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On the neutral Higgs boson masses in the MSSM for arbitrary stop mixing

Giuseppe Degrassi, Pietro Slavich, Fabio Zwirner

TL;DR

The paper computes the two-loop O(α_t α_s) corrections to the MSSM neutral Higgs masses using the effective potential in the zero-momentum limit, delivering compact analytical formulae valid for arbitrary m_A and stop mixing. It provides explicit expressions for the CP-even Higgs mass matrix corrections in DRbar and on-shell schemes, expressed through field-dependent top/stop parameters and the F_i functions, with careful treatment of scheme translations and renormalization-scale dependence. The authors verify their results against existing diagrammatic calculations in the zero-momentum limit and examine the heavy-gluino regime, highlighting non-decoupling effects in DRbar. This work offers practical, ready-to-implement formulas for precision Higgs mass predictions in the MSSM and outlines clear avenues for incorporating higher-order corrections and momentum-dependent effects in future studies.

Abstract

We compute the O(alpha_t alpha_s) two-loop corrections to the neutral Higgs boson masses in the Minimal Supersymmetric extension of the Standard Model. An appropriate use of the effective potential allows us to obtain simple analytical formulae, valid for arbitrary values of mA and of the mass parameters in the stop sector. We elucidate some subtleties of the effective potential calculation, and find full agreement with the numerical output of the existing diagrammatic calculation. We discuss in detail the limit of heavy gluino.

On the neutral Higgs boson masses in the MSSM for arbitrary stop mixing

TL;DR

The paper computes the two-loop O(α_t α_s) corrections to the MSSM neutral Higgs masses using the effective potential in the zero-momentum limit, delivering compact analytical formulae valid for arbitrary m_A and stop mixing. It provides explicit expressions for the CP-even Higgs mass matrix corrections in DRbar and on-shell schemes, expressed through field-dependent top/stop parameters and the F_i functions, with careful treatment of scheme translations and renormalization-scale dependence. The authors verify their results against existing diagrammatic calculations in the zero-momentum limit and examine the heavy-gluino regime, highlighting non-decoupling effects in DRbar. This work offers practical, ready-to-implement formulas for precision Higgs mass predictions in the MSSM and outlines clear avenues for incorporating higher-order corrections and momentum-dependent effects in future studies.

Abstract

We compute the O(alpha_t alpha_s) two-loop corrections to the neutral Higgs boson masses in the Minimal Supersymmetric extension of the Standard Model. An appropriate use of the effective potential allows us to obtain simple analytical formulae, valid for arbitrary values of mA and of the mass parameters in the stop sector. We elucidate some subtleties of the effective potential calculation, and find full agreement with the numerical output of the existing diagrammatic calculation. We discuss in detail the limit of heavy gluino.

Paper Structure

This paper contains 4 sections, 52 equations, 2 figures.

Table of Contents

  1. Introduction
  2. Higgs masses in the effective potential approach
  3. ${\cal O}(\alpha_t \alpha_s)$ two-loop corrections to the neutral Higgs boson masses
  4. Discussion

Figures (2)

  • Figure 1: Diagrams that contribute to the two--loop effective potential and affect the ${\cal O}(\alpha_t \alpha_s)$ calculation of the neutral Higgs boson masses.
  • Figure 2: The mass $m_h$ from our effective potential calculation, as a function of the gluino mass $m_{\tilde{g}}$, for (a) no mixing ($m_{\tilde{t}_1} = m_{\tilde{t}_2} = 1015$ GeV, $\,s_{2\theta}=0$) and (b) large mixing ($m_{\tilde{t}_1} = 1175$ GeV, $\,m_{\tilde{t}_2} = 825$ GeV, $\,s_{2\theta}=1$) in the stop sector. The other MSSM parameters are: $m_A = 500$ GeV, $\tan\beta = 10, \, \mu=0$ and $m_t=175$ GeV. The dashed line in fig. \ref{['gluinofig']}a is the approximate result of eq. (\ref{['hgl2']}).