Lepton flavor universality and CP violation in an S3 leptoquark model

Abstract

We introduce the $CP$ violating scalar leptoquark ${S}_{3}$ to explain the measured values of the lepton universality ratios ${R}_{{K}^{(*)}}$. We derive constraints on the $CP$-even and $CP$-odd components of the leptoquark Yukawa couplings stemming from effects in $b\ensuremath{\rightarrow}s\ensuremath{\mu}\ensuremath{\mu}$ and ${B}_{s}$ mixing. For the $b\ensuremath{\rightarrow}s\ensuremath{\mu}\ensuremath{\mu}$ processes we impose ${R}_{{K}^{(*)}}$, $\mathcal{B}({B}_{s}\ensuremath{\rightarrow}{\ensuremath{\mu}}^{+}{\ensuremath{\mu}}^{\ensuremath{-}})$, as well as $CP$-sensitive angular asymmetries ${A}_{7,8,9}$, whereas in the ${B}_{s}$ mixing sector $\mathrm{\ensuremath{\Delta}}{M}_{s}$ and ${S}_{\ensuremath{\psi}\ensuremath{\phi}}$ are considered. Combining the constraints within the ${S}_{3}$ model reveals that a large $CP$ phase with a definite sign is perfectly viable for a leptoquark of mass below a few TeV. For larger mass of the ${S}_{3}$ leptoquark the $CP$ phase is suppressed due to the observables pertaining to the ${B}_{s}$ system. We provide predictions of direct and mixing-induced $CP$ asymmetries in $B\ensuremath{\rightarrow}K\ensuremath{\mu}\ensuremath{\mu}$ that could reveal the presence of the novel $CP$ phase.