Higgs sector of the left-right model with explicitCPviolation

Abstract

We explore the Higgs sector of the Minimal Left-Right (LR) Model based on the gauge group $SU(2{)}_{L}\ifmmode\times\else\texttimes\fi{}SU(2{)}_{R}\ifmmode\times\else\texttimes\fi{}U(1{)}_{B\ensuremath{-}L}$ with explicit $CP$ violation in the Higgs potential. Since flavour-changing neutral current experiments and the small scale of neutrino masses both place stringent constraints on the Higgs potential, we seek to determine whether minima of the Higgs potential exist that are consistent with current experimental bounds. We focus on the case in which the right-handed symmetry-breaking scale is only moderately large, of order 15--50 TeV. Unlike the case in which the Higgs potential is $CP$-invariant, the $CP$ noninvariant case does yield viable scenarios, although these require a small amount of fine-tuning. We consider a LR model supplemented by an additional $U(1)$ horizontal symmetry, which results in a Higgs sector consistent with current experimental constraints and a realistic spectrum of neutrino masses.