Phase Transitions and Vacuum Tunneling Into Charge and Color Breaking Minima in the MSSM

TL;DR

This paper investigates vacuum stability in the MSSM, focusing on the possibility of charge- and color-breaking (CCB) minima and the fate of the Standard Model-like (SML) false vacuum under quantum tunneling. The authors develop and apply novel numerical methods to compute false-vacuum decay rates, showing that while some MSSM parameter regions yield rapid tunneling and are ruled out, a significant portion remains cosmologically viable with $S_E[\bar{\phi}]/\hbar \gtrsim 400$. They analyze zero-temperature tunneling and finite-temperature evolution, arguing that the early Universe is typically driven toward the SML minimum and that deep CCB minima are often decoupled from low-energy tunneling physics. The results provide important, not universally prohibitive, constraints on low-energy SUSY parameter space and offer a framework for incorporating vacuum stability into MSSM phenomenology and experimental planning.

Abstract

The scalar potential of the MSSM may have local and global minima characterized by non-zero expectation values of charged and colored bosons. Even if the true vacuum is not color and charge conserving, the early Universe is likely to occupy the minimum of the potential in which only the neutral Higgs fields have non-zero vev's. The stability of this false vacuum with respect to quantum tunneling imposes important constraints on the values of the MSSM parameters. We analyze these constraints using some novel methods for calculating the false vacuum decay rate. Some regions of the MSSM parameter space are ruled out because the lifetime of the corresponding physically acceptable false vacuum is small in comparison to the present age of the Universe. However, there is a significant fraction of the parameter space that is consistent with the hypothesis that the Universe rests in the false vacuum that is stable on a cosmological time scale.

Figures (6)

• Figure 1: Region of parameters which can be ruled out by requiring stability of the $SU(2)\times U(1)$ symmetric minimum above the electroweak transition temperature.
• Figure 2: The action of the bounce, $S$, does not depend sensitively on the depth of the CCB minimum, $\Delta V$, except in the "thin-wall" limit (small $\Delta V$).
• Figure 3: The domains of stability (stars) and instability (boxes) of the false SML vacuum with respect to tunneling into the global CCB minimum. Light top squark and large trilinear couplings generally correspond to a lower and thinner barrier and, thus, higher probability of tunneling.
• Figure 4: Each point represents the set of the MSSM parameters for which the global minimum of the potential is color and charge breaking. The stars correspond to the SML false vacua whose lifetime is large compared to the age of the Universe. The boxes indicate those points in the parameter space for which the false SML vacuum should have decayed via quantum tunneling. The dotted line represents the empirical criterion for the absence of the global CCB minima: $A_t^2+3 \mu^2 < 3 M^2$, where $M^2=m_{\tilde{t}_{_L}}^2+m_{\tilde{t}_{_R}}^2$. Taking into account the tunneling rates relaxes this constraint to, roughly, $A_t^2+3 \mu^2 < 7.5 M^2$, shown as the dashed line. The scale is logarithmic.
• Figure 5: Tunneling probability for unphysically large values of $A_t$ and $\mu$. As the CCB minimum moves farther away, it becomes "less dangerous". As before, the stars mark the points with $S>400$, while the boxes depict those with $S<400$.