Measurement of the impact-parameter dependent azimuthal anisotropy in coherent $\rho^0$ photoproduction in Pb$-$Pb collisions at $\sqrt{s_{\rm NN}}$ = 5.02 TeV

The first measurement of the impact-parameter dependent angular anisotropy in the decay of coherently photoproduced $\rho^0$ mesons is presented. The $\rho^0$ mesons are reconstructed through their decay into a pion pair. The measured anisotropy corresponds to the amplitude of the $\cos(2\phi)$ modulation, where $\phi$ is the angle between the two vectors formed by the sum and the difference of the transverse momenta of the pions, respectively. The measurement was performed by the ALICE Collaboration at the LHC using data from ultraperipheral Pb$-$Pb collisions at a center-of-mass energy of $\sqrt{s_{\mathrm{NN}}}~=~5.02$ TeV per nucleon pair. Different impact-parameter regions are selected by classifying the events in nuclear-breakup classes. The amplitude of the $\cos(2\phi)$ modulation is found to increase by about one order of magnitude from large to small impact parameters. Theoretical calculations, which describe the measurement, explain the $\cos(2\phi)$ anisotropy as the result of a quantum interference effect at the femtometer scale that arises from the ambiguity as to which of the nuclei is the source of the photon in the interaction.