claims depot shelf
The Hierarchy Problem
Formal claims (Lean)
Stated claims
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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 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 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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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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We propose that in a five-dimensional theory with two three-branes and a negative bulk cosmological constant, the metric is warped such that the effective scale on the brane containing the Standard Model fields is exponentially smaller than the fundamental scale. This generates the observed hierarchy between the Planck and weak scales through the background geometry without additional fine-tuning of parameters.