Quantum Interferometry in $\rho^0$ Production in Ultra-Peripheral Heavy Ion Collisions

In $\rho^0$ photoproduction in ultra-peripheral heavy ion collisions, either ion can be the photon emitter or the target. The two possibilities are indistinguishable, and they should be able to interfere, reducing $rho^0$ production at low transverse momentum, $p_T<\hbar/< b>$, where $<b>$ is the median impact parameter. The two $\rho^0$ production points are separated by $<b> \approx 18-46$ fm, while the $\rho^0$ decay before travelling 1 fm. The two decay points are well separated in space-time, so the decays proceed independently and any interference must involve the final state $\pi^+\pi^-$. This requires a non-local wave function.