Quantum numbers of the $X(3872)$ state and orbital angular momentum in its $ρ^0 Jψ$ decay

Abstract

Angular correlations in $B^+\to X(3872) K^+$ decays, with $X(3872)\to ρ^0 J/ψ$, $ρ^0\toπ^+π^-$ and $J/ψ\toμ^+μ^-$, are used to measure orbital angular momentum contributions and to determine the $J^{PC}$ value of the $X(3872)$ meson. The data correspond to an integrated luminosity of 3.0 fb$^{-1}$ of proton-proton collisions collected with the LHCb detector. This determination, for the first time performed without assuming a value for the orbital angular momentum, confirms the quantum numbers to be $J^{PC}=1^{++}$. The $X(3872)$ is found to decay predominantly through S wave and an upper limit of $4\%$ at $95\%$ C.L. is set on the fraction of D wave.

16 pages, 4 figures