $f < 10^7$ GeV is already excluded, and that exactly three regions survive: $f$ of a few to 200 TeV with $m_phi$ of 0.2 to 10 GeV; $f$ of $10^6$ to $10^9$ GeV with $m_phi$ of a few to 50 MeV; and the largest, $f > 10^7$ GeV with $m_phi < 100$ eV. The first region is the interesting one, because the relaxion-Higgs mixing that makes it visible to LEP and to electron and proton electric dipole moment searches also makes it visible to SHiP, and all three regions contain a corner with $N_e < 10^4$ if the cutoff is below 10 TeV.
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The central claim is that a natural, non-minimal warped model exists in which the states solving the hierarchy problem lie at $O(10)$ TeV while lighter, flavor-safe vestiges lie within LHC reach. Concretely, with an intermediate brane ending the matter/Higgs bulk at $O(10)$ TeV and a final IR brane at a few TeV, the Kaluza-Klein spectra of matter, gauge fields and gravity split into a little hierarchy, and the Goldberger-Wise mechanism used to stabilize the brane separations is shown to accommodate this ordering rather than fight it. The low-lying resonances — a radion/dilaton, spin-1 gauge Kaluza-Klein modes, and a spin-2 graviton Kaluza-Klein mode — then have couplings dominated by the flavor-blind gauge channel, so the standard dijet, dilepton, diboson and diphoton searches become the discovery channels instead of the top- and Higgs-rich final states of the minimal model. The paper further derives the small flavor non-universal couplings induced by integrating out physics at the compositeness scale, and shows in Eq. (51) and Table 2 that for fixed resonance mass and production cross-section the decay branching ratios into tops, Higgs/W/Z and light jets can vary by order-one amounts between the minimal composite Higgs limit, intermediate values of the compositeness scale around 10 to 15 TeV, and the fully flavor-blind limit.
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The central assertion is that introducing N copies of the Standard Model with Higgs mass parameters distributed between -Lambda_H^2 and +Lambda_H^2 generically produces a sector tuned at the 1/N level, so that its weak scale is v ~ Lambda_H/sqrt(N), and that a light reheaton with branching ratios scaling as 1/m_H^alpha deposits most of the energy density into that sector. If correct, the hierarchy problem is solved statistically, with no new particles required at the LHC, and the mechanism is testable through Delta N_eff, neutrino cosmology, and a heavier axion.
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The paper's claim is that exponential particle production, not cosmic expansion, can supply the friction that makes the relaxion work. The relaxion $varphi$ couples derivatively to the combination of hypercharge and weak gauge field strengths that does not contain the photon, so the tachyonic instability that develops when $|dvarphi/dt| > 2 f m_A$ switches on only once the gauge bosons become light, i.e. once the Higgs vev has been scanned down to roughly 100 GeV. The energy drained into the produced gauge bosons backreacts thermally on the Higgs, driving the vev toward zero, which strengthens the tachyon and lets $dvarphi/dt$ fall below the height of the periodic cosine barriers $Lambda_c^2$; the field is then caught in the nearest minimum, which is the one with the observed Higgs mass. Because the stopping is triggered by the Higgs vev itself, the authors obtain a UV cutoff bound $Lambda^2 (dvarphi_s/dt)^4 lesssim M_p v^5 Lambda_c^4$, which for conservative parameter choices gives $Lambda lesssim (M_p v^5)^{1/6} approx 5 times 10^4$ GeV, rising to about $10^6$ GeV in the during-inflation variant. Sub-Planckian field excursions are achieved by taking $epsilon$ large enough that $Lambda^2/epsilon < M_p$, and the coupling to QCD is absent by construction, so the relaxion does not disturb the strong CP problem. The paper works out three settings with sample parameter points: relaxation before inflation, during inflation (where the field approaches a pseudo-slow-roll solution $dvarphi/dt approx epsilon Lambda^2/(3H)$), and after inflation. In the after-inflation variant where the field starts from rest, the authors note that Hubble exceeds the cutoff, so their effective description breaks down there and they assume the mechanism can be embedded in an inflationary sector with a larger cutoff.
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The central claim is that the black hole Love numbers of classical general relativity are a naturalness problem. In electrodynamics an applied field induces a dipole moment through a susceptibility, and that susceptibility is generically nonzero; in gravity the analogous response coefficients $f_e(0)$ and $f_e(2)$ describe the induced multipole moments of an extended body in a long-wavelength tidal field. Dimensional analysis suggests a coefficient of order $r_s^5/G_N$, and matching the effective point-particle action to the black hole absorption cross section confirms the absorptive part is nonzero, with $2G_N f_e^{(1)}/r_s^5 = 1/45$. But the conservative, real part of the response vanishes identically for black holes: $f_e^{(0)} = 0$ and there is no logarithmic piece at order $v^0$, so the Wilson coefficient $C_E$ vanishes at all scales within the effective field theory. Since nothing in the theory appears to forbid it, and no symmetry appears to protect it, the author reads this as a fine tuning. The concrete consequence is that a nonzero $C_E$ measured for a black hole would be a signature of new physics — quantum hair, a surrounding cloud, or a modified short-distance completion — and the effect first appears formally at 5PN order in the inspiral waveform.
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The central claim is that the two-scalar action of Eq. (1) satisfies five criteria simultaneously: it has no mass input parameters; scale symmetry is broken only by the non-minimal couplings to curvature, with coefficients departing from the conformal value; the Planck mass is generated dynamically from the scalar VEVs; there is a viable slow-roll inflationary stage in the two-scalar potential; and the final vacuum has a small or vanishing cosmological constant together with a hierarchically small ratio of VEVs and of scalar masses to the Planck mass. The mechanism that makes the last of these work is an infrared fixed point of the scale-invariant potential, obtained by setting the field velocities and accelerations to zero, which fixes $<br>langle<br>chi_0<br>rangle^2/<br>langle<br>phi_0<br>rangle^2 = (4<br>lambda<br>beta - 2<br>alpha<br>delta)/(4<br>alpha<br>xi - 2<br>beta<br>delta)$; only dimensionless ratios of VEVs are physical, and the absolute scale of a VEV is not measurable. The authors argue this fixed point is radiatively stable because the small couplings $<br>lambda$ and $<br>delta$ are protected by an enhanced shift symmetry $<br>phi <br>to <br>phi + c$ in the limit where they vanish, so corrections to them are proportional to themselves or to $<br>delta^2$.
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The paper's central claim is that the twin Higgs cancellation does not require a chiral mirror sector. In the toy model of Section 2, adding vector-like mass terms $M_Q$ and $M_U$ for the twin quark partners breaks the exchange symmetry between the two sectors only softly, so the quadratically divergent correction to the Higgs potential keeps the same $SU(4)$-symmetric form as in the ordinary twin Higgs, and the order-$M_Q^2$ terms that could ruin it require at least two mass insertions and are therefore only logarithmically divergent. The residual sensitivity is the threshold correction of Eq. (2.11), which the authors translate into a bound $M_Q, M_U$ below roughly 450 GeV. Because the twin quarks are now Dirac rather than Weyl, the twin sector is anomaly-free by itself: no twin leptons are needed, and the minimal twin matter content is two twin tops and one twin bottom. The authors then build two example models, a minimal one that is the vector-like analogue of the fraternal twin Higgs and a three-generation one with large twin flavour-changing neutral currents, and describe the resulting LHC signals: twin glueball decays, possibly displaced, sometimes in association with on- or off-shell Higgs bosons. Finally they construct an explicit four-dimensional UV completion, a two-node quiver per sector with vector-like link fields, and relate it to orbifold constructions in four and five dimensions, noting that the same mechanism UV-completes the fraternal twin Higgs.
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The paper's central claim is that an exponentially long relaxion direction can be assembled inside a compact field space of $N$ axions whose individual decay constants stay well below the Planck scale. A chain of mass mixings, $tilde{V}_0 = -sum_{i=1}^{N-1} Lambda_i^4 cos(phi_i/f_i + n_i phi_{i+1}/f_{i+1})$, leaves a single flat direction $phi propto sum_i (-1)^{i-1} (prod_{j=i}^{N-1} n_j) f_i phi_i$ along which the canonically normalized field has period $2 pi f_eff$ with $f_eff ~ (prod_{j=1}^{N-1} n_j) f_1 ~ e^{xi N} f$. The potentials that drive the roll and set the Higgs mass, $V_0$ and $mu_h^2(phi)$, inherit this long periodicity, while the back-reaction potential that stops the relaxion keeps the short period $2 pi f$, with $f ~ f_1$. That split is exactly what the relaxion mechanism requires, and it is achieved with integers $n_i > 1$ rather than tuned continuous parameters. The authors then realize the construction in high-scale or (mini) split supersymmetry: $N$ global $U(1)$ symmetries and $N-1$ confining hidden gauge sectors generate the mixing chain, the axion scales come out as $f_i ~ sqrt(m_SUSY M_*)$, and the $phi$-dependent Higgs mass follows from $W_3 = (X_{N-1}^2/M_* + X_N^2/M_*) H_u H_d$.
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The central claim is that a pseudo-Nambu-Goldstone boson carries a discrete shift symmetry, $f: f + 2 f k$ with integer $k$, that is gauged rather than global, because the field is an angle and the shift maps the underlying complex scalar onto itself. Any local operator, including soft explicit breaking of the continuous shift, respects this periodicity; the relaxion's rolling potential $V(f) = g ^{3} f + g^{2} ^{2} f^{2}/2 + $ and the Higgs mass term $^{2} = g f - ^{2}$ do not. Hence a small $g$ is not technically natural. Requiring the field excursion to fit inside one period, $f /g f$, converts this into a bound: for a QCD-like axion, $ < 100 $ GeV up to order-one factors in the new strong sector's fermion mass and decay constant, and for a generic pNGB with back-reaction potential $(y v)^{n} M^{4-n} (f/f)$, the condition $^{4}/M^{4} < (y v)^{n} M^{n}$ can only be met if all scales, cutoff included, sit at the electroweak scale. The authors then examine four routes out, a non-compact relaxion that is not a pNGB, a back-reaction period $f_{UV} = n f$ shorter than the fundamental period, multiple pNGBs, and separate couplings for rolling and back-reaction, and find the last two give only modest gains, with $ 4 v n^{1/4}$ and $ M r^{1/2}$ with $r = g_{f}/g_{h} 1/(4)$ reaching at most about ten TeV.
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The paper presents an existence proof: a version of the cosmological Higgs-axion interplay (CHAIN) mechanism in which the scale of new physics can be pushed to $10^9$ GeV while the weak scale stays natural. In the original proposal a single axion-like field $e$ scans the Higgs mass through a term $-Lambda^2(1-g e/Lambda)|H|^2$, and is stopped by a Higgs-dependent barrier $epsilon Lambda^4 (|H|^2/Lambda^2) cos(e/f)$ once electroweak symmetry breaks, giving $v^2 simeq g Lambda f/epsilon$. The problem is that closing the Higgs in a loop also generates $epsilon Lambda^4 cos(e/f)$ and $epsilon Lambda^3 g e cos(e/f)$, whose barriers are not cancelled and which stop the rolling too early unless $Lambda_c$ lies near the weak scale. The authors introduce a second field $sigma$ that scans the overall amplitude of the oscillating term, $A(e,sigma,H) = epsilon Lambda^4(beta + c_e g e/Lambda - c_sigma g_sigma sigma/Lambda + |H|^2/Lambda^2)$, so that $sigma$ can hold the barrier at zero and let $e$ track it downhill. The tracking solution bends the wrong way once the Higgs turns on, so $e$ exits the barrier-free band and is trapped at the point where the Higgs barrier balances the linear slope. Requiring the tracking and trapping conditions, classical rolling, and enough inflation to scan the field range yields $Lambda^3/M_P^3 lesssim g_sigma lesssim g lesssim v^4/(f Lambda^3)$, hence $Lambda lesssim (v^4 M_P^3)^{1/7} simeq 2 imes 10^9$ GeV. Below that scale the only new states are $e$ and $sigma$, with masses anywhere in $[10^{-20}, 100]$ GeV and $[10^{-45}, 10^{-2}]$ GeV respectively, and mixings with the Higgs small enough that they escape collider searches; $sigma$ can reproduce the dark matter density through vacuum misalignment, while $e$ contributes at most $Omega_e sim 10^{-10}$.
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The central claim is that a composite pNGB Higgs addresses the naturalness problem without the fine tuning of an elementary scalar, and that its low-energy consequences are almost parameter-free. Because the Higgs enters the effective Lagrangian only through the Goldstone matrix, the leading operators are organised by the Callan-Coleman-Wess-Zumino construction, and for the minimal coset the two-derivative sigma-model term is the unique invariant. That uniqueness is what turns the scenario into a prediction: the Higgs couplings to vector bosons are rescaled by $k_V = 1 - 2xi$. The authors extend this to fermions through partial compositeness, where each Standard Model quark mixes linearly with a composite fermionic operator, so that its Yukawa coupling is a product of left- and right-handed mixing angles; depending on which symmetry multiplet the composite operator sits in, the top coupling shift is either $1 - 2xi$ or $1 - xi$, giving distinguishable benchmark models. The Notes then confront the whole construction with data: the Higgs coupling fits, electroweak precision tests, the $Zb_L b_L$ coupling, and direct resonance searches all push the compositeness parameter towards small values, of order $xi$ less than about 0.1 to 0.2, and the authors are explicit that obtaining such a small misalignment angle costs some tuning of the scalar potential.
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The central claim is that a scalar with a large, effectively non-compact field range and a soft, technically natural coupling $g$ to the Higgs can drive the Higgs mass-squared to a value much smaller than the cutoff $M$ without any new dynamics at the weak scale. The relaxion starts where $m_h^2$ is positive and rolls during inflation; when $m_h^2$ crosses zero the Higgs turns on, the QCD-induced barrier height $Λ^4$ (which scales with the Higgs vev through the pion mass) rises, and rolling stops once the potential slope $gM^2$ matches the barrier slope $Λ^4/f$. That stopping condition, combined with requiring the barriers to form below the QCD scale and the rolling to be classical rather than quantum, caps the cutoff at $M < (Λ^4 M_{pl}^3/f)^{1/6}$, about $10^7$ GeV for $f = 10^9$ GeV. The authors also report that the minimal version is ruled out by the strong CP problem — the stopping point displaces the axion from its QCD minimum by $O(f)$, giving $θ ∼ 1$ — and they repair it in two ways: by having the slope drop by a factor $θ ≲ 10^{-10}$ after inflation when the inflaton returns to zero, which lowers the bound to about $30$ TeV (or about $1000$ TeV if the classical-rolling constraint is dropped), or by replacing QCD with a new confining $SU(3)$ acting on weak-scale fermions, which raises the cutoff to roughly $3×10^8$ GeV.
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The paper's central claim is that a perturbative 2HDM with soft $Z_2$ breaking cannot relieve the Higgs mass hierarchy problem beyond $O(5)$ TeV, and that requiring a stable scalar potential up to the Planck scale pins the model into a small-coupling region that the LHC data then squeezes further. The hierarchy statement is the sharper one: the authors write the leading-logarithm expansion of the Higgs mass correction as $[f_0 + f_1 L + f_2 L^2 + ...]$ with $L = 16π^2$ and $L = 16π^2$ times the log, generate the higher coefficients from the one-loop result by the Einhorn-Jones recursion, and demand $|k_1|, |k_2| < 1$ together with $|δm_h^2| < m_h^2$. Under those conditions the maximal cut-off is 5.3 TeV in type I and X and 3.7 TeV in type II and Y. On the stability side, the two-loop running shows that a potential stable to the Planck scale requires $|λ_i(m_Z)| < 1$, $λ_2(m_Z) > 0.15$, $tan β(m_Z) > 1$ (and below 60 in type II and Y), and S-matrix eigenvalues at most 2.5 in magnitude — a value the authors derive rather than assume, replacing the commonly used tree-level $16π$ and the $2π$ bound adopted in earlier type-II work. Feeding these into the global fit, they find that in type II and Y the $Br(B → X_s γ)$ constraint on $m_{H^+}$ removes the low-mass branches and leaves $m_H > 340$ GeV and $m_A > 360$ GeV, while the maximal deviation of $β - α$ from $π/2$ is 0.43, 0.08, 0.33 and 0.07 in types I, II, X and Y respectively.
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The review's central claim, stated at the end of section 4, is that fermion masses and mixing angles are well described by a single map — eqs. (6), (30) and (31) — in which the Yukawa matrices are written as $y_u = F_{u^c}Y_u F_q$ and similarly for down quarks and charged leptons, with $F_X$ real diagonal suppression matrices fixed by charges or by wavefunction profiles, and $Y$ complex matrices of undetermined order-one entries. The observed hierarchy, from $m_e/m_��/approx ��^{5.4}$ up to $|V_{ub}|/approx ��^3$, then follows from the structure of $F_X$ alone. Feruglio argues this description is realized in several independent frameworks — Froggatt–Nielsen, flat or warped extra dimensions, partial compositeness, strongly coupled superconformal sectors — and that it is compatible with both $SU(5)$ and $SO(10)$ grand unification and with a solution to the gauge hierarchy problem. The price is stated plainly: the entries of $Y$ are independent free parameters, so no absolute prediction beyond order-of-magnitude accuracy is possible.
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The central claim is that the Twin Higgs cancellation can be promoted from a statement about quadratic divergences to a statement about the complete Higgs potential in a composite model with global symmetry breaking $SO(8)/SO(7)$. The elementary gauge fields gauge $SU(2)_L$, $U(1)_{3R}$ and a twin $SU(2)_L$ inside $SO(8)$; their couplings are treated as spurions in the adjoint $28$. Under $SO(7)$, $28=21+7$, and after subtracting the full $SO(8)$ singlet, exactly one non-trivial invariant remains, so the $g_2^2$ and $g_2^2$ terms must share the same Higgs-dependent function and cancel at $g_2=g_2$. This is stronger than the usual divergence argument, which only controls the high-scale propagation of light degrees of freedom and can miss finite heavy-resonance contributions. The paper contrasts this with the $SU(4)/SU(3)$ twin composite Higgs, where two invariants exist and the cancellation fails. It also shows that a realistic vacuum can arise if twin parity is broken only by hypercharge, yielding a positive $alpha sin^2(H/f)$ term and no massless twin photon.
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The paper's central claim is a negative one about the LHC's reach: precision Higgs physics will not be able to strongly disfavor naturalness in theories with colorless top partners. The argument runs through three concrete constructions. In the Mirror Twin Higgs the Higgs couplings to all Standard Model states are scaled by a common factor $c_0 = 1/2$, and the twin sector opens an invisible channel, so the observable is a correlated pair (suppressed visible rates, invisible branching fraction) fixed by the ratio $m_t/m_T$. In Folded Supersymmetry the tree-level Higgs couplings are Standard-Model-like and the only handle is the diphoton rate, shifted by loops of electrically charged folded stops, which can go either up or down depending on stop mixing. In the Quirky Little Higgs all couplings are again scaled by a common factor, but the top-partner loop interferes destructively with the top loop in $h to gamma gamma$, giving a distinctive pattern of suppressed rates everywhere except a partially compensated diphoton channel. For each model the authors draw the top-partner mass at which the tuning measure $Delta_m = |2 delta m^2 / m_h^2|^{-1}$ equals 30%, 20%, and 10%, and compare it with the projected LHC precision of about 5% on the clean signal strengths and 10% on the invisible branching fraction. In all three cases the 10%-tuning line sits beyond the reach of $3000$ fb$^{-1}$ at 14 TeV.
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The central claim is that orbifolding a parent gauge theory by a discrete group can leave the Higgs as a pseudo-goldstone boson even though the daughter theory has no continuous symmetry. The worked example takes a parent $SU(6)��SU(4)$ gauge theory with a scalar $H$ and fermions $Q$, $U$, and orbifolds by $Z_2$, giving a daughter theory $[SU(3)��SU(2)]_A �� [SU(3)��SU(2)]_B �� U(1)^2$ with two full copies of the Higgs, left-handed quark doublet, and right-handed quark, one per sector. The daughter potential is exactly the twin Higgs potential, with a common mass term and a quartic coupling of the form $��(|H_A|^2+|H_B|^2)^2$. The load-bearing calculation is that the one-loop quadratic divergence comes out proportional to the $SU(4)$ invariant $|H_A|^2+|H_B|^2$ even though no such symmetry exists in the daughter theory, so the potential for the pseudo-goldstone direction is insensitive to the cutoff. A soft or hard breaking of the residual $Z_2$ tilts the vacuum so that $��H_A�� �� ��H_B��$, aligning the uneaten goldstone with the physical Higgs and the radial mode with the scale $f$. Integrating out the radial mode gives the Higgs the couplings to $B$-sector tops that a fermionic top partner would have, but those tops are neutral under the Standard Model. The paper then generalizes from $Z_2$ to $Z_��$, where the parent is $SU(3��)��SU(2��)$ and the daughter has $��-1$ extra sectors and an accidental $SU(2��)$ symmetry, and to the nonabelian case $S_3$, where sectors of unequal relative dimension $d_��$ appear and the inherited couplings are rescaled accordingly.
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The report's load-bearing assertion is that the discovery of a Higgs boson has substantially refocused new-physics searches, so that the leading search areas now lie in deviations from Standard Model predictions in Higgs production and decay, and in probing so-called natural models where new physics eliminates or at least attenuates the hierarchy problem. On that premise the report assembles concrete machinery: updated decay codes that carry QCD corrections to third order and allow rescaled or new point-like Higgs couplings; global fits to LHC and Tevatron signal strengths that extract the ratio of the HWW to HZZ couplings and bound a CP-odd top-quark coupling; a proposal to read the longitudinal-versus-transverse polarization of vector bosons in vector boson scattering as a model-independent probe of the Higgs-to-gauge-boson coupling; and feasibility studies of double Higgs production, both non-resonant in composite-Higgs scenarios and resonant through a heavy graviton. The report is explicit that these are workshop studies of uneven maturity rather than a single result, and several of the collider projections are presented as preliminary.
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The paper's central claim is that a theory with no dimensionful parameter can generate the Planck scale and a flat background at the quantum level, provided a quartic scalar coupling and its $\beta$ function vanish together at the Planck scale (eq. 44). The authors reach this by computing, for the first time in a single consistent scheme, the one-loop $\beta$ functions of four-derivative ('agravity') gravity coupled to generic matter: the Yukawa RGE (eq. 21), the quartic RGE (eq. 23), the scalar-curvature RGE (eq. 31) and the gravitational RGE (eq. 34). Working in the Einstein frame, the potential for a scalar with $f(S) = xi_S S^2$ and $V(S) = lambda_S S^4/4$ becomes $V_E = bar M_{Pl}^4 lambda_S / (4 xi_S^2)$, so the minimum condition is not the Coleman-Weinberg condition $lambda_S = 0$ but $beta_{lambda_S}/lambda_S - 2 beta_{xi_S}/xi_S = 0$, with $lambda_S = 0$ demanded separately to keep the cosmological constant near zero. The authors point out that the Standard Model Higgs almost does exactly this: its quartic coupling and its $\beta$ function nearly vanish around $10^{17}$ GeV for $M_h approx 125$ GeV and $M_t approx 171$ GeV, which they read as encouragement that the required behaviour is achievable in nature rather than as an identification. They then show that the same flatness makes the slow-roll parameters equal to combinations of $\beta$ functions, and that a concrete model — a mirror copy of the Standard Model whose Higgs sits in the Planck-scale minimum — reproduces the observed scalar amplitude with $xi_S approx 210$ and predicts $r approx 0.128$, close to the quadratic-potential value $8/N$.
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The paper's central claim is that scalar quantum electrodynamics with a fundamental scalar of natural mass and $q^2 �� λ$ cannot satisfy the weak gravity conjecture, and is therefore inconsistent with a quantum theory of gravity. The reasoning is short. Naturalness fixes the physical scalar mass squared at its radiative correction, $m^2 = ��m^2 = ��^2(a q^2 + b λ)/(16��^2)$ with $a,b$ of order one. The charge-to-mass ratio is then $z = 4�� m_{Pl}/�� �� 1/��{a + bλ/q^2}$, so requiring $z>1$ in the regime $q^2 �� λ$ gives $�� < 4�� m_{Pl}��{q^2/(bλ)}$, which collapses as the charge shrinks unless $b �� 0$, i.e. unless the scalar mass is fine-tuned. The authors identify exactly two escapes: the gauge symmetry is spontaneously broken (in which case the black-hole argument for the conjecture does not apply, since no-hair theorems forbid stationary classical hair from a massive photon), or new states enter at the low cutoff $�� �� q m_{Pl}$ so that the hierarchy problem never arises. They then generalize the conjecture to $��_a U(1)_a$: the convex hull spanned by the vectors $�� �� z_i$ must contain the unit ball, which for $N$ orthogonally charged states of equal magnitude requires $z > ��N$ rather than $z>1$, and for two charges gives $(z_1^2-1)(z_2^2-1) > (1+|z_1��z_2|)^2$.
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The paper constructs the simplest supersymmetric mirror twin Higgs: two complete copies of the MSSM, an A-sector containing the visible fields and a B-sector containing a mirror copy, with couplings and soft masses tied by an exact $Z_2$ exchange symmetry and a single singlet superfield coupling the two sectors. The $Z_2$ plus gauge invariance forces the Higgs-singlet superpotential into a $U(4)$-symmetric form, so the quadratic sensitivity of the Higgs mass to the cutoff cancels between the two sectors, while supersymmetry supplies the ultraviolet completion above a few TeV. The authors then go beyond the pseudo-Goldstone limit, evaluating the full one-loop effective potential with top/stop and electroweak contributions from both sectors, and compute the tuning numerically by varying soft masses at the messenger scale and running them down. They find two independent tunings — one from creating the hierarchy $v^2 < f^2/2$ between the sector vevs, and one from fixing the total $U(4)$-breaking vev $f$ — whose product stays better than one percent out to stop masses of about 3.5 TeV and higgsino masses of about 1 TeV, with $125$ GeV obtained by choosing $m_A=1.5$ TeV, $f=3v$, and $m_S^2=(1~{TeV})^2$. The same construction maintains MSSM-like gauge coupling unification at the level the authors claim, gives no tree-level $S$ and $T$ contributions because the mirror gauge bosons are inert, and satisfies the Glashow-Weinberg condition automatically. The distinctive experimental consequences are therefore all in the Higgs sector: coupling shifts of order $v^2/f^2$, an invisible width from $h$ mixing into B-sector bottom quarks, a second-lightest CP-even state $h_2$ with mass $m_{h_2}approx lambda f sin 2beta$ that decays to $hh$ with branching ratio of order $0.1$–$0.4$, and vector boson fusion or $Z$-associated production of $h_2$ followed by invisible decay into mirror gauge bosons.
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The paper's central claim is that Higgs naturalness is a well-posed physical problem whose status has become experimental rather than rhetorical. Giudice makes the case in two steps. First, he shows that the sensitivity of the Higgs mass to heavy scales survives any regularization scheme: a heavy scalar coupled through $|H|^2|Φ|^2$ shifts the mass by $δm_H^2 ≈ (λ_Φ/16π^2) M^2$, and a heavy stop shifts it by $δm_H^2 = (3y_t^2/8π^2) m_t^2$ even though the supersymmetric theory has no quadratic divergences at all. Second, he converts that sensitivity into a number: for a mediation scale near $10^{16}$ GeV, a 600 GeV stop already gives a correction to $m_h^2$ about 100 times its measured value, a percent-level tuning that LHC8 bounds have not removed. He then sets out the three ways the story can end — Unnaturalness (a multiverse plus anthropic selection, addressing the cosmological constant and the weak scale together), UV Naturalness (a quantum-gravity 'miracle' fixing $m_H^2(M_{Pl}) ≈ 0$, so the Standard Model's own multiplicative running keeps the mass small below the Planck scale), and IR Naturalness (supersymmetry, extra dimensions, compositeness, or technicolour operating near the TeV). His own verdict is that IR Naturalness is under serious pressure but not dead, and that the final word belongs to the high-energy run.
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The central claim is that a UV-complete theory can exist whose low-energy limit is a tuned effective field theory with unprotected scalars sitting arbitrarily far below the scale of new physics, while the S-matrix — the only language available at all energies — contains no tuning whatsoever. The authors build this by 'gravitational dressing': starting from any two-dimensional UV-complete S-matrix $S(p_i)$, they multiply it by the phase $D(p_i)=e^{i(2/4^{2}/4?}$ — concretely $D(p_i)=e^{i(2/4^{2}/4}$ is not the form; the paper's expression is $D(p_i)=e^{i(2/4^{2}/4}$ replaced below by $D(p_i)=e^{i(2/4^{2}/4}$ — see the machinery field for the exact formula. The dressed matrix is shown to be unitary, crossing-symmetric, and analytic on the physical sheet, and it exhibits what the authors call asymptotic fragility: it has no ultraviolet fixed point, no local off-shell observables, and an essential singularity at infinite energy. They also separate two statements of naturalness — (I) unprotected relevant operators should set the highest scale in the theory, and (II) among scales set by relevant operators, unprotected ones should be the highest — and point out that these coincide in ordinary quantum field theory because every scale can be read as a relevant deformation of some UV fixed point, but not here, since the dressing scale $2^{-1}$ has no such reading. The paper presents itself explicitly as a proof of concept, not a demonstration that nature works this way.
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The central claim is that electroweak symmetry breaking and dark matter can share a single dynamical origin, and that the electroweak scale need not be put in by hand. Starting from a Higgs potential with only a quartic term, $V_H = (1/4)|H|^4$, the authors add a dark gauge sector with $N_f = 2$ techniquarks in the adjoint representation, a singlet scalar $S$ coupling to the Higgs as $g_h |S|^2 |H|^2$ and to the dark fermions through a Yukawa $y_Q S (Q Q + h.c.)$. Chiral symmetry breaking in the dark sector generates $v_3$ and hence a linear term that tilts the potential for $S$; $S$ acquires a vacuum expectation value, and that in turn induces the negative mass term for $H$. The chain is hierarchical, with $v_s = v_3/2$ and $v_h = (g_h/2)^{1/2} v_s$ in the paper's notation, so the weak scale sits naturally below the dark scale. In the adjoint (pseudoreal) case the global breaking $SU(4) o SO(4)$ yields nine Goldstones, six of which carry dark baryon number; the lightest of these is the dark matter candidate, annihilating mainly through the portal into Higgs bosons.
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The central claim is that naturalness should be judged by finite quantum corrections alone, and that judged this way the Standard Model is not fine-tuned. Writing the Higgs potential as $V = -m^2|H|^2/2 + |H|^4$, the authors compute the one-loop relation between the pole mass $M_h$ and the renormalized parameter $m$ in the MS scheme and find that the correction is a modest 13 percent rather than an amount proportional to an unknown cut-off squared. Because the divergent piece is discarded, the bounds on new physics become loop-suppressed: any new particle carrying Standard Model gauge interactions feeds into the Higgs mass only at two loops, through diagrams proportional to $g^4 M^2/(4pi)^4$ times a logarithm of the cut-off. Applying this to the three see-saw types gives upper bounds of $0.7$ times $10^7$ GeV for type I, $200$ GeV for type II and $940$ GeV for type III; applying it to minimal dark matter multiplets gives bounds from about $0.06$ to $1.9$ TeV times the square root of the fine-tuning factor, depending on the multiplet; and applying it to KSVZ axion models forces the new colored quarks below roughly $0.7$ to $9$ TeV.
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The paper's central claim is that weak-scale supersymmetry is neither confirmed nor excluded, and that the widespread reading of the 2012 data as a refutation rests on a naturalness argument that is far softer than it is usually presented as being. Concretely, the review argues that current bounds probe naturalness parameters around $N sim 100$, corresponding to gluino masses near 1 TeV, and that the upper bounds on superpartner masses scale as $sqrt{N_{max}}$, so a spectrum with multi-TeV scalars is not obviously ruled out. It further argues that the measured Higgs mass near 125 GeV, which in the minimal model requires stop masses of several TeV unless the left-right mixing is near maximal, is now at least as serious a challenge to naturalness as the absence of superpartners. Rather than declaring a winner, the review lays out the conditions under which the tension is real and the conditions under which it dissolves, and identifies the higher-energy collider run as the test that will decide.
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The central claim, stated in abstract:s3 and made concrete in Eqs. (2.11) and (2.12), is that dimensional transmutation survives the addition of a Higgs portal and delivers the electroweak scale naturally. In the classical potential $V_{cl} = λ_H (H^†H)^2/2 - λ_P (H^†H)|φ|^2 + λ_φ |φ|^4/24$ there is no mass term anywhere; the hidden scalar's self-coupling is driven to $λ_φ = 33 e_φ^4/(8π^2)$ at the scale of its vev by the same Coleman-Weinberg condition as in the original model, only mildly deformed by the portal. The resulting hierarchy is $√(λ_H/λ_P) ⟨H⟩ = ⟨φ⟩ ≃ Λ_{UV} exp[-24π^2/e_φ^2(⟨φ⟩)]$, so the weak scale is exponentially suppressed relative to the cutoff for perturbative hidden gauge coupling, and the ratio $⟨φ⟩/⟨H⟩$ is set by how small the portal coupling is. The paper's second contribution is a defence of the renormalisation condition behind all this — that the renormalised scalar masses vanish at the origin of field space — and its third is a phenomenological survey: the two free parameters can be taken as the portal coupling $λ_P$ and the hidden scalar mass $m_{h_2}$, with the mixing angle $ϑ ≃ κ m_h^2/(m_φ^2 - m_h^2)$ and $κ = √(2λ_P/λ_H)$ controlling every deviation from Standard Model Higgs behaviour.
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The paper proposes radiative natural SUSY, a scheme within the minimal supersymmetric standard model in which the little hierarchy problem is answered by running rather than by new fields. The mechanism is a high-scale non-universality: taking the soft Higgs mass parameter $m_{H_u}$ above the common matter scalar mass $m_0$ at the unification scale lets the large top-Yukawa-driven radiative correction cancel against the boundary value, so that $-m_{H_u}^2$ at the weak scale comes out of order $M_Z^2$ instead of being arranged by hand. Combined with large top-squark mixing, with $A_0$ near $-1.6 m_0$, the same large mixing that lifts the light Higgs mass to about 125 GeV also suppresses the top-squark contributions to the electroweak fine-tuning measure, so the authors report fine-tuning at the 3 to 10 percent level with top squarks of 1 to 5 TeV and gluinos of 1 to 4 TeV. Scans over the two-parameter non-universal Higgs model and over a split-generation version show that such points exist while $b$ to $s$ photon and $B_s$ to mu mu measurements are respected, and that first and second generation scalars may sit at 10 to 30 TeV, which softens the supersymmetric flavor, CP and gravitino problems.
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The paper's central claim is that the mSUGRA/CMSSM parameter space compatible with LHC7 sparticle mass limits, the LHCb $B_s^0$ to $B_s^0$ branching-fraction window of $(2 - 4.7) imes 10^{-9}$, and a light Higgs with $m_h = 123 - 127$ GeV is fine-tuned at no better than the 0.1 percent level on the high-scale measure $|Delta_{HS}$ and no better than the 1 percent level on the spectrum-only measure $|Delta_{EW}$. Requiring $m_h$ near 125 GeV is what does most of the damage: it forces large stop mixing, hence $|A_0|$ of order $1.5$ to $2$ times $m_0$, which removes the hyperbolic-branch/focus-point region where $|Delta_{EW}$ could otherwise fall to a few tens. The authors identify two benchmark points that minimize the two measures: HS1 with $m_0 = 1472$ GeV, $m_{1/2} = 711$ GeV, $|Delta_{HS} = 1105$ and $|Delta_{EW} = 583$; and EW1 with $m_0 = 7926$ GeV, $m_{1/2} = 595$ GeV, $|Delta_{HS} = 1.5 imes 10^4$ but $|Delta_{EW} = 92$. Both lie beyond LHC8 reach and would need roughly 10 to 100 inverse femtobarns at a 14 TeV LHC. The authors explicitly leave the judgement of how much tuning is too much to the reader.
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The central claim is that a classically conformal $B-L$ extension of the Standard Model, with boundary conditions $g_Y$–$g_{B-L}$ gauge mixing and scalar mixings all set to zero at $M_{UV} = 10^{17}$ GeV, radiatively generates everything else. Solving the one-loop RGEs, the authors show that the $U(1)_Y$–$U(1)_{B-L}$ kinetic mixing $g_{mix}$, itself generated radiatively from zero, drives the Higgs–singlet quartic $g_{mix}$-dependent coupling $g_{mix}$-mediated $g_{mix}$ term to a small negative value of order $10^{-3}$ at low energy — the value that had to be inserted by hand in the authors' earlier version of the model. The singlet quartic $g_{mix}$ crosses zero at a TeV-scale point, the Coleman-Weinberg mechanism breaks $B-L$ there, and the singlet scalar comes out roughly ten times lighter than the new gauge boson, $m_phi/m_{Z'} ~ sqrt{6 pi alpha_{B-L}}$. The induced mixing then gives the Higgs an effective negative mass squared and fixes $v = sqrt(-g_{mix}/g_{mix}) M_{B-L} = 246$ GeV, which translates into $M_{B-L} ~ 35$ GeV$/alpha_{B-L}$ and $m_{Z'} ~ 250$ GeV$/sqrt(alpha_{B-L})$. Since $v$ is an input, the dynamics collapses to a single free parameter, drawn as one line in the $alpha_{B-L}$–$m_{Z'}$ plane. The paper also argues that the extra $B-L$ gauge contribution to the Higgs quartic $\beta$ function flattens the running and lowers the vacuum stability bound; the abstract quotes a few GeV, while the body's Fig. 4 gives at most about 1 GeV over the allowed range $alpha_{B-L} < 0.006$.
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The central claim is that electroweak naturalness does not require a superpartner for every Standard Model particle, only for those with order-one couplings to the Higgs: the third-generation squarks $Q=(t_L,b_L)$, $t_R^c$, $b_R^c$, the Higgsinos, and the gauginos. With a 10 TeV cutoff this minimal content is enough to keep the Higgs mass-squared radiatively under control, with the natural ranges roughly $|m_{t}|$ below about 400 GeV for the stops, wino below about a TeV, $b_R^c$ below a few TeV, and gluino within a factor of two of the stop mass. The authors argue that this scenario is unusually safe against flavor and CP constraints, because the first two generations of squarks are simply absent from the low-energy theory, and that R-parity is not obligatory: in an effective theory with a 10 TeV cutoff, R-parity alone does not protect the proton from higher-dimension operators, so baryon or lepton number is needed anyway. They then compute LHC reach for the minimal R-parity-conserving subsystem of two stops, one sbottom and a bino-like neutralino, and find that $1/fa$ of 7 TeV data excludes squarks only up to roughly 300–400 GeV, with the strongest limits coming from jets plus missing energy and from $tbar t$ plus missing energy, not from searches designed for heavy gluino cascades.
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The central claim is that apparent unitarity violation in a non-renormalizable theory is an artifact of perturbation theory whenever the theory contains a field sourced by energy-momentum. Localizing energy $1/L$ inside a region of size $L$ gives an integrated source of strength $L_*/L$, so the linearized field obeys a Gauss-law-type equation whose gradient grows as $1/r^2$ until the field reaches its cutoff at a distance $r_*$. For a cubic self-coupling this gives $r_* = L_*^2/L$ (their eq. 8); for a general operator with $n$ fields and $2k$ derivatives, $r_* = L_* (L_*/L)^{(n-2)/(n+4k-6)}$ (eq. 22), and they show the same formula follows from pure dimensional analysis with $r_*$ surviving the limit $hbar to 0$ while both $L_*$ and the de Broglie length $L$ vanish (eq. 26). Two-to-two scattering at momentum transfer $sim 1/L$ then goes through a classical intermediate state and is exponentially suppressed, by $exp[-(sqrt{s}/v)^{4/3}]$ in the four-derivative model they use for the Higgsless case (eq. 80), while the inclusive cross section grows geometrically as $sigma sim r_*^2$, here $v^{-2}(sqrt{s}/v)^{2/3}$ (eq. 81). Applied to the Standard Model, the authors argue that the longitudinal components of the $W$ bosons classicalize on their own once the Higgs is decoupled, and separately that a Higgs with a coupling $kappa, H^dagger H, T^mu_mu / M_*^2$ forms 'Higgsions' whose radius grows with energy and whose loop contributions are cut off at $M_*$, which is how classicalization is supposed to stabilize the weak scale.
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The paper's central claim is the existence of a minimal scale-invariant model of maximal spontaneous CP violation that remains perturbatively renormalizable up to $M_{Planck}$. The potential is fixed to $V = (1/2)λ_1(Φ^†Φ)^2 + (1/2)λ_2(S^*S)^2 + λ_3 Φ^†Φ S^*S + (1/2)λ_6(S^4 + S^{*4})$ with real $λ_6$; CP invariance and a $Z_4$ symmetry $S → iS$ single out this form. Minimising it at the renormalization scale $Λ$ gives a flat direction with $σ = J$, i.e. a singlet vacuum at phase $θ_S = π/2$, which is maximal spontaneous CP violation. Along that direction the tree-level masses are $m_h^2 = 0$, $m_{H_1}^2 = [λ_1(Λ) - λ_3(Λ)]v_φ^2$ and $m_{H_2}^2 = [4λ_1(Λ)λ_6(Λ)/λ_3(Λ)]v_φ^2$, and the whole spectrum depends on only three quartic couplings. Requiring $β_{λ_{1,2,3,6}}(M_{Planck}) ≤ 1$ and boundedness from below up to the Planck scale leaves a viable window $0.39 ≲ λ_1(Λ) ≲ 0.52$, $0 < λ_2(Λ) ≲ 0.20$, $-0.1 ≲ λ_3(Λ) < 0$, with $m_{H_1}$ between roughly 155 and 181 GeV, $m_{H_2}$ between roughly 0.5 and 1.1 TeV, and the pseudo-Goldstone $h$ between roughly 11 and 78 GeV depending on $λ_2(Λ)$. The authors contrast this with the Type-I and $U(1)$-invariant Type-II cases, which they show develop Landau poles at $10^4$–$10^5$ GeV, and with the scale-invariant Standard Model itself, whose one-loop coefficient $β$ is negative and therefore gives a tachyonic Higgs mass.
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The paper constructs a class of quantum field theories that are scale invariant order by order in perturbation theory, and in a subclass of them the symmetry is spontaneously broken, leaving a massless dilaton. The construction rests on a change of renormalization prescription: wherever the standard procedure would insert the dimensional-regularization scale as $mu^{2varepsilon}$, the authors insert a field-dependent object of the same mass dimension, in their preferred version $[xi_chi chi^2 + xi_h h^2]^{varepsilon/(1-varepsilon)}$, built from the dilaton $chi$ and the Higgs $h$ and from the same non-minimal couplings that multiply the curvature scalar. Because the counter-terms are then made of fields, the renormalized theory carries no dimensionful parameter at all. For this to describe particles rather than a trivial free theory, the full effective potential must possess a flat direction; the authors show at one loop that this can be arranged by fixing two otherwise free finite parts of the counter-terms, and that the resulting potential is bounded from below near that direction. They then verify that for $zeta_R ll 1$ the low-energy physics of the Higgs sector reduces to the ordinary renormalizable scalar theory with $chi$ frozen at its vacuum value, including the standard one-loop running of the quartic coupling. The authors state plainly that whether the flat direction survives beyond one loop with a finite number of counter-terms, and whether the theory is renormalizable and unitary, is not established here, and that non-polynomial counter-terms such as $h^6/chi^2$ may be needed.
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The paper's central claim is that in the MSSM extended by TeV-scale matter in complete SU(5) multiplets — one pair of $10 + overline{10}$, up to four pairs of $5 + overline{5}$, or the combination $10 + overline{10} + 5 + overline{5}$ with or without standard-model singlets — the lightest CP-even Higgs boson can be as heavy as about 160 GeV, consistent with perturbative gauge coupling unification up to the GUT scale and with electroweak precision constraints. The mechanism is a new superpotential coupling of the extra charge-$2/3$ quark (or, in the $5 + overline{5}$ case, of the extra lepton doublet together with a singlet) to $H_u$, which contributes to the Higgs mass squared at one loop in proportion to the fourth power of that coupling. The authors fix the new coupling at the GUT scale near the perturbativity limit, $kappa_{10} approx 2$, run it down with two-loop renormalization group equations, and find $kappa_{10}(M_V) < 1.142$ at the vectorlike mass scale once the $T$ parameter bound $delta T < 0.1$ is imposed. Scanning the mixing parameters, they report ceilings of 141 GeV for $M_S = 500$ GeV, 148 GeV for $M_S = 1$ TeV, and 158 GeV for $M_S = 2$ TeV in the $10 + overline{10}$ case, about 127.5 GeV for $5 + overline{5}$, and about 144 GeV for the combined representations. On the fine-tuning side, the paper is explicit that the same couplings that raise the Higgs mass also raise the soft mass parameter $m_{H_u}^2$; the improvement over the MSSM appears only when those couplings are small, in which case the top Yukawa at the GUT scale is reduced from about 0.5 to about 0.15 and the Higgs mass stays below roughly 125 GeV.
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The central claim is conditional and quantitative: if the coefficient $kappa$ in the Higgs-mass correction $delta m_H^2 = kappa Lambda^2$ is of order $10^{-2}$, then requiring the Standard Model one-loop contribution in eq. (9) not to exceed the then-current 95% CL bound of 182 GeV implies $Lambda < 1.0$ TeV. In that reading, the LHC cannot reach the TeV scale without encountering particles tied to the cancellation of the Higgs mass's quadratic sensitivity, whether supersymmetry, compositeness, or another mechanism. The essay's contribution is to make that inference explicit, trace its history, and frame the LHC as the experiment that will decide whether naturalness is a reliable guide to new physics.