On the two-loop sbottom corrections to the neutral Higgs boson masses in the MSSM

TL;DR

The paper addresses two-loop corrections to MSSM neutral Higgs masses of order $O(\alpha_b \alpha_s)$ in the large $\tan\beta$ regime where sbottom–Higgs interactions dominate. Using an effective potential approach, it derives explicit formulas in a renormalization scheme that decouples heavy gluinos and resums large threshold effects into the one-loop piece, while keeping the results $Q$-independent. It also discusses $O(\alpha_b^2)$ contributions in a simple limit and provides a practical framework for implementing these corrections with physical input parameters, including resummed bottom-mquon threshold corrections via $\epsilon_b$ and related redefinitions. Numerically, the genuine $O(\alpha_b \alpha_s)$ corrections are typically a few GeV and can be enhanced for small $m_A$, but are kept under control by the chosen renormalization scheme, ensuring perturbative reliability in MSSM Higgs-mass predictions.

Abstract

We compute the O(ab*as) two-loop corrections to the neutral Higgs boson masses in the Minimal Supersymmetric Standard Model, using the effective potential approach. Such corrections can be important in the region of parameter space corresponding to tan(beta)>>1 and sizeable mu. In spite of the formal analogy with the O(at*as) corrections, there are important differences, since the dominant effects are controlled by the sbottom-Higgs scalar couplings. We propose a convenient renormalization scheme that avoids unphysically large threshold effects associated with the bottom mass, and absorbs the bulk of the O(ab*as + ab*at) corrections into the one-loop expression. We give general explicit formulae for the O(ab*as) corrections to the neutral Higgs boson mass matrix. We also discuss the importance of the O(ab^2) corrections and derive a formula for their contribution to mh in a simple limiting case.

Figures (4)

• Figure 1: The Yukawa coupling $h_b$, as defined in Eq. (\ref{['mbnoantri']}): as a function of $\mu$ for $\tan\beta = 40$ (left panel); as a function of $\tan\beta$ for $\mu = 1.2$ TeV (right panel). The other parameters are $A_b = 2$ TeV, $m_Q = m_D = m_{\tilde{g}} = 1$ TeV. The quantity $h_b^{pole} \equiv \sqrt{2} \, M_b / v_1$ is also shown for comparison.
• Figure 2: The mass $m_h$ as a function of $\tan\beta$, for $m_{ A} = 120$ GeV (left panel) or 1 TeV (right panel). The other parameters are $\mu = 1.2$ TeV, $A_t = A_b = 2$ TeV, $m_{Q,\tilde{t}} = m_U = m_D = m_{\tilde{g}} = 1$ TeV. The meaning of the different curves is explained in the text.
• Figure 3: The mass $m_h$ as a function of $\mu$, for $m_{ A} = 120$ GeV (left panel) or 1 TeV (right panel). The other parameters are $\tan\beta = 30$, $A_t = A_b = 2$ TeV, $m_{Q,\tilde{t}} = m_U = m_D = m_{\tilde{g}} = 1$ TeV. The meaning of the different curves is explained in the text.
• Figure 4: The masses $m_h$ and $m_{ H}$ as a function of $m_{ A}$, for $\mu = 1.2$ TeV and $m_{Q,\tilde{t}} = m_U = m_D = m_{\tilde{g}} = 1$ TeV. The other parameters are (a) $\tan\beta = 40,\, A_t = A_b = 2$ TeV and (b) $\tan\beta = 45,\, A_t = 1.5$ TeV, $A_b = 0$. The meaning of the different curves is explained in the text.