The Lightest Higgs Boson Mass in the Minimal Supersymmetric Standard Model
J. A. Casas, J. R. Espinosa, M. Quirós, A. Riotto
TL;DR
The paper derives a model-independent upper bound on the MSSM lightest Higgs mass by matching a renormalization-group–improved SM effective potential between the electroweak and SUSY scales, including stop-threshold corrections and self-energy effects that connect running masses to physical pole masses. It finds that two-loop radiative corrections are negative relative to the one-loop result and are small (≲3%), yielding tight bounds: for $M_S\leq 1$ TeV and $X_t^2=6M_S^2$, $M_H\leq 140$ GeV for $M_t\leq 190$ GeV, and $M_H\leq 86$ GeV in the IR fixed-point top scenario with $M_t=170$ GeV. The analysis reconciles discrepancies with other works by emphasizing proper scale choices and wave-function renormalization, and demonstrates that the MSSM remains predictive with an overall estimated uncertainty of about 2 GeV. These results yield concrete targets for Higgs searches at LEP/LHC and inform the viability of low-energy SUSY scenarios.
Abstract
We compute the upper bound on the mass of the lightest Higgs boson in the Minimal Supersymmetric Standard Model in a model-independent way, including leading (one-loop) and next-to-leading order (two-loop) radiative corrections. We find that (contrary to some recent claims) the two-loop corrections are negative with respect to the one-loop result and relatively small ($\simlt 3$\%). After defining physical (pole) top quark mass $M_t$, by including QCD self-energies, and physical Higgs mass $M_H$, by including the electroweak self-energies $Π\left(M_H^2\right)-Π(0)$, we obtain the upper limit on $M_H$ as a function of supersymmetric parameters. We include as supersymmetric parameters the scale of supersymmetry breaking $M_S$, the value of $\tan β$ and the mixing between stops $X_t= A_t + μ\cotβ$ (which is responsible for the threshold correction on the Higgs quartic coupling). Our results do not depend on further details of the supersymmetric model. In particular, for $M_S\leq 1$ TeV, maximal threshold effect $X_t^2=6M_S^2$ and any value of $\tanβ$, we find $M_H\leq 140$ GeV for $M_t\leq 190$ GeV. In the particular scenario where the top is in its infrared fixed point we find $M_H\leq 86$ GeV for $M_t = 170$ GeV.