New physics in the angular distribution of $$ {B}_c^{-} $$ → J/ψ(→ μ+μ−)τ−(→ π−ντ)$$ {\overline{\nu}}_{\tau } $$ decay

Abstract

In $$ {B}_c^{-} $$ B c − → J/ψ(→ μ+μ−)τ−$$ {\overline{\nu}}_{\tau } $$ ν ¯ τ decay, the three-momentum $$ {\boldsymbol{p}}_{\tau^{-}} $$ p τ − cannot be determined accurately due to the decay products of τ− inevitably include an undetected ντ. As a consequence, the angular distribution of this decay cannot be measured. In this work, we construct a measurable angular distribution by considering the subsequent decay τ− → π−ντ. The full cascade decay is $$ {B}_c^{-} $$ B c − → J/ψ(→ μ+μ−)τ−(→ π−ντ)$$ {\overline{\nu}}_{\tau } $$ ν ¯ τ , in which the three-momenta $$ {\boldsymbol{p}}_{\mu^{+}},{\boldsymbol{p}}_{\mu^{-}} $$ p μ + , p μ − , and $$ {\boldsymbol{p}}_{\pi^{-}} $$ 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 ℐi(q2, Eπ). Integrating over the energy of pion Eπ, we construct twelve normalized angular observables $$ {\hat{\mathrm{\mathcal{I}}}}_i $$ ℐ ̂ i (q2) and two lepton-flavor-universality ratios $$ R\left({P}_{L,T}^{J/\psi}\right) $$ R P L , T J / ψ (q2). Based on the Bc → J/ψ form factors calculated by the latest lattice QCD and sum rule, we predict the q2 distribution of all $$ {\hat{\mathrm{\mathcal{I}}}}_i $$ ℐ ̂ i and $$ R\left({P}_{L,T}^{J/\psi}\right) $$ 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 ℐi and $$ R\left({P}_{L,T}^{J/\psi}\right) $$ R P L , T J / ψ , except $$ {\hat{\mathrm{\mathcal{I}}}}_5 $$ ℐ ̂ 5 . The ratios $$ R\left({P}_{L,T}^{J/\psi}\right) $$ R P L , T J / ψ are more sensitive to the NP with pseudo-scalar operators than the ℐi. Finally, we discuss the symmetries in the angular observables and present a model-independent method to determine the existence of tensor operators.