Study of exclusive decays of \texorpdfstring{$B_s \to \psi(1S,2S) K_s$}{Lg} and \texorpdfstring{$B_s \to \eta_c(1S,2S) K_s$}{Lg}

TL;DR

This paper predicts branching fractions for specific $B_s$ meson decays involving charmonium states and a $K_s$ meson using a relativistic quark model, aligning well with existing experimental data.

Contribution

It introduces a novel calculation of weak form factors and decay rates for $B_s$ decays within the relativistic independent quark model, including excited states.

Findings

Predicted branching fractions agree with LHCb data.

Decay $B_s o J/A \,K_s$ matches experimental measurements.

Ratios of branching fractions are consistent with observations.

Abstract

We analyze the exclusive two-body nonleptonic decays of $B_s$ meson to ground as well as radially excited $2S$ charmonium state with a light meson $K_s$, induced by the $b\to c\bar{c}d$ transition. Within the framework of relativistic independent quark (RIQ) model based on a flavor-independent interaction potential in scalar-vector harmonic form, we calculate the weak form factors from the overlapping integrals of meson wave function obtained in this model. Using the factorization approximation, we predict the branching fractions for the $B_s \to \psi(1S,2S) K_s$ and $B_s \to \eta_c(1S,2S) K_s$, which can be compared with future theoretical predictions. Branching fraction for $B_s\to J/\psi K_s$ decay is found to be in good agreement with the data from LHCb Collaboration, whereas for $B_s\to \psi(2S) K_s$, it is found to be within the detection ability of the CMS Collaboration. We also predict the ratios of branching fractions $(\cal{R})$, which are in broad agreement with the data from LHCb Collaboration. These results indicate that the present approach works well in the description of exclusive nonleptonic $B_s$ decays within the framework of the RIQ model.