$B$ Meson Anomalies in a Pati-Salam Model within the Randall-Sundrum Background

Lepton number as a fourth color is the intriguing theoretical idea of the famous Pati-Salam (PS) model. While in conventional PS models, the symmetry breaking scale and the mass of the resulting vector leptoquark are stringently constrained by $K_L\to\mu e$ and $K\to\pi\mu e$, the scale can be lowered to a few TeV by adding vector-like fermions. Furthermore, in this case, the intriguing hints for lepton flavour universality violation in $b\to s\mu^+\mu^-$ and $b\to c\tau\nu$ processes can be addressed. Such a setup is naturally achieved by implementing the PS gauge group in the five-dimensional Randall-Sundrum background. The PS symmetry is broken by boundary conditions on the fifth dimension and the resulting massive vector leptoquark automatically has the same mass scale as the vector-like fermions and all other resonances. We consider the phenomenology of this model in the context of the hints for lepton flavour universality violation in semileptonic $B$ decays. Assuming flavour alignment in the down sector we find that 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. Even though we find sizable effects in $R(D)$, $R(D^*)$ and $R(J/\Psi)$ one cannot account for the current central values in the constrained setup of our minimal model due to the stringent constraints from $D-\bar D$ mixing and $\tau\to 3\mu$.