$B_c^{-}\to J/\psi (\to {\mu }^{+}{\mu }^{-}){\tau }^{-}(\to {\pi }^{-}{\nu }_{\tau },{\rho }^{-}{\nu }_{\tau },{\ell }^{-}{\bar{\nu }}_{\ell }{\nu }_{\tau }){\bar{\nu }}_{\tau }$ decays with visible final-state kinematics

Abstract

The semitauonic $B_c^{-}\to J/\psi {\tau }^{-}{\bar{\nu }}_{\tau }$ decay is optimal to scrutinize possible new physics effects in $b\to c{\tau }^{-}{\bar{\nu }}_{\tau }$ transitions as indicated by the current data on $R(D^{(\ast )})$ anomalies. In this work, we study the $B_c^{-}\to J/\psi {\tau }^{-}{\bar{\nu }}_{\tau }$ decay with both polarized $\tau$ and $J/\psi$. Their subsequent decays, with $J/\psi \to {\mu }^{+}{\mu }^{-}$ as well as ${\tau }^{-}\to {\pi }^{-}{\nu }_{\tau }$, ${\tau }^{-}\to {\rho }^{-}{\nu }_{\tau }$ and ${\tau }^{-}\to {\ell }^{-}{\bar{\nu }}_{\ell }{\nu }_{\tau }$, are exploited to extract the energy and angular distributions of the charged final-state particles in the processes. Starting with the most general effective Hamiltonian relevant for the $b\to c{\tau }^{-}{\bar{\nu }}_{\tau }$ transitions, including all possible Lorentz structures of the dimension-six operators with both left- and right-handed neutrinos, we first derive the five-fold differential decay rate in terms of the visible final-state kinematics. From this distribution, we then construct in total 34 normalized observables, among which nine refer to the CP-violating triple product asymmetries that vanish within the Standard Model. We also construct five new observables based on the combinations of these normalized observables that can only be attributed to the right-handed neutrinos. On the other hand, considering the low statistics of the fully differential distribution, we introduce some integrated observables with only one kinematic variable left, which are more promising to be measured due to the largely increased statistics. The sensitivities of all these observables to the different new physics scenarios are investigated in detail. Finally, assuming an ideal circumstance, we give an estimate of the statistical uncertainties of the nine CP-conserving observables at LHCb and found that ${\tau }^{-}\to {\pi }^{-}{\nu }_{\tau }$ has the highest analyzing power among the three $\tau$ decay channels.

40 pages, 7 figures and 2 tables; SM predictions in different q2 bins added, final version published in the journal

References in corpus (19)

• Physics at Super B Factory
• The lifetime of the $B_c^{-}$ meson and the anomalies in $B\to D^{(\ast )}\tau \nu$
• $SU(2)\times U(1)$ gauge invariance and the shape of new physics in rare $B$ decays
• Study of exclusive semileptonic and nonleptonic decays of $B_c^{-}$ in a nonrelativistic quark model
• Charged-Higgs effects in a new B -> D tau nu differential decay distribution
• New Physics in the Visible Final States of $B\to D^{(\ast )}\tau \nu$
• A model independent spin analysis of fundamental particles using azimuthal asymmetries
• Estimation of Semileptonic Decays of $B_c$ Meson to S-wave Charmonia with NRQCD
• On lepton flavour universality in semileptonic $B_c\to {\eta }_c,J/\psi$ decays
• Measurement of the $D^{\ast -}$ polarization in the decay $B^0\to D^{\ast -}{\tau }^{+}{\nu }_{\tau }$
• Lepton flavor universality violation in semileptonic tree level weak transitions
• CP violation in $B\to D\tau {\nu }_{\tau }$ using multi-pion tau decays
• A Measurable Angular Distribution for $\bar{B}\to D^{\ast }{\tau }^{-}{\bar{\nu }}_{\tau }$ Decays
• QCD corrections to the $B_c$ to charmonia semi-leptonic decays
• The measurable angular distribution of ${\Lambda }_b^0\to {\Lambda }_c^{+}(\to {\Lambda }^0{\pi }^{+}){\tau }^{-}(\to {\pi }^{-}{\nu }_{\tau }){\bar{\nu }}_{\tau }$ decay
• Semileptonic B_{c} to P-Wave Charmonia Transitions within QCD Sum Rules
• Lepton Flavor Universality tests through angular observables of $\overline{B}\to D^{(\ast )}\ell \overline{\nu }$ decay modes
• The role of right-handed neutrinos in $b\to c\tau (\pi {\nu }_{\tau },\rho {\nu }_{\tau },\mu {\bar{\nu }}_{\mu }{\nu }_{\tau }){\bar{\nu }}_{\tau }$ from visible final-state kinematics
• The $B$ Anomalies and non-SMEFT New Physics