Quantum numbers of the $X(3872)$ state and orbital angular momentum in its ${\rho }^{0}J\psi$ decay

Angular correlations in $B^{+}\to X(3872)K^{+}$ decays, with $X(3872)\to \rho^0 J/\psi$,$\rho^0\to\pi^+\pi^-$and$J/\psi \to\mu^+\mu^-$, 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 $4\mathrm{\%}$ at $95\mathrm{\%}$ C.L. is set on the fraction of D wave.