Exploring dark matter, neutrino mass and $R_{K^{(\ast )},\varphi }$ anomalies in $L_{\mu }-L_{\tau }$ model

We investigate Majorana dark matter in a new variant of $U(1{)}_{L_{\mu }-L_{\tau }}$ gauge extension of Standard Model, where the scalar sector is enriched with an inert doublet and a $(\bar{3},1,1\mathrm{/}3)$ scalar leptoquark. We compute the WIMP-nucleon cross section in leptoquark portal and the relic density mediated by inert doublet components, leptoquark and the new $Z^{\mathrm{\prime }}$ boson. We constrain the parameter space consistent with Planck limit on relic density, PICO-60 and LUX bounds on spin-dependent direct detection cross section. Furthermore, we constrain the new couplings from the present experimental data on $\mathrm{B}\mathrm{r}(\tau \to \mu {\nu }_{\tau }{\bar{\nu }}_{\mu })$, $\mathrm{B}\mathrm{r}(B\to X_s\gamma )$, $\mathrm{B}\mathrm{r}(B^0\to K^0{\mu }^{+}{\mu }^{-})$, ${\rm Br}(B^+ \to K^+ \tau^+ \tau^-)$and$B_s-\bar{B_s}$ mixing, which occur at one-loop level in the presence of $Z^{\mathrm{\prime }}$ and leptoquark. Using the allowed parameter space, we estimate the form factor independent $P_{4,5}^{\mathrm{\prime }}$ observables and the lepton non-universality parameters $R_K$, $R_{K^{\ast }}$ and $R_{\varphi }$. We also briefly discuss about the neutrino mass generation at one-loop level and the viable parameter region to explain current neutrino oscillation data.