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We report the first measurement of the full angular distribution forinclusive $J/\psi\rightarrow\mu^{+}\mu^{-}$ decays in $p$$+$$p$ collisions at$\sqrt{s}=510$ GeV. The measurements are made for $J/\psi$ transverse momentum$2<p_{T}<10$ GeV/$c$ and rapidity $1.2<y<2.2$ in the Helicity, Collins-Soper,and Gottfried-Jackson reference frames. In all frames the polar coefficient$\lambda_{\theta}$ is strongly negative at low $p_{T}$ and becomes close tozero at high $p_{T}$, while the azimuthal coefficient $\lambda_{\phi}$ is closeto zero at low $p_{T}$, and becomes slightly negative at higher $p_{T}$. Theframe-independent coefficient $\tilde{\lambda}$ is strongly negative at all$p_{T}$ in all frames. The data are compared to the theoretical predictionsprovided by nonrelativistic quantum chromodynamics models.

Angular decay coefficients of $J/\psi$ mesons at forward rapidity from $p+p$ collisions at $\sqrt{s}=510$ GeV