Contributions of $\psi_{2}(3823)$ and $\psi(4040)$ charmonium in $B^+\rightarrow J/\psi\eta K^+$ decay

TL;DR

This paper reports on the measurement of branching fractions and ratios involving the $ ext{ extpsi}_2(3823)$ and $ ext{ extpsi}(4040)$ charmonium states in $B^+ ightarrow J/\psi\eta K^+$ decays, including first-time calculations using factorization.

Contribution

The study provides the first calculation of these branching fractions using factorization and offers updated measurements of the ratios and products related to these charmonium states.

Findings

Measured ratios $F_{X}$ for $ ext{ extpsi}_2(3823)$ and $ ext{ extpsi}(4040)$.

Reported branching fractions $B_{X}$ for both states.

Estimated new values of $B_{ extpsi_{2}(3823)}$ and $B_{ extpsi(4040)}$ at different scales.

Abstract

Recently, a study on the $J/\psi\eta$ mass spectrum from $B^+\rightarrow J/\psi\eta K^+$ decays was reported by the LHCb detector. The results of this study are reported as a ratio of branching fractions as $F_{X}\equiv\frac{\mathcal{B}r(B^+\rightarrow XK^+)\times\mathcal{B}r(X\rightarrow J/\psi\eta)}{\mathcal{B}r(B^+\rightarrow \psi(2S) K^+)\times\mathcal{B}r(\psi(2S)\rightarrow J/\psi\eta)}$ for $X=\psi_2(3823),\psi(4040)$, which are $(5.95^{+3.38}_{-2.55})\times10^{-2}$ and $(40.60\pm11.20)\times10^{-2}$, respectively. Also, the products related to $B_{X}\equiv\mathcal{B}r(B^+\rightarrow XK^+)\times\mathcal{B}r(X\rightarrow J/\psi\eta)$ branching fractions are $B_{\psi_2(3823)}=(1.25^{+0.71}_{-0.53}\pm0.04)\times10^{-6}$ and $B_{\psi(4040)}=(8.53\pm2.35\pm0.30)\times10^{-6}$. For the first time, we calculated this branching fraction using factorization. According to our calculations, $F_X$ to be $F_{\psi_{2}(3823)}=(6.55\pm1.88)\times10^{-2}$ and $F_{\psi(4040)}=(14.33\pm4.15)\times10^{-2}$ at $\mu=m_b/2$. We have estimated $B_{\psi_{2}(3823)}=(0.26\pm0.05)\times10^{-6}$ at $\mu=m_b/2$ and $B_{\psi(4040)}=(2.88\pm0.64)\times10^{-6}$ at $\mu=2m_b$.