Yukawa coupling quantum corrections to the self couplings of the lightest MSSM Higgs boson

TL;DR

This work analyzes the leading one-loop Yukawa corrections from the top/stop sector to the self-couplings of the MSSM's lightest Higgs boson $h^0$, focusing on the $O(m_t^4)$ terms. By deriving explicit expressions for the corrections to the $h^0$ tadpole, mass, and three- and four-point vertex functions, and renormalizing in the on-shell scheme, the authors show that in the heavy-stop and decoupling limits these large corrections are largely absorbed into the $h^0$ mass $M_{h^0}$, causing the $h^0$ self-couplings to approach those of the SM Higgs with the same mass. The residual genuine loop effects, when expressed in terms of $M_{h^0}$, are small—typically at the percent level—even for substantial stop mass splittings—and become negligible in the MSSM decoupling limit with large $M_A$. Numerically, the results corroborate the analytic decoupling, reinforcing the SM-like character of the MSSM Higgs sector in the decoupling regime. These findings have implications for collider probes of Higgs self-interactions and MSSM parameter discrimination in the heavy-supersymmetric-spectrum scenario.

Abstract

A detailed analysis of the top-quark/squark quantum corrections to the lightest CP-even Higgs boson (h^0) self-couplings is presented in the MSSM. By considering the leading one-loop Yukawa-coupling contributions of O(m_t^4), we discuss the decoupling behaviour of these corrections when the top-squarks are heavy compared to the electroweak scale. As shown analytically and numerically, the large corrections can almost completely be absorbed into the h^0-boson mass. Our conclusion is that the h^0 self-couplings remain similar to the coupling of the SM Higgs boson for a heavy top-squark sector.

Figures (3)

• Figure 1: Generic diagrams contributing to the one-, two-, three- and four-point 1PI Green functions of the lightest Higgs boson $h^0$ at the one-loop level: a) with top-squark loops, $\tilde{f} \equiv \tilde{t}_1, \tilde{t}_2$ , b) with top-quark loops.
• Figure 2: Exact and asymptotic result of ${\cal O}(m_t^4)$ for a)${\Delta \lambda_{hhh}}/{\lambda_{hhh}^0}$${(h\equiv h^{0})}$ as a function of $M_{A^0}$ and b)${\Delta \lambda_{hhh}}/{\lambda_{hhh}^0}$ and ${\Delta M_{h^0}^2}/{M_{h^0}^2}$ as a function of $\tan^{}\!\beta$, for $M_{A^0}=1$ TeV. The SUSY parameters have been chosen as in (\ref{['eq:equal']}).
• Figure 3: Leading Yukawa radiative corrections ${\cal O}(m_t^4)$ to the trilinear $h^{0}$ self-coupling and to the $h^{0}$ mass as a function of a)$M_{A^0}$, and b)$\tan^{}\!\beta$, for choices of the SUSY parameters as in (\ref{['eq:difscale']}).