The first measurement of the polarisation of coherently photoproduced J/$\psi$ mesons in ultra-peripheral Pb$-$Pb collisions, using data at $\sqrt{s_{\rm NN}}=5.02$ TeV, is presented. The J/$\psi$ meson is measured via its dimuon decay channel in the forward rapidity interval $-4.0 < y < -2.5$ using the ALICE detector at the CERN LHC. An event sample corresponding to an integrated luminosity of 750 $\mu{\rm b}^{-1}$$\pm$ 5% (syst) is analysed. Hadronic activity is highly suppressed since the interaction is mediated by a photon. The polar and azimuthal angle distributions of the decay muons are measured, and the polarisation parameters $\mathbf{\lambda_{\theta}}$, $\mathbf{\lambda_{\varphi}}$, $\mathbf{\lambda_{\theta\varphi}}$ are extracted. The analysis is carried out in the helicity frame. The results are found to be consistent with a transversely polarised J/$\psi$. These values are compared with previous measurements by the H1 and ZEUS experiments. The polarisation parameters of coherent J/$\psi$ photoproduction in Pb$-$Pb collisions are found to be consistent with the $s$-channel helicity conservation hypothesis.
Measured polarisation parameter in the lambda formalism for coherent J/psi in the helicity frame. The central values are given with statistical and total systematic uncertainties.
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