Towards gauge coupling unification in left-right symmetric $\mathrm{SU}(3{)}_{\mathrm{c}}\times \mathrm{SU}(3{)}_{\mathrm{L}}\times \mathrm{SU}(3{)}_{\mathrm{R}}\times \mathrm{U}(1{)}_{\mathrm{X}}$ theories

Abstract

We consider the possibility of gauge coupling unification within the simplest realizations of the $\mathrm{SU}(3{)}_{\mathrm{c}}\times \mathrm{SU}(3{)}_{\mathrm{L}}\times \mathrm{SU}(3{)}_{\mathrm{R}}\times \mathrm{U}(1{)}_{\mathrm{X}}$ gauge theory. We present a first exploration of the renormalization group equations governing the "bottom-up" evolution of the gauge couplings in a generic model with free normalization for the generators. Interestingly, we find that for a $\mathrm{SU}(3{)}_{\mathrm{c}}\times \mathrm{SU}(3{)}_{\mathrm{L}}\times \mathrm{SU}(3{)}_{\mathrm{R}}\times \mathrm{U}(1{)}_{\mathrm{X}}$ symmetry breaking scale $M_X$ as low as a few TeV one can achieve unification in the presence of leptonic octets. We briefly comment on possible grand unified theory frameworks which can embed the $\mathrm{SU}(3{)}_{\mathrm{c}}\times \mathrm{SU}(3{)}_{\mathrm{L}}\times \mathrm{SU}(3{)}_{\mathrm{R}}\times \mathrm{U}(1{)}_{\mathrm{X}}$ model as well as possible implications, such as lepton flavour violating physics at the LHC.

Comments: 15 pages, 3 figures