The upper bound on the lightest Higgs mass in the NMSSM revisited

TL;DR

This paper revisits the NMSSM upper bound on the lightest Higgs mass by incorporating complete one- and two-loop radiative corrections alongside constraints from perturbativity up to the GUT scale and vacuum stability. It uses the NMHDECAY3 tool to scan NMSSM parameter space with 1 TeV squarks/sleptons and maximal mixing, identifying the maximal bound near $\tanβ \approx 2$ and showing $m_h$ can reach about $m_h \approx 141$ GeV for $m_{top} \approx 178$ GeV (and ~$139.9$ GeV for $m_{top} \approx 171.4$ GeV), exceeding the MSSM bound by roughly $12$–$16$ GeV in this region. The analysis clarifies the dependence on $λ$, $κ$, $μ$, $A_λ$, and $A_κ$, and discusses how LEP constraints, singlet–doublet mixing, and an upper limit on $m_A$ influence the maximum, noting that at large $\tanβ$ the NMSSM bound approaches the MSSM value. Overall, the work provides a more precise, model-specific upper bound and highlights parameter regions where NMSSM predictions could be distinguishable from MSSM in Higgs measurements.

Abstract

We update the upper bound on the lightest CP even Higgs mass in the NMSSM, which is given as a function of tan(beta) and lambda. We include the available one and two loop corrections to the NMSSM Higgs masses, and constraints from the absence of Landau singularities below the GUT scale as well as from the stability of the NMSSM Higgs potential. For m_top varying between 171.4 and 178 GeV, squark masses of 1 TeV and maximal mixing the upper bound is assumed near tan(beta) ~ 2 and varies between 139.9 and 141.4 GeV.

Figures (2)

• Figure 1: Upper bound on the lightest Higgs mass in the NMSSM for $m_{top}=178$ GeV (thick full line: $m_A$ arbitrary, thick dotted line: $m_A = 1$ TeV) and $m_{top} = 171.4$ GeV (thin full line: $m_A$ arbitrary, thick dotted line: $m_A = 1$ TeV) and in the MSSM (with $m_A = 1$ TeV) for $m_{top}=178$ GeV (thick dashed line) and $m_{top} = 171.4$ GeV (thin dashed line) as obtained with NMHDECAY as a function of $\tan\!\beta$. Squark and gluino masses are 1 TeV and $A_{top}=2.5$ TeV.
• Figure 2: Upper bound on the lightest Higgs mass in the NMSSM for $m_{top}=178$ GeV, $\tan\!\beta=2.2$, electroweak/Yukawa corrections included (thick full line) and omitted (thick dotted line), and $m_{top} = 171.4$ GeV, $\tan\!\beta = 2$, electroweak/Yukawa corrections included (thin full line) and omitted (thin dotted line). Squark and gluino masses and $A_{top}$ are as in fig. 1.