Effects of the transverse coherence length in relativistic collisions

Effects of the quantum interference in collisions of particles have a twofold nature: they arise because of the auto-correlation of a complex scattering amplitude and due to spatial coherence of the incoming wave packets. Both these effects are neglected in a conventional scattering theory dealing with the delocalized plane waves, although they sometimes must be taken into account in particle and atomic physics. Here, we study the role of a transverse coherence length of the packets, putting special emphasis on the case in which one of the particles is twisted, that is, it carries an orbital angular momentum $\ell\hbar$. In $ee, ep$, and $pp$ collisions the interference results in corrections to the plane-wave cross sections, usually negligible at the energies $\sqrt{s} \gg 1$ GeV but noticeable for smaller ones, especially if there is a twisted hadron with $|\ell| > 10^3$ in initial state. Beyond the perturbative QCD, these corrections become only moderately attenuated allowing one to probe a phase of the hadronic amplitude as a function of $s$ and $t$. In this regime, the coherence effects can compete with the loop corrections in QED and facilitate testing the phenomenological models of the strong interaction at intermediate and low energies.