The decays $B^+rightarrow J/psi pi^+ pi^- K^+$ 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 $psi_2(3823)$, $chi_{c1}(3872)$ and $psi(2S)$ states are reported. The decay of $B^+rightarrow psi_2(3872)K^+$ with $psi_2(3823)rightarrow Jpsipi^+pi^-$ is observed for the first time with a significance of 5.1 standard deviations. The mass differences between the $psi_2(3823)$, $chi_{c1}(3872)$ and $psi(2S)$ states are measured to be $$ begin{array}{rcl} m_{chi_{c1(3872)}} - m_{psi_2(3823)} &= & 47.50 pm 0.53 pm 0.13,mathrm{MeV/}c^2,, m_{psi_2(3823)} - m_{psi(2S)} &= & 137.98 pm 0.53 pm 0.14,mathrm{MeV/}c^2,, m_{chi_{c1}(3872)} - m_{psi(2S)} &= & 185.49 pm 0.06 pm 0.03,mathrm{MeV/}c^2,, end{array} $$ resulting in the most precise determination of the $chi_{c1}(3782)$ mass. The width of the $psi_2(3823)$ state is found to be below 5.2MeV at 90% confidence level. The Breit-Wigner width of the $chi_{c1}(3872)$ state is measured to be $$ Gamma^{mathrm{BW}}_{chi_{c1}(3872)} = 0.96^{+0.19}_{-0.18}pm0.21 mathrm{MeV},$$ which is inconsistent with zero by 5.5 standard deviations.
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