New physics in the angular distribution of $B_c^- \to J/ψ(\to μ^+ μ^-)τ^- (\to π^- ν_τ)\barν_τ$ decay (2104.04942v2)

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.