Measurement of elliptic flow of J$\mathrm{/}\psi$ in $\sqrt{s_{{}_{NN}}}=200$ GeV Au$+$Au collisions at forward rapidity

We report the first measurement of the azimuthal anisotropy of J$\mathrm{/}\psi$ at forward rapidity ($1.2<\mathrm{\mid }\eta \mathrm{\mid }<2.2$) in Au$+$Au collisions at $\sqrt{s_{{}_{NN}}}=200$ GeV at the Relativistic Heavy Ion Collider. The data were collected by the PHENIX experiment in 2014 and 2016 with integrated luminosity of 14.5~nb${}^{-1}$. The second Fourier coefficient ($v_2$) of the azimuthal distribution of $J\mathrm{/}\psi$ is determined as a function of the transverse momentum ($p_T$) using the event-plane method. The measurements were performed for several selections of collision centrality: 0%–50%, 10%–60%, and 10%-40%. We find that in all cases the values of $v_2(p_T)$, which quantify the elliptic flow of J$\mathrm{/}\psi$, are consistent with zero. The results are consistent with measurements at midrapidity, indicating no significant elliptic flow of the J$\mathrm{/}\psi$ within the quark-gluon-plasma medium at collision energies of $\sqrt{s_{{}_{NN}}}=200$ GeV.