Study of the $ψ_2(3823)$ and $χ_{c1}(3872)$ states in $B^+ \rightarrow \left( Jψπ^+π^-\right)K^+$ decays

The decays $B^+\rightarrow J/ψπ^+ π^- K^+$ are studied using a data set corresponding to an integrated luminosity of 9fb$^{-1}$ collected with the LHCb detector in proton-proton collisions between 2011 and 2018. Precise measurements of the ratios of branching fractions with the intermediate $ψ_2(3823)$, $χ_{c1}(3872)$ and $ψ(2S)$ states are reported. The decay of $B^+\rightarrow ψ_2(3823)K^+$ with $ψ_2(3823)\rightarrow Jψπ^+π^-$ is observed for the first time with a significance of 5.1 standard deviations. The mass differences between the $ψ_2(3823)$, $χ_{c1}(3872)$ and $ψ(2S)$ states are measured to be $$ \begin{array}{rcl} m_{χ_{c1(3872)}} - m_{ψ_2(3823)} &= & 47.50 \pm 0.53 \pm 0.13\,\mathrm{MeV/}c^2\,, \\ m_{ψ_2(3823)} - m_{ψ(2S)} &= & 137.98 \pm 0.53 \pm 0.14\,\mathrm{MeV/}c^2\,, \\ m_{χ_{c1}(3872)} - m_{ψ(2S)} &= & 185.49 \pm 0.06 \pm 0.03\,\mathrm{MeV/}c^2\,, \end{array} $$ resulting in the most precise determination of the $χ_{c1}(3782)$ mass. The width of the $ψ_2(3823)$ state is found to be below 5.2MeV at 90\% confidence level. The Breit-Wigner width of the $χ_{c1}(3872)$ state is measured to be $$ Γ^{\mathrm{BW}}_{χ_{c1}(3872)} = 0.96^{+0.19}_{-0.18}\pm0.21 \mathrm{MeV},$$ which is inconsistent with zero by 5.5 standard deviations.