Analysis of $B_s^0\to {\chi }_{c1}(3872){\pi }^{+}{\pi }^{-}$ decay

Abstract

Recently, the LHCb collaboration has analyzed the decay of $B_s^0\to {\chi }_{c1}(3872)(\to J/\psi {\pi }^{+}{\pi }^{-}){\pi }^{+}{\pi }^{-}$ and reported the ratio of the branching fractions to the $B_s^0\to \psi (2S)(\to J/\psi {\pi }^{+}{\pi }^{-}){\pi }^{+}{\pi }^{-}$ 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 $\mathcal{R}=(4.38\pm 1.36)\times 10^{-2}$ at $\mu =m_b/2$ and the products related to branching fractions have been estimated ${\mathcal{B}}_{\mathcal{X}}=(1.08\pm 0.62)\times 10^{-6}$ at $\mu =m_b$. The results are consistent with the experiment reported.