On the O(alpha_t^2) two-loop corrections to the neutral Higgs boson masses in the MSSM

TL;DR

This work advances the precision of MSSM Higgs predictions by computing the ${ m O}(\\alpha_t^2)$ two-loop corrections to the neutral CP-even Higgs mass matrix within the effective potential framework, valid for arbitrary $m_A$ and stop-sector parameters. It provides complete analytic expressions for the momentum-independent part and discusses how to include momentum-dependent effects and scheme translations between DR-bar and OS definitions. The results show that these two-loop corrections can raise the lightest Higgs mass $m_h$ by several GeV, especially with large stop mixing, and are often comparable to or exceed leading logarithmic renormalization-group improvements. The findings enable more accurate interpretations of experimental Higgs searches and offer practical, implementable formulae for precision MSSM phenomenology.

Abstract

We compute the O(alpha_t^2) two-loop corrections to the neutral CP-even Higgs boson mass matrix in the Minimal Supersymmetric Standard Model, for arbitrary values of mA and of the parameters in the stop sector, in the effective potential approach. In a large region of parameter space these corrections are sizeable, increasing the prediction for mh by several GeV. We present explicit analytical formulae for a simplified case. We discuss the inclusion of momentum-dependent corrections and some possible ways of assigning the input parameters.

Figures (6)

• Figure 1: The classes of Feynman diagrams that contribute to the two--loop effective potential and affect the ${\cal O}(\alpha_t^2)$ calculation of the neutral Higgs boson masses [$q=(t,b)$, $\varphi = (H, h, G, A, H^\pm, G^\pm)$, $\tilde{h} = (\tilde{h}^0_{1,2}, \tilde{h}^\pm)$, $\tilde{q} = (\tilde{t}_1, \tilde{t}_2, \tilde{b}_L)$].
• Figure 2: The mass $m_h$ as a function of $m_{ A}$, for $\tan\beta = 2$ or 20 and $X_t^{\rm OS} = 0$ or 2 TeV. The other parameters are $m_Q^{\rm OS} = m_U^{\rm OS} = 1$ TeV, $\mu = 200$ GeV, $m_{\tilde{g}} = 800$ GeV. The meaning of the different curves is explained in the text.
• Figure 3: The masses $(m_h,m_{ H})$ as functions of $m_{ A}$, for $\tan\beta = 2$ or 20 and $X_t^{\rm OS} = 2$ TeV. The other input parameters are as in Fig. \ref{['mhvsma']}.
• Figure 4: The effective CP--even Higgs mixing angle $\overline{\alpha}$, in the combination $\sin^2 (\beta - \overline{\alpha})$, as a function of $m_{ A}$, for $\tan\beta = 2$ or 20 and $m_Q^{\rm OS} = m_U^{\rm OS} = 1$ TeV, $X_t^{\rm OS} = 2$ TeV, $\mu = 200$ GeV, $m_{\tilde{g}} = 800$ GeV. The meaning of the curves, explained in the text, is the same in the two frames.
• Figure 5: The CP--even Higgs masses as functions of the stop mixing parameter $X_t^{OS}$, for $m_{ A} = 120$ GeV or 1 TeV. For large $m_{ A}$ only $m_h$ is shown. The other input parameters are $m_Q^{\rm OS} = 1$ TeV, $m_U^{\rm OS} = 700$ GeV, $\tan\beta = 2$, $\mu = 200$ GeV, $m_{\tilde{g}} = 800$ GeV.