New physics in the angular distribution of $B_c^- \to J/ψ(\to μ^+ μ^-)τ^- (\to π^- ν_τ)\barν_τ$ decay
In $B_c^- \to J/ψ(\to μ^+ μ^-)τ^-\barν_τ$ decay, the three-momentum $\boldsymbol{p}_{τ^-}$ cannot be determined accurately due to the decay products of $τ^-$ inevitably include an undetected $ν_τ$. 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 $τ^- \to π^- ν_τ$. The full cascade decay is $B_c^- \to J/ψ(\to μ^+ μ^-)τ^- (\to π^- ν_τ)\barν_τ$, in which the three-momenta $\boldsymbol{p}_{μ^+}$, $\boldsymbol{p}_{μ^-}$, and $\boldsymbol{p}_{π^-}$ 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 $\mathcal{I}_i (q^2, E_π)$. Integrating over the energy of pion $E_π$, we construct twelve normalized angular observables $\widehat{\mathcal{I}}_i(q^2)$ and two lepton-flavor-universality ratios $R(P_{L,T}^{J/ψ})(q^2)$. Based on the $B_c \to J/ψ$ form factors calculated by the latest lattice QCD and sum rule, we predict the $q^2$ distribution of all $\widehat{\mathcal{I}}_i$ and $R(P_{L,T}^{J/ψ})$ 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 $R(P_{L,T}^{J/ψ})$, except $\widehat{\mathcal{I}}_{5}$. The ratios $R(P_{L,T}^{J/ψ})$ 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.