Investigating the role of new physics in semileptonic \(\varUpsilon (nS) \rightarrow B_c l^-{\bar{\nu }}_{l} \) weak decays

Abstract

Recently, the excess in the measurement of the branching fractions of \({\bar{B}} \rightarrow D^{(*)} \tau ^- {\bar{\nu }}_{\tau }\) and \(B_c \rightarrow J/\varPsi \tau ^-{\bar{\nu }}_{\tau }\) compared to the standard model expectation hints the existence of new physics beyond the standard model. Motivated by these inspiring anomalies, which may imply hints of new physics, as well as abundant \(\varUpsilon (nS)\) data samples, in this work, we perform the analysis of the semileptonic decays \(\varUpsilon (nS) \rightarrow B_c l^- \bar{\nu _{l}}(n=1,2,3)\), which is also induced by \( b \rightarrow c l^- \bar{\nu _{l}}\) transitions at the quark level, both within the standard model and beyond. Starting with the most general effective Hamiltonian relevant for the \(b \rightarrow c l^-\bar{\nu _{l}}\) transition, we report the prediction of standard model for various observables, such as branching ratios, the ratio of branching fractions, the lepton side forward-backward asymmetries, the initial hadron and final lepton longitudinal polarization asymmetries and the convexity parameter, as well as for some new observable that is similar to lepton non-universality, \(R_{B_c}(q^2)\), which is related to the processes \(\varUpsilon (nS) \rightarrow B_c l^- \bar{\nu _{l}}(n=1,2,3)\). These predictions are made using transition form factors which are calculated in the Bauer Stech Wirbel framework. Using previously obtained significant fits of the new physics couplings, predictions for the \(q^2\) dependence of different observable within various new physics scenarios are also presented. Some observable of the decay modes are sizeable and deviate significantly from their corresponding prediction of the standard model, especially in new physics scenarios with \(S_R\) coupling parameter. We hope that the corresponding investigation in this work will be testified by future experiments. Additionally, the study of the meson decays will also enhance the study of b hadron decay processes, as they provide good complementary environment for searching new physics signal.