Flavour Anomalies, Light Dark Matter and Rare \(\boldsymbol{B}\) Decays with Missing Energy in \(\boldsymbol{L}_{{\mu}}\boldsymbol{-}\boldsymbol{L}_{{\tau}}\) Model

There are several hints of lepton flavor universality violation (LFUV) observed in recent times in semileptonic B meson decays, which point towards the possible existence of New Physics. In this regard, we consider a new variant of \(U(1)_{L_{\mu}-L_{\tau}}\) gauge extension of the Standard Model, that includes three additional neutral fermions \(N_{e},N_{\mu},N_{\tau}\) , along with a \((\bar{3},1,1/3)\) scalar leptoquark (SLQ) and an inert scalar doublet, to study the phenomenology of light dark matter, neutrino mass and flavor anomalies. The lightest mass eigenstate of the neutral fermions \(N_{\mu},N_{\tau}\) , plays the role of dark matter. The model parameters are constrained by using the LFUV observables \(R_{K^{(*)}}\) and branching fraction of \(b\to s\gamma\) decay processes. We then show the implications of the model on the branching fractions of some rare semileptonic \(B\) decay processes with missing energy, e.g., \(B\to(K^{(*)},\phi)+{E\!\!\!/}\) .