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The first measurement of the polarisation of coherently photoproducedJ/$\psi$ 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 viaits 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 anintegrated luminosity of 750 $\mu{\rm b}^{-1}$ $\pm$ 5% (syst) is analysed.Hadronic activity is highly suppressed since the interaction is mediated by aphoton. The polar and azimuthal angle distributions of the decay muons aremeasured, 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 beconsistent with a transversely polarised J/$\psi$. These values are comparedwith previous measurements by the H1 and ZEUS experiments. The polarisationparameters of coherent J/$\psi$ photoproduction in Pb$-$Pb collisions are foundto be consistent with the $s$-channel helicity conservation hypothesis.

First polarisation measurement of coherently photoproduced J/$\psi$ in ultra-peripheral Pb$-$Pb collisions at $\sqrt{s_{\rm NN}}$ = 5.02 TeV