Complete Two-loop Dominant Corrections to the Mass of the Lightest CP-even Higgs Boson in the Minimal Supersymmetric Standard Model

TL;DR

This paper delivers a complete two-loop calculation of the dominant MSSM corrections to the lightest CP-even Higgs mass, $M_{h^0}$, at ${\cal O}(\alpha_t^2)$ using an effective potential framework with general stop mixing and $\tan\beta$. It derives both full analytic expressions and compact RG-improved forms, showing that large logarithms can be absorbed into a one-loop term evaluated at appropriate scales plus smaller two-loop threshold contributions. Numerically, for a SUSY scale around 1 TeV and $M_t=175\pm5$ GeV, the upper bound on $M_{h^0}$ is about $129\pm5$ GeV, with two-loop $\alpha_t^2$ effects capable of increasing the mass by up to ~5 GeV in the maximal mixing scenario. The results are validated against existing diagrammatic calculations, and the analytic approximations achieve sub-GeV precision across most of the parameter space, providing practical tools for precision MSSM Higgs phenomenology and Higgs searches.

Abstract

Using an effective potential approach, we compute two-loop radiative corrections to the MSSM lightest ${\cal CP}$-even Higgs boson mass $M_{h^0}$ to ${\cal O}(α_t^2)$ for arbitrary left-right top-squark mixing and $\tanβ$. We find that these corrections can increase $M_{h^0}$ by as much as 5 GeV; assuming a SUSY scale of 1 TeV, the upper bound on the Higgs boson mass is $M_{h^0}\approx 129\pm 5$ GeV for the top quark pole mass $175\pm 5$ GeV. We also derive an analytical approximation formula for $M_{h^0}$ which is good to a precision of $\lsim 0.5$ GeV for most of the parameter space and suitable to be further improved by including renormalization group resummation of leading and next-to-leading order logarithmic terms. Our final compact formula admits a clear physical interpretation: radiative corrections up to the two-loop level can be well approximated by a one-loop expression with parameters evaluated at the appropriate scales, plus a smaller finite two-loop threshold correction term.

Figures (8)

• Figure 1: Higgs boson mass $M_{h^0}$ vs. the on-shell top-squark mixing parameter $\hat{X}^{\rm OS}_t$. Dotted, dot-dashed lines show one-loop and two-loop ${\cal O}(\alpha_s\alpha_t)$ results from the program FeynHiggs, corresponding results from our numerical analyses are shown in dashed and solid lines respectively.
• Figure 2: Higgs boson mass $M_{h^0}$ vs. the on-shell SUSY scale $M_S$, for two top-squark mixing parameters $\hat{X}^{\rm OS}_t=0$ and 2. One-loop mass, two-loop masses to ${\cal O}(\alpha_s\alpha_t)$ and ${\cal O}(\alpha_s\alpha_t+\alpha_t^2)$ are shown in dashed, dot-dashed and solid lines respectively.
• Figure 3: Higgs boson mass $M_{h^0}$ vs. $\tan\beta$ for the top-squark mixing parameters $\hat{X}^{\rm OS}_t=0$ and $2$. Dot-dashed and solid lines correspond to two-loop Higgs boson masses to ${\cal O}(\alpha_s\alpha_t)$ and ${\cal O}(\alpha_s\alpha_t+\alpha_t^2)$ respectively for $M_t=175$ GeV. Two-loop masses to ${\cal O}(\alpha_s\alpha_t+\alpha_t^2)$ for $M_t=170$ and $180$ GeV are also shown in dotted and dashed lines.
• Figure 4: Higgs boson masses $M_{h^0}$ vs. $\hat{X}^{\rm OS}_t$. One-loop masses, two-loop masses to ${\cal O}(\alpha_s\alpha_t+\alpha_t^2)$ and their approximations are shown in dashed, solid and dot-dashed lines.
• Figure 5: Higgs boson masses $M_{h^0}$ vs. $\hat{X}^{\rm OS}_t$. Two-loop masses to ${\cal O}(\alpha_s\alpha_t)$ and ${\cal O}(\alpha_s\alpha_t+\alpha_t^2)$ are shown in dotted and dashed lines, their corresponding RG-corrected masses are shown in dot-dashed and solid lines.