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Two-Loop Effective Potential Calculation of the Lightest CP-Even Higgs-Boson Mass in the MSSM

Ren-Jie Zhang

TL;DR

The paper addresses the two-loop radiative corrections to the lightest CP-even Higgs mass in the MSSM by computing the two-loop effective potential to ${\cal O}(\lambda_t^2 \alpha_s)$ and extracting $m_h$ for arbitrary $\tan\beta$ and top-squark mixing via tadpoles and zero-momentum self-energies. It presents a straightforward, programmable two-loop EP method, and demonstrates that the two-loop corrections shift $m_h$ by only a few GeV while significantly reducing the renormalization-scale dependence. The results largely agree with previous analyses based on RGE-improved EP and diagrammatic calculations, with some differences at large squark mixing. The work reinforces an MSSM Higgs-m mass upper bound near $125$ GeV for large $\tan\beta$ and mixing and provides a practical framework for two-loop Higgs-mass calculations in supersymmetric models.

Abstract

We calculate a two-loop effective potential to the order of {\cal O}(λ_t^2α_s) in the MSSM. We then study the corresponding two-loop corrections to the CP-even Higgs-boson mass for arbitrary \tanβand left-right top-squark mixings. We find that the lightest Higgs-boson mass is changed by at most a few GeV. We also show the improved scale dependence and compare to previous two-loop analyses.

Two-Loop Effective Potential Calculation of the Lightest CP-Even Higgs-Boson Mass in the MSSM

TL;DR

The paper addresses the two-loop radiative corrections to the lightest CP-even Higgs mass in the MSSM by computing the two-loop effective potential to and extracting for arbitrary and top-squark mixing via tadpoles and zero-momentum self-energies. It presents a straightforward, programmable two-loop EP method, and demonstrates that the two-loop corrections shift by only a few GeV while significantly reducing the renormalization-scale dependence. The results largely agree with previous analyses based on RGE-improved EP and diagrammatic calculations, with some differences at large squark mixing. The work reinforces an MSSM Higgs-m mass upper bound near GeV for large and mixing and provides a practical framework for two-loop Higgs-mass calculations in supersymmetric models.

Abstract

We calculate a two-loop effective potential to the order of {\cal O}(λ_t^2α_s) in the MSSM. We then study the corresponding two-loop corrections to the CP-even Higgs-boson mass for arbitrary \tanβand left-right top-squark mixings. We find that the lightest Higgs-boson mass is changed by at most a few GeV. We also show the improved scale dependence and compare to previous two-loop analyses.

Paper Structure

This paper contains 4 sections, 21 equations, 4 figures.

Table of Contents

  1. Introduction
  2. Effective Potential and the $CP$-even Higgs-boson Masses
  3. Numerical Procedure and Results
  4. Conclusions

Figures (4)

  • Figure 1: Bubble diagrams for the two-loop effective potential to the order of ${\cal O}(\lambda_t^2\alpha_s)$ in the MSSM.
  • Figure 2: Renormalization-scale ($Q$) dependence of the lightest $CP$-even Higgs-boson mass $m_h$. The dashed and solid lines correspond to the one- and two-loop masses respectively. We have fixed the universal boundary conditions, $M_0 = 500$ GeV, $M_{1/2}=200$ GeV, $A_0=0$, and chosen a negative $\mu$-parameter.
  • Figure 3: Higgs boson masses $m_h$ vs. the squark soft masses $M_S$ in the no-squark-mixing case $A_t=\mu=0$. The solid lines are results from the two-loop EP approach. For comparison, we also show the results from the RGE-improved one-loop EP approach in dashed lines.
  • Figure 4: Higgs-boson masses $m_h$ vs. $X_t/M_S$, where $X_t=A_t+\mu/\tan\beta$. Both the results from the RGE-improved one-loop EP and two-loop EP approaches are shown.