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., $$B\to(K^{(*)},\phi)+{E\!\!\!/}$$ .