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CMB amplitude fixes Higgs mass and predicts 3 TeV wino dark matter

2026-07-09 17:35 UTC pith:DTNO522M

load-bearing objection Starobinsky supergravity + MSSM links CMB amplitude to Higgs mass and 3 TeV thermal wino DM, but the chain rests on two acknowledged fine-tunings and the wino mass is set externally. the 1 major comments →

arxiv 2607.07193 v1 pith:DTNO522M submitted 2026-07-08 hep-ph astro-ph.COgr-qchep-th

Higgs boson mass and thermal wino dark matter from Starobinsky supergravity with the MSSM

Daniel Frolovsky , Alexander Belyaev , Sergei V. Ketov This is my paper
classification hep-ph astro-ph.COgr-qchep-th
keywords Starobinsky inflationsupergravityMSSMHiggs boson masswino dark matteranomaly mediationrenormalisation groupdisappearing tracks
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper builds a single theoretical bridge from the largest observable scales of the cosmos to the smallest. On the cosmological side sits Starobinsky inflation, a model of the early universe driven by a correction to Einstein gravity. On the particle side sits the Minimal Supersymmetric Standard Model (MSSM), an extension of the Standard Model that doubles its particle content and provides a dark matter candidate. The authors supersymmetrise Starobinsky inflation using old-minimal supergravity. In the resulting theory, the same hidden sector that produces the inflaton also spontaneously breaks supersymmetry. The amplitude of primordial density fluctuations measured in the cosmic microwave background fixes the mass scale of this hidden sector, which sits near 10^13 GeV. That scale, transmitted gravitationally, sets every supersymmetric soft-breaking parameter in the MSSM. The authors then impose that one Higgs doublet remains light at this high scale, which fixes the goldstino vacuum expectation value and thereby removes the last free parameter of the hidden sector. With the boundary conditions fully determined, three-loop renormalisation-group evolution down to the electroweak scale yields a Higgs boson mass of 125 to 127 GeV, consistent with the measured 125.25 GeV within theoretical and parametric uncertainties. For dark matter, the heavy scalars and higgsinos decouple, and anomaly-mediated contributions to gaugino masses make the wino the lightest supersymmetric particle. The observed dark matter relic abundance selects a nearly pure thermal wino with a mass of about 3 TeV. The authors compute the loop-induced wino-nucleon scattering cross section at roughly 2.3 x 10^-47 cm^2, below current direct-detection limits but within reach of next-generation multi-ton xenon detectors. Electroweak corrections split the charged and neutral wino masses by about 160 MeV, giving the charged wino a lifetime of about 0.2 nanoseconds, which produces a disappearing-track signature at colliders. A future 100 TeV proton collider could discover or fully exclude this signal.

Core claim

The central mechanism is a chain of scale-fixing: the CMB scalar amplitude determines the Starobinsky mass parameter m, which (through the goldstino VEV s0, fixed by demanding a light Higgs doublet) determines the gravitino mass m_{3/2}, which determines all MSSM soft parameters, which determine the Higgs quartic coupling boundary condition, whose three-loop running yields the physical Higgs mass. The chain has no free intermediate parameters once the CMB amplitude and the light-Higgs condition are imposed. A parallel chain selects dark matter: the same soft spectrum makes higgsinos and scalars heavy, anomaly mediation makes the wino the lightest supersymmetric particle, and the thermal-reli

What carries the argument

Starobinsky supergravity in the old-minimal formulation, dualised to an Einstein-frame theory with Kähler potential K = -3 M_P^2 ln[1 + T + T_bar + gamma(S + S_bar) - 2 S S_bar + ...] and superpotential W = 6 m T S. The goldstino VEV s0 is fixed by the determinant condition det(M_H^2) = 0, which yields s0 = sqrt(5/17) for a bare mu-term or s0 approx 0.746 for a dynamically generated mu-term from the operator S^2 H_u H_d. Universal soft scalar masses m_0 = m_{3/2}, trilinear A = -m_{3/2}, and tan(beta) = 1 follow. Anomaly-mediated gaugino masses M_a^{AMSB} = (b_a alpha_a / 4pi) m_{3/2} create a hierarchy where the wino is lightest. Three-loop RG evolution of the Higgs quartic lambda from m_0~

Load-bearing premise

The framework requires that the determinant of the Higgs mass-squared matrix vanish at the high scale, which is an acknowledged fine-tuning: without it, the goldstino VEV and hence the gravitino mass remain undetermined, and the Higgs mass prediction loses its anchor. Separately, the gauge kinetic function is not derived from the supergravity framework, and achieving a TeV-scale wino requires a precise cancellation between tree-level and anomaly-mediated gaugino masses that

What would settle it

A 100 TeV collider failing to observe disappearing tracks at the 3 TeV wino mass would exclude the thermal wino branch. A next-generation xenon detector measuring a spin-independent cross section significantly below 2.3 x 10^-47 cm^2 would rule out the pure-wino prediction. On the inflation side, a tensor-to-scalar ratio r inconsistent with the Starobinsky prediction (r ~ 0.003-0.004) at future CMB experiments would undermine the supergravity embedding.

Watch this falsifier — get emailed when new claim-graph text bears on it.

If this is right

  • A future 100 TeV proton collider could discover the disappearing-track signal from a 3 TeV wino or fully exclude the thermal wino dark matter scenario predicted by this framework.
  • Next-generation multi-ton liquid-xenon detectors (DARWIN/XLZD) can probe the predicted wino-nucleon scattering cross section of ~2.3 x 10^-47 cm^2, which lies below current LUX-ZEPLIN sensitivity but above the irreducible neutrino background.
  • Improved measurements of the top-quark mass and the strong coupling at the HL-LHC would tighten the Higgs mass prediction, reducing the allowed parameter space and providing an indirect test of the high-scale SUSY breaking scenario.
  • The framework can be extended to include SO(10) grand unification with right-handed neutrinos, light neutrino masses via the seesaw mechanism, and leptogenesis, all within the same supergravitational hidden sector.
  • Non-thermal wino production from gravitationally produced scalar decays remains an unexplored branch that could yield a different dark matter mass and detection phenomenology.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • If the determinant condition det(M_H^2) = 0 is interpreted not as fine-tuning but as a selection rule from an underlying symmetry or dynamics not yet identified, then the entire parameter-fixing chain would become a genuine prediction rather than a postdiction, and the 3 TeV wino mass would acquire theoretical rather than purely phenomenological status.
  • The framework's structure suggests that any viable inflationary model with a supersymmetric completion and gravitational mediation could, in principle, link its CMB-normalised mass scale to the Higgs mass and dark matter spectrum through an analogous chain, making the Starobinsky choice one instance of a broader class.
  • The high-precision cancellation required between tree-level and anomaly-mediated contributions to the wino mass may point to a deeper connection between the gauge kinetic function and the R-symmetry breaking sector that is not captured by the current ansatz.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Referee Report

1 major / 8 minor

Summary. This paper constructs a framework in which Starobinsky supergravity, formulated in the Jordan frame and dualized to the Einstein frame, provides a hidden sector that drives both inflation and SUSY breaking. When coupled to the MSSM in the Einstein frame, the inflationary scale (fixed by the CMB scalar amplitude) determines the gravitino mass and, through gravitational mediation, the MSSM soft terms. The authors impose the standard high-scale SUSY condition det(M_H^2)=0 to ensure a light SM Higgs doublet, which fixes the goldstino VEV s0 and thereby the gravitino mass. Two scenarios for the mu-term are considered: a bare mu-term and a dynamically generated one via the goldstino superfield S. Three-loop RG evolution of the Higgs quartic coupling, using both SusyHD and HSSUSY, yields Mh in the range 126.6--127.6 GeV, consistent with the measured 125.25 GeV within uncertainties. With conserved R-parity, the LSP is stable; the thermal relic abundance selects a nearly pure wino at ~3 TeV, testable via disappearing tracks at a future 100 TeV collider and via loop-induced direct detection at next-generation xenon experiments. The framework is internally consistent and provides clear falsifiable predictions.

Significance. The paper makes a genuine attempt to connect CMB observables to particle physics observables through a single supergravity framework, which is a worthwhile goal. The use of two independent EFT codes (SusyHD and HSSUSY) for the Higgs mass calculation, including the discovery and correction of a bug in SusyHD's interpolation table, is commendable and strengthens the reliability of the numerical results. The falsifiable predictions for disappearing-track searches at 100 TeV colliders and direct detection at multi-ton xenon experiments are concrete and well-motivated. The dynamical generation of the mu-term from the goldstino superfield, without introducing an ad hoc singlet, is an elegant feature. However, the significance of the CMB-to-Higgs-mass link is tempered by the fact that it is conditional on the externally imposed det(M_H^2)=0 fine-tuning and on the unspecified gauge kinetic function, as discussed below.

major comments (1)
  1. Sec. 5, Eqs. (44)--(51) and Sec. 5, Eqs. (54)--(58): The goldstino VEV s0, which fixes the gravitino mass m3/2 and all soft parameters, is determined by imposing det(M_H^2)=0 (Eq. 44). The authors acknowledge this as 'the usual EW fine-tuning in high-scale SUSY.' This condition is not derived from the Starobinsky supergravity framework but is imposed externally to ensure a light Higgs doublet. Consequently, the claim in the abstract that the framework links 'the amplitude of primordial scalar perturbations to the Higgs boson mass' is conditional on this additional assumption. The authors should explicitly state in the abstract and conclusion that the CMB-to-Higgs-mass connection requires the det(M_H^2)=0 boundary condition, and clarify that without it, s0 remains a free parameter in the interval (0.438, 0.886) and m3/2 is not uniquely determined by CMB data alone. This is a presentation/
minor comments (8)
  1. Sec. 6, Eqs. (70)--(73): The wino mass M2 ≈ 3 TeV is not predicted by the framework but is set by the external thermal relic abundance condition. The gauge kinetic function coefficients cT, cS are adjusted to achieve the required cancellation between the tree-level and AMSB contributions. The authors are transparent about this ('significantly fine-tuned'), but the abstract's phrasing 'the observed relic abundance selects a nearly pure thermal wino' could be read as a framework prediction. A brief clarification that the wino mass is an input from cosmology rather than a derived quantity would improve precision.
  2. Eq. (74): All four Higgs mass central values (126.58--127.61 GeV) lie above the measured 125.25 GeV. The HSSUSY bare-mu case (126.58 ± 0.48_th ± 0.65_αs) is the closest, with the central value ~1.3 GeV high, roughly 1.2σ in combined uncertainty. The SusyHD central values are ~1.8--2.4 GeV high. While the authors note the ~0.5 GeV agreement between the two codes, they do not discuss the systematic upward offset of all central values relative to the measured mass. A brief comment on whether this offset might indicate missing higher-order corrections or a preference for one mu-term scenario over the other would strengthen the analysis.
  3. Sec. 6, discussion of non-thermal wino DM (Eqs. 65--67): The non-thermal branch is mentioned but its calculation is deferred to future work. Given that the MSSM scalars are lighter than the inflaton (minf/m0 ≈ 1.1 for the bare mu-term case) and can be gravitationally produced, the non-thermal branch is a natural consequence of the framework. The authors should at least comment on whether the non-thermal branch could dominate over the thermal branch for their parameter space, or whether the thermal branch is robustly selected.
  4. Figure 4(a) and Figure 5(a): The red dashed lines marking the model predictions for m0 are described in the captions, but the stability bound (solid red line in Fig. 4a) is mentioned only in the caption of Fig. 4(a) and not in the main text. A brief reference in the text would help the reader.
  5. Sec. 4, Eq. (31): The coupling constant tilde-lambda is stated to be 'suppressed' and potentially generated by instantons, but no quantitative estimate or reference to a specific instanton calculation is provided. While the authors cite string theory compactification references [55--57], a more specific pointer to how such a suppression arises would be helpful.
  6. Appendix A: The bug discovery and correction in SusyHD v1.0.2 is documented thoroughly. The authors should consider submitting the corrected table upstream to the SusyHD repository so that the broader community benefits, if they have not already done so.
  7. Sec. 3, Eq. (17): The gravitino mass formula involves the parameter s0, but the notation switches between s0 (dimensionless VEV of S/MP) and ⟨S⟩ = s0·MP (dimensionful) in different places (e.g., Eq. 32 vs. Eq. 17). A consistent notation would improve readability.
  8. The paper uses both 'bare mu-term' and 'dynamically generated mu-term' scenarios but does not clearly state which is the preferred or default scenario. In the conclusion, both are discussed on equal footing. If there is a theoretical preference (e.g., the dynamical mechanism is more motivated), this should be stated.

Circularity Check

0 steps flagged

No significant circularity found; the fine-tuning conditions are acknowledged assumptions, not circular derivations.

full rationale

The paper's derivation chain is: CMB scalar amplitude A_s fixes the mass parameter m (Eq. 23); m together with the goldstino VEV s_0 fixes the gravitino mass m_{3/2} (Eq. 17); m_{3/2} fixes all soft MSSM parameters (Eqs. 33-38); these set the boundary condition for RG evolution of the Higgs quartic coupling; three-loop RG running yields the Higgs pole mass. The key question is whether the condition det(M²_H) = 0 (Eq. 44), which fixes s_0 and hence m_{3/2}, is circular with the Higgs mass prediction. It is not: det(M²_H) = 0 is a structural requirement that a light Higgs doublet exists at all (i.e., much lighter than m_{3/2}), but it does not determine the numerical value of the Higgs mass. The actual prediction M_h ≈ 125-127 GeV comes from independent RG evolution of λ and threshold corrections, which depend on the SUSY scale and soft parameters but not on the measured Higgs mass. The authors transparently acknowledge this as 'the usual EW fine-tuning in high-scale SUSY' — it is an assumption, not a circularity. Similarly, the wino mass ~3 TeV is explicitly stated as an input from the external relic abundance condition ('We therefore adopt M_2 ≃ 3 TeV as the thermal target and do not recalculate the freeze-out abundance'), not a prediction from the framework. The gauge kinetic function is acknowledged as unspecified by Starobinsky supergravity, and the required cancellation is called 'significantly fine-tuned.' These are honest disclosures of assumptions and fine-tunings, not instances where outputs reduce to inputs by construction. Self-citations (e.g., Ref. [31] by Addazi and Ketov) provide framework setup but are not load-bearing for the central Higgs mass prediction, which relies on standard RG tools (SusyHD, HSSUSY) and boundary conditions derived within the paper. The derivation is self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

7 free parameters · 6 axioms · 2 invented entities

The framework introduces no genuinely new particles beyond what Starobinsky supergravity and the MSSM already contain. The hidden sector fields S and T are derived from the supergravity dual description, not postulated ad hoc. The main ad hoc elements are the choice of f-function, the det(M²_H)=0 condition, and the gauge kinetic function.

free parameters (7)
  • m (Starobinsky mass) = ~1.78×10^13 GeV (for N=55)
    Fixed by CMB scalar amplitude A_s, not a free parameter in the traditional sense, but depends on the choice of e-folds N
  • s0 (goldstino VEV) = √(5/17)≈0.542 (bare μ) or ≈0.746 (dynamical μ)
    Fixed by the det(M²_H)=0 fine-tuning condition, not by independent measurement
  • N (e-folds) = 50-60 (pivot N=55)
    Cosmological input with a range; affects m and hence m3/2
  • cT, cS (gauge kinetic function coefficients) = Chosen to cancel AMSB and yield M2≈3 TeV
    Not determined by the framework; fixed to produce the desired wino mass
  • n (power in μ-term coupling) = 2
    Chosen because n=1 is incompatible with positive gravitino mass condition; n≥2 required
  • ˜λ (μ-term coupling) = ~2.26×10^-5
    Fixed by other parameters once n=2 and s0 are determined, but requires non-perturbative justification
  • Xt (stop mixing) = 0
    Assumed minimal choice to suppress threshold corrections and avoid CCB minima
axioms (6)
  • domain assumption Starobinsky supergravity with the f-function in Eq. (11) correctly describes the gravitational effective action at inflationary scales
    Sec. 2-3; the specific form of f(R,R) with R-symmetry breaking terms is a model choice, not derived from a more fundamental theory
  • domain assumption The MSSM is the correct visible sector below the Planck scale
    Sec. 4; standard assumption in SUSY phenomenology
  • domain assumption R-parity is conserved, making the LSP stable
    Sec. 6; assumed for DM stability
  • domain assumption The thermal wino relic abundance calculation from literature (2.7-3.0 TeV) applies to this framework
    Sec. 6; the wino mass is taken from existing calculations rather than recomputed within the framework
  • ad hoc to paper The det(M²_H)=0 condition (Eq. 44) is a valid high-scale boundary condition
    Sec. 5; this is a fine-tuning condition acknowledged as 'the usual EW fine-tuning in high-scale SUSY'
  • domain assumption Standard supergravity soft term derivation (flat limit MP→∞ with m3/2 fixed) applies to this higher-derivative supergravity
    Sec. 5; the higher-derivative nature of the Jordan-frame theory may introduce corrections to the standard soft term formulas
invented entities (2)
  • Goldstino superfield S independent evidence
    purpose: Hidden sector chiral superfield carrying SUSY breaking; also generates μ-term via VEV
    Emerges from the dual Einstein-frame description of Starobinsky supergravity; its VEV and the resulting gravitino mass are constrained by CMB data. Falsifiable through the Higgs mass prediction and collider signatures.
  • Inflaton superfield T independent evidence
    purpose: Hidden sector chiral superfield carrying the inflaton degree of freedom
    Emerges from the supergravity dual; inflationary predictions (ns, r) are testable against CMB data

pith-pipeline@v1.1.0-glm · 32880 in / 4808 out tokens · 209908 ms · 2026-07-09T17:35:18.173629+00:00 · methodology

0 comments
read the original abstract

We propose a framework connecting cosmic microwave background (CMB) observables with high-energy particle phenomenology, based on Starobinsky supergravity coupled to the Minimal Supersymmetric Standard Model (MSSM). Cosmic inflation and supersymmetry (SUSY) breaking occur within the hidden sector emerging from Starobinsky supergravity. The inflationary scale fixes the characteristic mass scale of the hidden sector, which determines the MSSM soft terms through gravitational mediation of SUSY breaking. The same hidden sector can also dynamically generate a high-scale $\mu$ term. The resulting MSSM spectrum fixes the high-scale threshold corrections and the boundary conditions for the renormalisation-group (RG) evolution of the Higgs quartic coupling. Three-loop RG evolution of the Higgs quartic coupling gives a Higgs boson mass consistent with the measured value within the theoretical and experimental uncertainties, thereby linking the amplitude of primordial scalar perturbations to the Higgs boson mass. With conserved R-parity, the lightest supersymmetric particle is stable, making it a compelling dark matter candidate. The observed relic abundance selects a nearly pure thermal wino with a physical mass of about 3 TeV. Its loop-induced spin-independent wino-nucleon scattering cross section lies below the current sensitivity of the LUX-ZEPLIN experiment, but within the projected reach of next-generation multi-ton liquid-xenon detectors. Electroweak radiative corrections generate a small mass splitting between the charged and neutral wino states, leading to a long-lived charged wino and the characteristic disappearing-track signature. A future 100 TeV proton collider can discover the disappearing-track signal from a 3 TeV wino or fully exclude this thermal wino dark matter scenario.

Figures

Figures reproduced from arXiv: 2607.07193 by Alexander Belyaev, Daniel Frolovsky, Sergei V. Ketov.

Figure 1
Figure 1. Figure 1: The scalar potential V(t, s) overlayed by the ∂V/∂s = 0 trajectory is on the left-hand side. Due to its large effective mass, the field s is stabilised at the minimum of the potential for any given t, leading to a function s = Q(t). A slice of the scalar potential along the ∂V/∂s = 0 trajectory is on the right-hand side. During inflation, the scalar field s slowly oscillates near a local minimum of the pot… view at source ↗
Figure 2
Figure 2. Figure 2: (a) Numerical evaluation of the inflaton mass parameter m (in units of 1013 GeV) as a function of the pivot e-folds N over the interval [50, 60] and the goldstino VEV s0 in the allowed interval (0.438, 0.886). (b) Gravitino mass m3/2 (in units of 1013 GeV) as a function of the goldstino VEV s0 in the log log scale. The thin band in light blue highlights the variation of the results across the range of e-fo… view at source ↗
Figure 3
Figure 3. Figure 3: The evolution of the scalar masses in the hidden sector and the cosmological predictions. [PITH_FULL_IMAGE:figures/full_fig_p011_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: (a) The Higgs boson mass Mh as a function of the mass scale m0 with the ATLAS+CMS combined top-quark mass Mt = 172.5 GeV [71] after assuming m1/2 = m0. The red dashed line marks the model prediction for m0 at γ = 8/ √ 85 and N = 55, and the solid red line shows the stability bound for γ = 0.17. The shaded red vertical band shows the variation of the m0 prediction for N ∈ [50, 60]. (b) Mh as a function of t… view at source ↗
Figure 5
Figure 5. Figure 5: (a) The Higgs boson mass Mh as a function of the mass scale m0 with the ATLAS+CMS combined top-quark mass Mt = 172.5 GeV [71] after assuming m1/2 = m0. The red dashed line marks the model prediction for m0 at γ ≈ 0.397 and N = 55. The shaded red vertical band shows the variation of the m0 prediction for N ∈ [50, 60]. (b) Mh as a function of the mass parameter m1/2 for Mt = 172.5 GeV and the scale m0 fixed … view at source ↗
Figure 6
Figure 6. Figure 6: Higgs boson mass Mh as a function of the ATLAS+CMS combined top-quark pole mass Mt [71]. Panels (a) and (c) correspond to the bare-µ scenario with γ = 8/ √ 85, while panels (b) and (d) correspond to the dynamically generated µ scenario with γ ≃ 0.397. In all panels, the high-scale total gaugino masses are chosen so that RG evolution gives a physical low-energy wino mass M2 ≃ 3 TeV. The green shaded regions… view at source ↗

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