MSSM Lightest CP-Even MSSM Higgs Boson Mass to O(alpha_s alpha_t): the Effective Potential Approach

TL;DR

This work addresses the precise prediction of the MSSM lightest CP-even Higgs mass $m_{h^0}$ by deriving a simple analytical, RG-improved formula that includes dominant radiative corrections up to ${\cal O}(α_s α_t)$. Starting from a two-loop MSSM effective potential, the authors combine effective-potential, diagrammatic, and RG methods to resum large logarithms and incorporate finite mixing effects from the top-squark sector. The resulting expression, valid for a heavy SUSY threshold $M_S$, matches known diagrammatic results where overlap exists and clarifies discrepancies with previous RG analyses as arising from scheme choices and two-loop threshold terms. They also provide a structured framework to extend to ${\cal O}(α_t^2)$ corrections, highlighting the practical impact for Higgs phenomenology and SUSY parameter interpretation.

Abstract

Starting with the two-loop effective potential of the MSSM, and assuming a supersymmetric scale well above $M_Z$, we derive a simple analytical approximation for the lightest CP-even Higgs boson mass including resummation of higher order logarithmic terms via RG-improvement and finite non-logarithmic terms up to ${\cal O}(α_sα_t)$. This formula describes the most relevant radiative corrections to the MSSM Higgs boson mass, in particular, those associated with non-zero top-squark mixing.

Figures (1)

• Figure 1: Higgs boson mass $m_{h^0}$ versus ${\widehat{X}}_t/{\widehat{m}}_{\tilde{t}}$. The solid lines and dotdashes correspond to the two-loop Higgs boson masses calculated from the RG-improved mass formula Eq. (\ref{['mhrg']}), with and without including the two-loop finite threshold corrections. One-loop masses are shown in dashes for reference.