Exclusive $B_s$ decays to the charmed mesons $D_s^+(1968,2317)$ in the standard model

TL;DR

This paper calculates form factors and branching ratios for $B_s$ decays to specific charmed mesons using light cone sum rules and factorization, providing predictions testable at current colliders.

Contribution

It offers the first detailed analysis of $B_s$ decays to $D_s^+(1968,2317)$ using light cone sum rules combined with heavy quark effective theory.

Findings

Branching ratio of $ar B_s^0 o D_s^+(2317) \mu ar{ u}_\mu$ is about $2.3 imes 10^{-3}$.

Decays to $D_s^+(1968)$ have branching fractions nearly ten times larger than those to $D_s^+(2317)$.

Predictions are consistent across different factorization approaches, supporting the color transparency mechanism.

Abstract

The transition form factors of $\bar B_s^0\to D_{s}^+(2317)$ and $\bar B_s^0\to D_s^+(1968)$ at large recoil region are investigated in the light cone sum rules approach, where the heavy quark effective theory is adopted to describe the form factors at small recoil region. With the form factors obtained, we carry out a detailed analysis on both the semileptonic decays $\bar B_s^0\to D_s^+(1968,2317) l \bar{\nu}_l$ and nonleptonic decays $B_s \to D_s^+(1968,2317) M$ with $M$ being a light meson or a charmed meson under the factorization approach. Our results show that the branching fraction of $\bar B_s^0\to D_s^+(2317) \mu \bar{\nu}_\mu$ is around $2.3 \times 10^{-3}$, which should be detectable with ease at the Tevatron and LHC. It is also found that the branching fractions of $\bar B_s^0\to D_s^+(1968) l \bar{\nu}_l$ are almost one order larger than those of the corresponding $B_s^0\to D_s^+(2317) l \bar{\nu}_l$ decays. The consistency of predictions for $B_s \to D_s^+(1968,2317) L$ ($L$ denotes a light meson) in the factorization assumption and $k_T$ factorization also supports the success of color transparency mechanism in the color allowed decay modes. Most two-charmed meson decays of $B_s$ meson possess quite large branching ratios that are accessible in the experiments. These channels are of great importance to explore the hadronic structure of charmed mesons as well as the nonperturbative dynamics of QCD.