Vacuum structure of the left-right symmetric model

TL;DR

This paper investigates the vacuum structure of the left-right symmetric model, revealing that achieving a desirable charge-conserving and parity-violating ground state is rare and depends on specific parameter choices.

Contribution

It provides an analytical and numerical analysis of the Higgs potential, identifying conditions for successful symmetry breaking in the LRSM.

Findings

Most parameter space does not yield a good vacuum.

Analytical conditions help identify viable parameter regions.

Implications for scalar mass spectra are discussed.

Abstract

The left-right symmetric model (LRSM), originally proposed to explain parity violation in low energy processes, has since emerged as an attractive framework for light neutrino masses via the seesaw mechanism. The scalar sector of the minimal LRSM consists of an $SU(2)$ bi-doublet, as well as left- and right-handed weak isospin triplets, thus making the corresponding vacuum structure much more complicated than that of the Standard Model. In particular, the desired ground state of the Higgs potential should be a charge conserving, and preferably global, minimum with parity violation at low scales. We show that this is not a generic feature of the LRSM potential and happens only for a small fraction of the parameter space of the potential. We also analytically study the potential for some simplified cases and obtain useful conditions (though not necessary) to achieve successful symmetry breaking. We then carry out a detailed statistical analysis of the minima of the Higgs potential using numerical minimization and find that for a large fraction of the parameter space, the potential does not have a good vacuum. Imposing the analytically obtained conditions, we can readily find a small part of the parameter space with good vacua. Consequences for some scalar masses are also discussed.