  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$.
