Analysis of $B^0_s\rightarrow \chi_{c1}(3872)\pi^+\pi^-$ decay

Recently, the LHCb collaboration has analyzed the decay of $B_s^0\rightarrow \chi_{c1}(3872)(\rightarrow J/\psi \pi^+ \pi^-) \pi^+ \pi^-$ and reported the ratio of the branching fractions to the $B_s^0\rightarrow \psi(2S)(\rightarrow J/\psi\pi^+\pi^-)\pi^+\pi^-$ decay. The results of this study have measured as a ratio of branching fractions as{\setlength\arraycolsep{.75pt} \begin{eqnarray} \mathcal{R}&=&\frac{\mathcal{B}r(B_s^0\rightarrow\chi_{c1}(3872)\pi^+\pi^-)\times\mathcal{B}r(\chi_{c1}(3872)\rightarrow J/\psi\pi^+\pi^-)}{\mathcal{B}r(B_s^0\rightarrow\psi(2S)\pi^+\pi^-)\times\mathcal{B}r(\psi(2S)\rightarrow J/\psi\pi^+\pi^-)}\nonumber\\&=&(6.8\pm1.1\pm0.2)\times10^{-2},\nonumber \end{eqnarray}} and{\setlength\arraycolsep{.75pt} \begin{eqnarray} \mathcal{B_X}&=&\mathcal{B}r(B_s^0\rightarrow\chi_{c1}(3872)\pi^+\pi^-)\times\mathcal{B}r(\chi_{c1}(3872)\rightarrow J/\psi\pi^+\pi^-)\nonumber\\&=&(1.6\pm0.3\pm0.1\pm0.3)\times10^{-6}.\nonumber \end{eqnarray}} For the first time, we calculated this branching fraction using factorization. According to our calculations, ratio of branching fractions to be $\mathcal{R}=(4.38\pm1.36)\times10^{-2}$ at $\mu=m_b/2$ and the products related to branching fractions have been estimated $\mathcal{B_X}=(1.08\pm0.62)\times10^{-6}$ at $\mu=m_b$. The results are consistent with the experiment reported.