Supersymmetric Electroweak Phase Transition: Beyond Perturbation Theory

TL;DR

This work develops a dimensionally reduced 3D effective theory for the MSSM near the finite-temperature electroweak phase transition, retaining the dominant one-loop top/stop effects and matching to physical observables. By combining this perturbative reduction with nonperturbative lattice results for 3D gauge theories, the authors evaluate the sphaleron washout bound and find that electroweak baryogenesis remains viable in a substantially larger MSSM parameter space than previously thought, including regimes with large $\tan\beta$ when $m_{A^0}$ lies between 40 and 120 GeV. The analysis emphasizes a robust, scale-independent mapping from MSSM parameters to the 3D action and shows that the strength of the phase transition can be strong enough to preserve the baryon asymmetry in many scenarios. The findings expand the phenomenologically allowed region for MSSM baryogenesis and highlight the importance of nonperturbative input in electroweak phase transition studies.

Abstract

We compute the three-dimensional effective action for the minimal supersymmetric standard model, which describes the light modes of the theory near the finite-temperature electroweak phase transition, keeping the one-loop corrections from the third generation quarks and squarks. Using the lattice results of Kajantie {\it et al.}\ for the phase transition in the same class of 3-D models, we find that the strength of the phase transition is sufficient for electroweak baryogenesis, in much broader regions of parameter space than have been indicated by purely perturbative analyses. In particular we find that, while small values of $\tanβ$ are favored, positive results persist even for arbitrarily large values of $\tanβ$ if the mass of the $A^0$ boson is between 40 and 120 GeV, a region of parameters which has not been previously identified as being favorable for electroweak baryogenesis.

Figures (8)

• Figure 1: The 1PI diagrams needed for the scalar 2-point function. Thin line in the loop represents quarks and the heavy lines squarks. Indices labeling external legs refer to doublet; when index is a letter either 1 or 2 is allowed. The example shown corresponds to top quark or squark in the loop; for bottom sector reverse 1 and 2.
• Figure 2: The 1PI diagrams needed for the 4-point function. For explanations see figure 1.
• Figure 3: Diagrams contributing to the effective gauge coupling ${\bar{g}}_3$ in the heavy scale (zero-Matsubara-frequency) integration.
• Figure 4: The tadpole diagrams needed for the 1-loop effective potential in the present approximation. The vertices marked by heavy circles (open circles) come from quartic terms of order $y^2$ ($g^2$), where one external Higgs field is replaced by its VEV.
• Figure 5: Diagrams contributing to the irreducible two point functions of the higgs fields in the broken phase. Vertices induced by spontaneous symmetry breaking do not contribute to the CP-odd two-point function. Again the indices on the external legs correspond to the top sector.