⚛️ phenomenology

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

This paper proposes a Starobinsky supergravity framework coupled to the MSSM that simultaneously explains the observed Higgs boson mass through three-loop renormalization-group evolution and predicts a 3 TeV thermal wino dark matter candidate with a disappearing-track signature detectable by future 100 TeV colliders.

Original authors: Daniel Frolovsky, Alexander Belyaev, Sergei V. Ketov

Published 2026-07-09

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Daniel Frolovsky, Alexander Belyaev, Sergei V. Ketov

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

The Big Picture: Connecting the Very Big to the Very Small

Imagine the universe as a giant, complex machine. Scientists have two main instruction manuals for how this machine works:

The Cosmology Manual: Describes the very beginning of the universe (the Big Bang) and how it expanded rapidly (Inflation).
The Particle Physics Manual: Describes the tiny building blocks of matter (like atoms and subatomic particles) and how they interact.

For a long time, these two manuals have been written in different languages and didn't seem to fit together. This paper proposes a way to stitch them together. The authors suggest that the same "hidden engine" that drove the universe's rapid expansion in the beginning is also responsible for the masses of the tiny particles we see today.

The Engine: Starobinsky Supergravity

The authors use a specific type of theoretical engine called Starobinsky Supergravity. Think of this engine as having two main parts:

The Inflaton (The Driver): A particle that pushed the universe to expand incredibly fast right after the Big Bang.
The Hidden Sector (The Transmission): A secret compartment in the engine where "Supersymmetry" (a theory that says every particle has a heavy twin) gets broken.

In this paper, the authors show that the "transmission" isn't just a random add-on; it emerges naturally from the shape of the engine itself. When the universe stopped expanding rapidly, this hidden sector "cracked," breaking the symmetry and giving mass to the particles we know.

The Domino Effect: From Space to the Higgs

Here is the chain reaction the paper describes, using a "Domino" analogy:

The First Domino (Cosmic Microwave Background): We can measure the "faint echo" of the Big Bang (the Cosmic Microwave Background). This tells us exactly how hard the engine pushed during inflation.
The Second Domino (The Hidden Sector): That push sets the size of the "hidden sector" in the engine. This determines how heavy the "gravitino" (the super-twin of the gravity particle) is.
The Third Domino (The Higgs Mass): The weight of the gravitino acts like a pressure gauge that sets the rules for the Higgs boson (the particle that gives other particles mass).

The authors ran a complex calculation (like a high-speed simulation) to see if the weight of the Higgs boson predicted by this chain reaction matches what we actually measured in the lab.

The Result: It matches! The paper claims that if you start with the observed expansion of the universe, the math naturally leads to a Higgs boson mass of about 125 GeV, which is exactly what scientists have measured. This links the history of the entire universe to the mass of a single particle.

The Mystery of Dark Matter: The "Wino"

The paper also tackles Dark Matter, the invisible stuff that holds galaxies together.

The Candidate: The authors propose that the Dark Matter particle is a "Wino." Think of the Wino as a specific type of heavy, invisible twin particle.
The Weight: For this Wino to be the right amount of Dark Matter (not too much, not too little), it needs to weigh about 3 TeV. That is roughly 3,000 times heavier than a proton.
The "Disappearing Act": Because the Wino is so heavy and interacts weakly, it has a very strange behavior. It has a charged twin that lives for a tiny fraction of a second before turning into a neutral Wino and a tiny, soft particle (a pion).
- The Analogy: Imagine a runner in a race who suddenly vanishes into thin air just a few meters after the starting line. In a particle detector, this looks like a "disappearing track." The paper predicts that if we build a super-powerful collider (a 100 TeV machine), we should be able to see these tracks and confirm the existence of this 3 TeV Wino.

The "Fine-Tuning" Problem

The paper acknowledges that for this to work, the numbers have to line up perfectly. It's like balancing a pencil on its tip.

The "tree-level" mass (the basic weight) of the Wino and the "anomaly-mediated" mass (a quantum correction) have to cancel each other out almost perfectly to leave us with that specific 3 TeV weight.
The authors argue that this "fine-tuning" isn't a mistake; it's a feature of their specific engine design. It makes the theory very predictive: if you find a 3 TeV Wino, you confirm the whole story. If you don't, the story falls apart.

What This Means for the Future

The paper concludes with a clear roadmap for testing these ideas:

Direct Detection: Next-generation underground detectors (using huge tanks of liquid xenon) might be able to "feel" the Wino bumping into atoms, though it will be very faint.
Colliders: The current Large Hadron Collider (LHC) isn't strong enough to create a 3 TeV Wino. However, a future 100 TeV proton collider would be powerful enough to create them and spot their "disappearing tracks."

Summary

This paper builds a bridge between the beginning of the universe and the particles inside us. It suggests that the force that blew up the universe also set the rules for the Higgs boson's mass and created a specific type of Dark Matter (the Wino). The theory is mathematically consistent with current data and offers a clear, testable prediction: a 3 TeV Wino that can be found by future giant particle colliders.

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

Problem Statement
A central challenge in high-energy physics is establishing a concrete connection between the Standard Model (SM) of particle physics and the mechanism of cosmic inflation. The SM is incomplete, lacking a description of gravity, dark matter (DM), and the origin of neutrino masses. Conversely, inflation offers a window into physics beyond the SM, constrained by Cosmic Microwave Background (CMB) observations. Existing approaches to linking inflation with the Minimal Supersymmetric Standard Model (MSSM) are often highly model-dependent. This paper addresses the need for a unified framework where the inflationary scale, the mechanism of Supersymmetry (SUSY) breaking, the MSSM soft parameters, and the Higgs boson mass are not independent inputs but are dynamically linked through a specific supergravity construction.

Methodology
The authors propose a framework based on Starobinsky supergravity coupled to the MSSM. The methodology proceeds through the following steps:

Supergravity Setup: The Starobinsky model is supersymmetrized in the Jordan frame using the old-minimal supergravity formulation. This introduces higher-derivative terms that, upon transformation to the Einstein frame, manifest as two chiral supermultiplets: the inflaton supermultiplet ( $T$ ) and the goldstino supermultiplet ( $S$ ). These form the "hidden sector."
Inflation and SUSY Breaking: The scalar potential is constructed to support single-field inflation driven by the real part of $T$ . The vacuum expectation value (VEV) of the scalar component of $S$ ( $s_0$ ) triggers spontaneous SUSY breaking. The model requires specific R-symmetry breaking terms to ensure a Minkowski vacuum with broken SUSY and to stabilize the scalar potential.
Coupling to MSSM: The MSSM is coupled to this hidden sector in the Einstein frame. The Kähler potential and superpotential are defined such that SUSY breaking is mediated gravitationally to the visible sector.
- $\mu$ -term Generation: The framework naturally generates a high-scale $\mu$ term. The goldstino superfield $S$ , already present in the theory, acts as the singlet required for the Giudice-Masiero mechanism or via superpotential interactions ( $S^n H_u H_d$ ), eliminating the need to introduce an ad-hoc singlet sector.
- Soft Parameters: The soft SUSY-breaking masses ( $m_0$ ), trilinear couplings ( $A$ ), bilinear couplings ( $B$ ), and gaugino masses are derived as functions of the gravitino mass ( $m_{3/2}$ ) and the VEV $s_0$ .
Renormalization Group (RG) Evolution: The high-scale boundary conditions (fixed by the inflationary scale and SUSY breaking mechanism) are evolved down to the electroweak (EW) scale using three-loop RG equations. The authors utilize two independent Effective Field Theory (EFT) codes, SusyHD and HSSUSY (within FlexibleSUSY), to match the MSSM onto the SM at the high scale and calculate the physical Higgs boson mass ( $M_h$ ).
Dark Matter Constraints: The framework assumes conserved R-parity. The authors analyze the gaugino mass spectrum, specifically focusing on the wino branch. They impose the condition that the thermal relic abundance of the Lightest Supersymmetric Particle (LSP) matches the observed DM density.

Key Contributions and Results

Unified Scale Linking: The inflationary scale, determined by the CMB scalar perturbation amplitude ( $A_s$ ), fixes the mass parameter $m \sim 10^{13}$ GeV. This scale determines the gravitino mass $m_{3/2}$ and, consequently, the universal soft scalar mass $m_0 \approx m_{3/2}$ .
Higgs Mass Prediction: By enforcing the existence of a light SM-like Higgs doublet (requiring $\det(M_H^2) \approx 0$ $det (M_{H}^{2}) \approx 0$ at the high scale), the model fixes the ratio of Higgs VEVs ( $\tan \beta = 1$ $tan β = 1$ ) and the relationship between soft parameters ( $A = \mu_{eff} = -m_{3/2}$ $A = μ_{e f f} = - m_{3/2}$ for the bare $\mu$ $μ$ case).
- The three-loop RG evolution yields a Higgs boson mass consistent with the measured value ( $125.25 \pm 0.17$ GeV) within theoretical and experimental uncertainties.
- The prediction is robust against variations in the number of e-folds ( $N \in [50, 60]$ ) and the gaugino mass scale $m_{1/2}$ (provided $m_{1/2} \leq m_0$ ).
- The authors identify and correct a bug in the SusyHD v1.0.2 interpolation table regarding the strong coupling dependence, ensuring accurate parametric uncertainty estimates.
Thermal Wino Dark Matter: The model predicts a split-SUSY spectrum where scalars and higgsinos are heavy ( $\sim 10^{13}$ $\sim 1 0^{13}$ GeV), while the wino LSP is light.
- To satisfy the observed relic abundance via thermal freeze-out, the physical wino mass must be approximately 2.7–3.0 TeV.
- Achieving this mass requires a precise cancellation between the universal tree-level gaugino mass contribution and the anomaly-mediated supersymmetry breaking (AMSB) contribution to the wino mass ( $M_2$ ).
Phenomenological Signatures:
- Direct Detection: The loop-induced spin-independent wino-nucleon scattering cross-section is predicted to be $\sigma_{SI} \approx 2.3 \times 10^{-47}$ cm $^2$ . This is below current LUX-ZEPLIN (LZ) sensitivity but within the projected reach of next-generation multi-ton liquid-xenon detectors (e.g., DARWIN/XLZD).
- Collider Signatures: Electroweak radiative corrections induce a mass splitting of $\sim 160$ MeV between the charged and neutral wino states, resulting in a long-lived charged wino ( $\tau \approx 0.2$ ns). This leads to a "disappearing-track" signature.
- Collider Reach: The High-Luminosity LHC (HL-LHC) is projected to exclude winos up to $\sim 1.1$ TeV, insufficient to reach the 3 TeV thermal target. However, a future 100 TeV proton collider is projected to have the discovery reach necessary to detect the 3 TeV disappearing-track signal or fully exclude this scenario.

Significance and Claims
The paper claims to provide a predictive and parameter-free (regarding the SUSY breaking scale and gravitino mass) framework that links cosmological observables (CMB amplitude and spectral tilt) to particle physics observables (Higgs mass and DM properties).

Theoretical Economy: The hidden sector emerges naturally from the dual description of Starobinsky supergravity, avoiding the ad-hoc introduction of singlets for the $\mu$ -problem or separate SUSY-breaking sectors.
Consistency: The model successfully reconciles the high-scale inflationary dynamics with the low-energy Higgs mass measurement and the thermal wino dark matter requirement.
Testability: The scenario makes sharp, falsifiable predictions. The specific 3 TeV wino mass is a direct consequence of the thermal relic density condition in this high-scale SUSY framework. The authors emphasize that while current experiments cannot probe this mass scale, the scenario is "sharply testable" by future 100 TeV colliders via disappearing tracks and by next-generation direct detection experiments.

The authors conclude that their framework effectively eliminates the free parameters typically associated with the phenomenological MSSM, establishing a direct link between the amplitude of primordial scalar perturbations and the Higgs boson mass, while identifying a specific, testable thermal wino dark matter candidate.