Left-right symmetry, orbifold $S^1/Z_2$, and radiative breaking of $U(1{)}_{\mathrm{R}}\times U(1{)}_{\mathrm{B}-\mathrm{L}}$

Abstract

We study the origin of electroweak symmetry under the assumption that $SU(4{)}_{\mathrm{C}}\times SU(2{)}_{\mathrm{L}}\times SU(2{)}_{\mathrm{R}}$ is realized on a five-dimensional space-time. The Pati-Salam type gauge symmetry is reduced to $SU(3{)}_{\mathrm{C}}\times SU(2{)}_{\mathrm{L}}\times U(1{)}_{\mathrm{R}}\times U(1{)}_{\mathrm{B}-\mathrm{L}}$ by orbifold breaking mechanism on the orbifold $S^1/Z_2$. The breakdown of residual gauge symmetries occurs radiatively via the Coleman-Weinberg mechanism, such that the $U(1{)}_{\mathrm{R}}\times U(1{)}_{\mathrm{B}-\mathrm{L}}$ symmetry is broken down to $U(1{)}_{\mathrm{Y}}$ by the vacuum expectation value of an $SU(2{)}_{\mathrm{L}}$ singlet scalar field and the $SU(2{)}_{\mathrm{L}}\times U(1{)}_{\mathrm{Y}}$ symmetry is broken down to the electric one $U(1{)}_{\mathrm{EM}}$ by the vacuum expectation value of an $SU(2{)}_{\mathrm{L}}$ doublet scalar field regarded as the Higgs doublet. The negative Higgs squared mass term is originated from an interaction between the Higgs doublet and an $SU(2{)}_{\mathrm{L}}$ singlet scalar field as a Higgs portal. The vacuum stability is recovered due to the contributions from Kaluza-Klein modes of gauge bosons.

Comments: 17 pages, 3 figures, Reference added