Explaining the hints for lepton flavour universality violation with three $S_2$ leptoquark generations

Abstract

Leptoquarks are prime candidates for explaining the intriguing hints for lepton flavour universality violation. In particular, the $SU(2{)}_L$ doublet of scalar leptoquarks $S_2$ is capable of providing an explanation for the tensions between the measurements and the Standard Model predictions in $(g-2{)}_{\mu }$, $b\to s{\ell }^{+}{\ell }^{-}$ and $b\to c\tau \nu$ processes, as well as in non-resonant di-electron production. However, in the minimal setup with a single leptoquark generation, a common explanation for all these issues is not possible as this would lead to unacceptably large charged lepton flavour violation. We therefore propose a model with three generations of $S_2$, each coupling exclusively to a single lepton flavour, \textit{i.e.}~a model extending the Standard Model particle content by an electroquark, a muoquark and a tauquark. We show that after taking into account other constraints, such as those originating from electroweak precision observables and $\Delta F=2$ processes, it is possible to provide a combined explanation for all these hints of lepton flavour universality violation. Moreover, we find that the presence of the tauquark can generate a dimension-six ${\mathcal{O}}_9^U$ operator via off-shell photon penguin diagrams, which, together with the muoquark contribution, further improves the global fit to $b\to s{\ell }^{+}{\ell }^{-}$ data.

48 pages, 11 figures

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