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

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.