ANALYTICAL EXPRESSIONS FOR RADIATIVELY CORRECTED HIGGS MASSES AND COUPLINGS IN THE MSSM

TL;DR

This work addresses the precise computation of radiatively corrected Higgs masses and couplings in the MSSM. It develops a renormalization-group improved leading-log framework with the scale fixed at the top-quark mass $M_t$, yielding high-accuracy results and a analytic two-loop LL expression for the light Higgs mass. It treats two regimes: (i) $m_A \sim M_{ m SUSY}$, where the LL result closely matches the next-to-leading-log calculations and an analytic $m_h^2$ formula is provided; (ii) $m_A \lesssim M_{ m SUSY}$, where the low-energy theory is a two-Higgs-doublet model with quartic couplings $\lambda_i$ and threshold corrections, from which analytic expressions for all Higgs masses, the mixing angle, and couplings are derived. Across the parameter space, the analytic results reproduce the full numerical RG-improved LL results within about $2$–$3$ GeV for masses and equivalent precision for couplings, offering fast, reliable predictions and clarifying the domain of validity for the expansions used.

Abstract

We propose, for the computation of the Higgs mass spectrum and couplings, a renormalization-group improved leading-log approximation, where the renormalization scale is fixed to the top-quark pole mass. For the case $m_A\sim M_{\rm SUSY}$, our leading-log approximation differs by less than 2 GeV from previous results on the Higgs mass computed using a nearly scale independent renormalization-group improved effective potential up to next-to-leading order. Moreover, for the general case $m_A\simlt M_{\rm SUSY}$, we provide analytical formulae (including two-loop leading-log corrections) for all the masses and couplings in the Higgs sector. For $M_{\rm SUSY}\simlt 1.5$ TeV and arbitrary values of $m_A$, $\tanβ$ and the stop mixing parameters, they reproduce the numerical renormalization-group improved leading-log result for the Higgs masses with an error of less than 3 GeV. For the Higgs couplings, our analytical formulae reproduce the numerical results equally well. Comparison with other methods is also performed.

Figures (8)

• Figure 1: The lightest CP-even Higgs mass as a function of the physical top-quark mass, for $M_{\rm SUSY}=1$ TeV, evaluated in the limit of large CP-odd Higgs mass, as obtained from the two-loop renormalization-group improved effective potential (solid lines), the one-loop improved RG evolution (dashed lines) and the analytical formulae, Eq. (\ref{['mhsm']}) (dotted lines). The four sets of lines correspond to: a)$\tan \beta =$ 15 with maximal squark mixing, $\tilde{X}_t$ = 6; b)$\tan \beta =$ 15 with zero mixing, $\tilde{X}_t$ = 0; c) the minimal value of $\tan \beta$ allowed by perturbativity constraints for the given value of $M_t$ (IR fixed point), with $\tilde{X}_t$ = 6; and, d)$\tan \beta$ the same as in (c) with zero mixing.
• Figure 2: The lightest CP-even Higgs mass as a function of the supersymmetric scale $M_{\rm SUSY}$, for $M_t=175$ GeV, and evaluated in the limit of large CP-odd Higgs mass. Solid, dashed and dotted lines are as in Fig. 1. The different sets of curves correspond to the values of $\tilde{X}_t$ and $\tan\beta$ for cases (a) to (d) of Fig. 1.
• Figure 3: The lightest CP-even Higgs mass as a function of the CP-odd Higgs mass for a physical top-quark mass $M_t =$ 175 GeV and $M_{\rm SUSY}$ = 1 TeV, as obtained from the one-loop improved RG evolution (solid lines) and the analytical formulae, Eq. (\ref{['mhH']}), (dashed lines). The four sets of curves correspond to: a)$\tan \beta=$ 15 with large squark mixing, $X_t$ = 6 ($\mu=0$); b)$\tan \beta=$ 15 with zero mixing $X_t=\mu$ = 0; c) the minimal value of $\tan \beta$ allowed by perturbativity constraints for the given value of $M_t$ (IR fixed point), $\tan\beta\simeq 1.6$, with large squark mixing; and, d)$\tan\beta\simeq 1.6$ with zero mixing.
• Figure 4: The heaviest CP-even Higgs mass as a function of the CP-odd Higgs mass for the same set of parameters as in Fig. 3.
• Figure 5: The charged Higgs mass as a function of the CP-odd Higgs mass for the same set of parameters as in Fig. 3 (upper overlapping curves), and for $\mu = 2 M_{\rm SUSY}$ and $\tan\beta = 15$, for which the radiative corrections become observable (solid and dashed lower curves).