Model of vector leptoquarks in view of the $B$-physics anomalies

Lepton number as a fourth color is an intriguing theoretical idea which is combined with a possible left-right symmetry within the famous Pati-Salam (PS) model. In the conventional PS model, a spontaneous breaking of the PS gauge group down to the SM, one can only take place at very high scales (above the PeV scale) due to the stringent bounds from $K_L\to \mu e$ and $K\to \pi \mu e$ induced by the resulting vector leptoquarks. In this paper, we show that these constraints can be avoided once additional vectorlike fermions are introduced and, thus, a breaking at the TeV scale is possible. We consider the flavor phenomenology of this model in the context of the intriguing hints for new physics in semileptonic $B$ decays. The necessary violation of lepton flavor universality is induced by mixing SM and vectorlike fermions. Concerning $R(D)$ and $R(D^{*})$, we find that sizable effects are possible while respecting the bounds from other flavor observables but predicting a large enhancement of $B_s\to {\tau }^{+}{\tau }^{-}$. Furthermore, also in $b\to s{\ell }^{+}{\ell }^{-}$ transitions, the observed deviations from the SM predictions [including $R(K)$ and $R(K^{*})$] can be explained with natural values for the free parameters of the model without any fine-tuning, predicting sizable decay rates for $b\to s\tau \mu$. Finally, the anomaly in the anomalous magnetic moment of the muon can be accounted for by a loop contribution involving the vector leptoquark and vectorlike leptons.

Figure 1

Couplings of the gauge bosons to the heavy vectorlike fermions ($L$, $Q$) and light SM-like fermions ($\ell$, $q$). After mixing among SM-like and vectorlike fermions, the couplings to the leptoquark result become flavor nonuniversal, whereas the couplings to the other gauge bosons (in particular the one associated to $B-L$) remain flavor diagonal.

Figure 2

Left: Allowed regions from $R(D^{(*)})$ for $M_{LQ}=2\mathrm{TeV}$ and $s_3^L=1/\sqrt{2}$. Here we used the weighted average for $R(D)$ and $R(D^{*})$. The contour lines denote $\text{Br}(B_s\to {\tau }^{+}{\tau }^{-})\times {10}^4$. Right: Combined results for $R(D^{(*)})$ and $b\to s{\ell }^{+}{\ell }^{-}$, and contours for $[\text{Br}(B\to K{\tau }^{+}{\mu }^{-})+\text{Br}(B\to K{\tau }^{-}{\mu }^{+})]/2$. The red region is preferred by the global fit to $b\to s{\ell }^{+}{\ell }^{-}$ data.