Investigating the Effect of New Physics on  \(\Upsilon \) and  \(\psi \) Leptonic Decays

The recent measurements on \(R_D\) , \(R_{D^*}\) and \(R_{J/\psi }\) by BaBar, Belle, and LHCb experiments, which deviate substantially from their Standard Model predictions indicate that the notion of lepton flavor universality (LFU) is violated in the weak charged-current processes, originated through \(b \rightarrow c \ell \bar{\nu }_\ell \) transitions. These intriguing results hint towards the possible implication of new physics in \( b \rightarrow c \tau \bar{\nu }\) transition. This, in turn, opens up another avenue, i.e., \( b \bar{b} \rightarrow \tau \bar{\tau }\) processes, to look for new physics, i.e., the new physics contributions to \( b \rightarrow c \tau \bar{\nu }\) process would necessarily modify the \( b \bar{b} \rightarrow \tau \bar{\tau }\) transitions. In this context, we study the implications of LFU violating new physics scenarios of the ratio of branching fractions of leptonic \(\Upsilon \equiv \Upsilon (ns) (n=1,2,3)\) decays, i.e., \( R_{\Upsilon }(ns)= Br(\Upsilon (ns) \rightarrow \tau \bar{\tau })/ Br(\Upsilon (ns) \rightarrow \mu \bar{\mu })\) . We find that \( R_{\Upsilon }(ns)\) values deviate significantly from their standard model predictions due to the impact of new physics.