Final State Interaction Analysis and Branching Fraction Calculations of $\varvec{B^+_c\rightarrow D^+{\bar{D}}^0(D^+D^0)}$ Decays

Abstract

The LHC experiments have been measured the branching fractions for $B^+_c$ decays to two pseudoscalar charm mesons by multiplying the production rates for $B^+_c$ relative to $B^+_u$ mesons (in units of $10^{-6}$):

$$\begin{aligned} (f_c/f_u){\mathcal {B}}(B^+_c\rightarrow D^+{\bar{D}}^0)_{EXP}=3.04\pm 2.87,\quad (f_c/f_u){\mathcal {B}}(B^+_c\rightarrow D^+D^0)_{EXP}=1.10\pm 2.02. \end{aligned}$$

We have calculated the branching fractions of these decay modes by using the QCD factorization (QCDF) approach and obtained; ${\mathcal {B}}(B^+_c \rightarrow D^+{\bar{D}}^0)_{QCDF}=(0.28\pm 0.08)\times 10^{-4}$ and ${\mathcal {B}}(B^+_c \rightarrow D^+D^0)_{QCDF}=(0.60\pm 0.17)\times 10^{-6}$. Consider to upper limit of production ratio ($f_c/f_u=0.012$), the QCDF results are 10 and $10^2$ times smaller than experimental results, respectively. The effects of the final state interaction (FSI) have compensated for the smallness of the theoretical results. After entering the effects of FSI, acceptable results have been obtained (in units of $10^{-6}$):

$$\begin{aligned} (f_c/f_u){\mathcal {B}}(B^+_c\rightarrow D^+{\bar{D}}^0)_{FSI}=3.08\pm 0.32,\quad (f_c/f_u){\mathcal {B}}(B^+_c\rightarrow D^+D^0)_{FSI}=0.62\pm 0.07. \end{aligned}$$