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#### Vacuum structure of the left-right symmetric model

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##### Citation

Dev, B., Mohapatra, R. N., Rodejohann, W., & Xu, X. (2019). Vacuum structure of
the left-right symmetric model.* Journal of high energy physics: JHEP,* *2019*(02):
154. doi:10.1007/JHEP02(2019)154.

Cite as: https://hdl.handle.net/21.11116/0000-0005-4408-6

##### 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.

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.