Investigating $ Υ(ns) \to τ^+ τ^- $ decay in the Leptoquark scenario

Abstract: Several measurements on $R_D, R_{D^*}$, and $R_{J/ \psi}$ by the BaBar, Belle, and LHCb experiments show significant deviations from their Standard Model (SM) predictions, which illustrate the fact that the concept of lepton flavor universality (LFU) is violated in semileptonic $B$ meson as well as leptonic $\Upsilon(ns)(n=1,2,3)$ decays. Recently BaBar experiment announced that at $1.8\sigma$ level, $R_\Upsilon(3s)= {\rm Br}(\Upsilon(3s) \to \tau \bar{\tau})/{\rm Br}(\Upsilon(3s) \to \mu \bar{\mu})$ shows an acceptance with the SM. These fascinating findings point towards the possible implication of new physics in the $b \to c \tau \bar{\nu}$ transitions, which in turn, creates a new direction to look for new physics in $b \bar{b} \to \tau \bar{\tau} $ process. Thereby, the new physics contributions to the $b \to c \tau \bar{\nu}$ process would inevitably alter the $b \bar{b} \to \tau \bar{\tau} $ transitions. Here we conduct a $\chi^{2}$ fit to constraining the new parameters by using the measured values of $ R_D$, $R{D*}$, $ R{J/ \psi}$, $ R_{X_C}$, $F_L (D^*)$ and $P_{\tau} (D^*)$. In this context, we investigate the effect of constrained new physics couplings on the branching ratios and LFU parameters $R_{\Upsilon(ns)}$ through leptoquark models such as $S_3, \tilde{S_1}, \tilde{R_2}, U_1, U_3 $ and $ V_2$.