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

Angular correlations in $B^+to X(3872) K^+$ decays, with $X(3872)to rho^0 J/psi$, $rho^0topi^+pi^-$ and $J/psi tomu^+mu^-$, 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.