Exclusive nonleptonic <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mi>B</mml:mi></mml:mrow><mml:mrow><mml:mi>c</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math>-meson decays to <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>S</mml:mi></mml:math>-wave charmonium states
Lopamudra Nayak, P. C. Dash, Susmita Kar, N. Barik
Abstract
We study the exclusive two-body nonleptonic ${B}_{c}\ensuremath{\rightarrow}{X}_{c\overline{c}}M$ decays, where ${X}_{c\overline{c}}$ is either a ground ($1S$) or a radially excited ($2S$ or $3S$) charmonium, and $M$ is a pseudoscalar ($P$) or a vector ($V$) meson. We consider here three categories of decays: ${B}_{c}\ensuremath{\rightarrow}PP,PV,VP$ decays within the framework of a relativistic independent quark (RIQ) model based on a flavor-independent interaction potential in scalar-vector harmonic form. Using the factorization approximation, we calculate the weak form factors from the overlapping integrals of meson wave functions obtained in the RIQ model and predict the branching fractions for a set of exclusive nonleptonic ${B}_{c}$ decays in reasonable agreement with other model predictions. Some of the decays of interest are found to have branching fractions $\ensuremath{\sim}({10}^{\ensuremath{-}3}\ensuremath{-}{10}^{\ensuremath{-}4})$ within the detection ability of the current experiments and can be precisely measured at LHCb in the near future. In the wake of the recent measurement of ${B}_{c}\ensuremath{\rightarrow}J/\ensuremath{\psi}\ensuremath{\pi}(K)$, ${B}_{c}\ensuremath{\rightarrow}J/\ensuremath{\psi}\ensuremath{\pi}({D}_{s})$, ${B}_{c}\ensuremath{\rightarrow}\ensuremath{\pi}(J/\ensuremath{\psi},\ensuremath{\psi}(2S))$, and ${B}_{c}\ensuremath{\rightarrow}J/\ensuremath{\psi}(\ensuremath{\pi},\ensuremath{\mu}\ensuremath{\nu})$ reported by the LHCb and ATLAS Collaborations, we predict the ratios ${\mathcal{R}}_{K/\ensuremath{\pi}}$, ${\mathcal{R}}_{{D}_{s}/\ensuremath{\pi}}$ and ${\mathcal{R}}_{\ensuremath{\psi}(2S)/J/\ensuremath{\psi}}$ in broad agreement with the data from LHCb and ATLAS Collaborations. Our predicted ratio ${\mathcal{R}}_{\ensuremath{\pi}/\ensuremath{\mu}\ensuremath{\nu}}$ is found to be underestimated. The results indicate that the present approach works well in the description of exclusive nonleptonic ${B}_{c}$ decays within the framework of the RIQ model.