New physics in the angular distribution of $B_c^- \to J/\psi (\to \mu^+ \mu^-)\tau^- (\to \pi^- \nu_\tau)\bar{\nu}_\tau$ decay

TL;DR

This paper develops a measurable angular distribution for the decay $B_c^- o J/\psi au^- ar{ u}_ au$ by analyzing the cascade decay involving $ au^-$ decay products, enabling tests of new physics effects.

Contribution

It constructs a full angular analysis framework for the cascade decay, including twelve angular observables and ratios, incorporating new physics effects and providing predictions based on lattice QCD form factors.

Findings

Tensor operator benchmark significantly affects angular observables.

Lepton-flavor ratios are more sensitive to pseudo-scalar operators.

Predictions align with Standard Model and eight new physics scenarios.

Abstract

In $B_c^- \to J/\psi (\to \mu^+ \mu^-)\tau^-\bar{\nu}_\tau$ decay, the three-momentum $\boldsymbol{p}_{\tau^-}$ cannot be determined accurately due to the decay products of $\tau^-$ inevitably include an undetected $\nu_{\tau}$. As a consequence, the angular distribution of this decay cannot be measured. In this work, we construct a {\it measurable} angular distribution by considering the subsequent decay $\tau^- \to \pi^- \nu_\tau$. The full cascade decay is $B_c^- \to J/\psi (\to \mu^+ \mu^-)\tau^- (\to \pi^- \nu_\tau)\bar{\nu}_\tau$, in which the three-momenta $\boldsymbol{p}_{\mu^+}$, $\boldsymbol{p}_{\mu^-}$, and $\boldsymbol{p}_{\pi^-}$ can be measured. The five-fold differential angular distribution containing all Lorentz structures of the new physics (NP) effective operators can be written in terms of twelve angular observables $\mathcal{I}_i (q^2, E_\pi)$. Integrating over the energy of pion $E_\pi$, we construct twelve normalized angular observables $\widehat{\mathcal{I}}_i(q^2)$ and two lepton-flavor-universality ratios $R(P_{L,T}^{J/\psi})(q^2)$. Based on the $B_c \to J/\psi$ form factors calculated by the latest lattice QCD and sum rule, we predict the $q^2$ distribution of all $\widehat{\mathcal{I}}_i$ and $R(P_{L,T}^{J/\psi})$ both within the Standard Model and in eight NP benchmark points. We find that the benchmark BP2 (corresponding to the hypothesis of tensor operator) has the greatest effect on all $\widehat{\mathcal{I}}_{i}$ and $R(P_{L,T}^{J/\psi})$, except $\widehat{\mathcal{I}}_{5}$. The ratios $R(P_{L,T}^{J/\psi})$ are more sensitive to the NP with pseudo-scalar operators than the $\widehat{\mathcal{I}}_{i}$. Finally, we discuss the symmetries in the angular observables and present a model-independent method to determine the existence of tensor operators.