The Two-Loop Finite-Temperature Effective Potential of the MSSM and Baryogenesis

TL;DR

This work develops a two-loop finite-temperature analysis of the MSSM by constructing a three-dimensional bosonic effective theory in the large-$m_A$ limit and performing a detailed dimensional reduction. It combines a first-stage reduction to a multi-field 3D theory with a second-stage integration of heavy thermal modes, followed by a calculation of the unresummed 2-loop potential in both the $\phi$- and $\chi$-directions and a meticulous matching to fix the heavy-scale parameters $\Lambda_{H_3}$ and $\Lambda_{U_3}$. The main result is a precise mapping of the sphaleron constraint region in the $m_h$-$m_{\tilde{t}_R}$ plane, showing that a strong first-order transition and thus viable electroweak baryogenesis in the MSSM persist only for a small window with $m_h \lesssim 110$ GeV and $m_{\tilde{t}_R} \lesssim m_t$ (for $m_Q=300$ GeV, with similar trends for other $m_Q$). The findings are in broad agreement with prior 3D and 4D analyses, while highlighting the limited impact of the new corrections on the allowed parameter space and emphasizing the importance of non-perturbative lattice checks for the two-stage transition region.

Abstract

We construct an effective three dimensional theory for the MSSM at high temperatures in the limit of large-$m_{A}$. We analyse the two-loop effective potential of the 3D theory for the case of a light right handed stop to determine the precise region in the $m_{h}$-$m_{\tilde{t}_{R}}$ plane for which the sphaleron constraint for preservation of the baryon asymmetry is satisfied. We also compare with results previously obtained usind 3D and 4D calculations of the effective potential. A two-stage phase transition still persists for a small range of values of $m_{\tilde{t}_{R}}$. The allowed region requires a value of $m_{\tilde{t}_{R}} \lsi m_{t}$ and $m_{h} \lsi 100$ (110) GeV for $m_{Q} = 300$ GeV (1 TeV).

Figures (6)

• Figure 1: Critical temperatures in the $\phi$- (solid) and $\chi$- (dotted) directions as functions of $m_{\tilde{t}_{R}}$ for $\tan\beta =3,5,12$ and $m_{Q} = 300$ GeV.
• Figure 2: Plot of ${v\over T}$ as a function of $m_{\tilde{t}_{R}}$ in the $\phi$- (solid line) and $\chi$- (dotted line) directions for $\tan\beta =3,5,12$ and $m_{Q} = 300$ GeV. For a given value of $\tan\beta$ the lines end at the same value of the right handed stop mass.
• Figure 3: Contours of ${v\over T} =1$ in the $m_{h}$-$m_{\tilde{t}_{R}}$ plane. The solid (dotted) line corresponds to the results obtained within our approximations for $m_{Q}= 300$ GeV ($1$TeV). The dashed line is the result using the approximations of ref. Laine2 for $m_{Q} = 300$ GeV. The region to the left of the lines gives a sufficiently strong first-order phase transition, for a given value of $m_{Q}$.
• Figure 4: Allowed region in $m_{h}$-$m_{\tilde{t}_{R}}$ plane for $m_{Q}=300$ GeV. To the left of the solid line there is a sufficiently strong first-order phase transition, to the right of the dotted line the physical vacuum is absolutely stable. The dashed line separates the region for which a two-stage phase transition can occur.
• Figure 5: Same as fig. \ref{['comp1']}, for $m_{Q}=1$TeV.