Coherent J/$\psi$ photoproduction and polarization in peripheral Pb-Pb collisions with ALICE

Photonuclear reactions are induced by the strong electromagnetic field generated by ultrarelativistic heavy ions. These processes have been extensively studied in ultraperipheral collisions. In recent years, the observation of coherent J/$\psi$ photoproduction has been claimed in nucleus-nucleus (A-A) collisions with nuclear overlap, based on the measurement of an excess in the very low transverse momentum ($p_{\rm T}$) J/$\psi$ yield. Such quarkonium measurements can help constraining the nuclear gluon distribution at low Bjorken-$x$ and can shed light on the theory behind photon induced reactions in A-A collisions with nuclear overlap. In order to confirm the photoproduction origin of the very low-$p_{\rm T}$ J/$\psi$ yield excess, polarization measurement is a golden observable. It is indeed expected that the produced quarkonium would keep the polarization of the incoming photon due to $s$-channel helicity conservation. ALICE can measure inclusive and exclusive quarkonium production down to zero transverse momentum, at forward rapidity (2.5 $< y <$ 4) and midrapidity ($|y| <$ 0.9). In this contribution, we will report on the new preliminary measurement of the $y$-differential cross section and the first polarization analysis at LHC of coherently photoproduced J/$\psi$ in peripheral Pb-Pb collisions. Both measurements are conducted at forward rapidity in the dimuon decay channel.