Angular distribution of the FCNC process $B_c\to D_s^{\ast }(\to D_s\pi ){\ell }^{+}{\ell }^{-}$

Abstract

In this work, we study the flavor-changing neutral-current process $B_c\to D_s^{\ast }(\to D_s\pi ){\ell }^{+}{\ell }^{-}$ ($\ell$= $e$, $\mu$, $\tau$). The relevant weak transition form factors are obtained by using the covariant light-front quark model, in which, the main inputs, i.e., the meson wave functions of $B_c$ and $D_s^{\ast }$, are adopted as the numerical wave functions from the solution of the Schrödinger equation with the modified Godfrey-Isgur model. With the obtained form factors, we further investigate the relevant branching fractions and their ratios, and some angular observables, i.e., the forward-backward asymmetry $A_{FB}$, the polarization fractions $F_{L(T)}$, and the $CP$-averaged angular coefficients $S_i$ and the $CP$ asymmetry coefficients $A_i$. We also present our results of the clean angular observables $P_{1,2,3}$ and $P_{4,5,6,8}^{\prime }$, which can reduce the uncertainties from the form factors. Our results show that the corresponding branching fractions of the electron or muon channels can reach up to $10^{-8}$. With more data being accumulated in the LHCb experiment, our results are helpful for exploring this process, and deepen our understanding of the physics around the $b\to s{\ell }^{+}{\ell }^{-}$ process.

Comments: 25 pages, 8 tables and 9 figures