Coulomb nuclear interference effect in dipion production in ultraperipheral heavy ion collisions

We study exclusive $\pi^+ \pi^-$ pair production near $\rho^0$ resonance peak in ultraperipheral heavy ion collisions. Pion pair can either be produced via two photon fusion process or from the decay of $\rho^0$ in photon-nuclear reaction. At very low pair transverse momentum, the electromagnetic and nuclear amplitudes become comparable. We show that the Coulomb nuclear interference amplitude gives rise to sizable $\cos \phi$ and $\cos 3\phi$ azimuthal asymmetries, which can be used to constrain the phase of the dipole-nucleus scattering amplitude.