6533b7d8fe1ef96bd126ac80

RESEARCH PRODUCT

Towards gauge coupling unification in left-right symmetric SU(3)c×SU(3)L×SU(3)R×U(1)X theories

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We consider the possibility of gauge coupling unification within the simplest realizations of the $\mathrm{SU}(3{)}_{\mathrm{c}}\ifmmode\times\else\texttimes\fi{}\mathrm{SU}(3{)}_{\mathrm{L}}\ifmmode\times\else\texttimes\fi{}\mathrm{SU}(3{)}_{\mathrm{R}}\ifmmode\times\else\texttimes\fi{}\mathrm{U}(1{)}_{\mathrm{X}}$ 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 $\mathrm{SU}(3{)}_{\mathrm{c}}\ifmmode\times\else\texttimes\fi{}\mathrm{SU}(3{)}_{\mathrm{L}}\ifmmode\times\else\texttimes\fi{}\mathrm{SU}(3{)}_{\mathrm{R}}\ifmmode\times\else\texttimes\fi{}\mathrm{U}(1{)}_{\mathrm{X}}$ 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 $\mathrm{SU}(3{)}_{\mathrm{c}}\ifmmode\times\else\texttimes\fi{}\mathrm{SU}(3{)}_{\mathrm{L}}\ifmmode\times\else\texttimes\fi{}\mathrm{SU}(3{)}_{\mathrm{R}}\ifmmode\times\else\texttimes\fi{}\mathrm{U}(1{)}_{\mathrm{X}}$ model as well as possible implications, such as lepton flavor violating physics at the LHC.