Was the Electroweak Phase Transition Preceded by a Color-Broken Phase?

TL;DR

The paper investigates whether a color-breaking vacuum could precede the electroweak phase transition in the MSSM and whether tunneling from color-breaking to electroweak vacua could occur on cosmological timescales. It builds a finite-temperature effective potential for the Higgs and right-handed stop fields, incorporating one-loop and approximate two-loop corrections, and computes the bubble-nucleation action for the color-breaking to electroweak transition. Across a broad but physically reasonable MSSM parameter space, the minimal action E/T remains orders of magnitude above the percolation threshold, implying that the transition cannot complete; two-loop effects further suppress nucleation. The authors discuss potential beyond-MSSM mechanisms, such as R-parity violation, that could alleviate the barrier, but within the MSSM the color-breaking scenario is cosmologically excluded. These results constrain light-stop scenarios for electroweak baryogenesis and indicate that realizing color breaking would require new physics beyond the MSSM.

Abstract

It has been suggested, in connection with electroweak baryogenesis in the Minimal Supersymmetric Standard Model (MSSM), that the right-handed top squark has a negative mass squared parameter, such that its field could condense prior to the electroweak phase transition (EWPT). Thus color and electric charge could have been broken just before the EWPT. Here we investigate whether the tunneling rate from the color-broken vacuum can ever be large enough for the EWPT to occur in this case. We find that, even when all parameters are adjusted to their most favorable values, the nucleation rate is many orders of magnitude too small. We conclude that, without additional physics beyond the MSSM, the answer to our title question is ``no.'' This gives constraints in the plane of the light stop mass versus parameters related to stop mixing. However it may be possible to get color breaking in extended models, such as those with R-parity violation.

Figures (12)

• Figure 1: The effective potential at the nucleation temperature for the electroweak phase transition, in the standard scenario where color breaking never occurs. The barrier between phases is small compared to the difference in depths of the phases.
• Figure 2: A tree level correction caused by a heavy left stop at nonzero mixing. It effectively lowers the quartic coupling between the Higgs and stop fields.
• Figure 3: Gluino loop contributions to (a) the quartic coupling $\lambda_s$ and (b) the light squark thermal mass and wave function renormalization.
• Figure 4: Higgsino loop contributions to (a) the quartic coupling $\lambda_s$ and (b) the light squark thermal mass and wave function renormalization.
• Figure 5: Schematic dependence of critical and bubble nucleation temperatures for the two competing phase transitions (symmetric to CCB and symmetric to electroweak) as a function of squark mass.