Recently, the LHCb collaboration has analyzed first observation of the \(B_s^0\rightarrow (\chi _{c1}(3872)\rightarrow J/\psi \pi ^+\pi ^-)\pi ^+\pi ^-\) decay. The ratio of branching fractions relative to the \(B_s^0\rightarrow (\psi (2\,S)\rightarrow J/\psi \pi ^+\pi ^-)\pi ^+\pi ^-\) decay is measured to be \(\begin{aligned} \mathcal {R}= & \frac{\mathcal {B}r(B_s^0\rightarrow \chi _{c1}(3872)\pi ^+\pi ^-)\times \mathcal {B}r(\chi _{c1}(3872)\rightarrow J/\psi \pi ^+\pi ^-)}{ \mathcal {B}r(B_s^0\rightarrow \psi (2S)\pi ^+\pi ^-)\times \mathcal {B}r(\psi (2S)\rightarrow J/\psi \pi ^+\pi ^-)}\\= & (6.8\pm 1.1\pm 0.2)\times 10^{-2}. \end{aligned}\) They also measured the product of the branching fraction for the \(B_s^0\rightarrow (\chi _{c1}(3872)\rightarrow J/\psi \pi ^+\pi ^-)\pi ^+\pi ^-\) decay as \(\begin{aligned} \mathcal {B_X}= & \mathcal {B}r(B_s^0\rightarrow \chi _{c1}(3872)\pi ^+\pi ^-)\times \mathcal {B}r(\chi _{c1}(3872)\rightarrow J/\psi \pi ^+\pi ^-)\\= & (1.6\pm 0.3\pm 0.1\pm 0.3)\times 10^{-6}. \end{aligned}\) For the first time, we have estimated the theoretical calculation of the ratio of branching fractions and products related to branching fractions using factorization with values of \(\mathcal {R}=(6.80\pm 2.40)\times 10^{-2}\) and \(\mathcal {B_X}=(1.43\pm 0.25)\times 10^{-6}\) at \(\mu =m_b\) . The results are consistent with the reported experiment.
