Studying time-like proton form factors using vortex state $p\bar{p}$ annihilation

Vortex states of particles - non-plane-wave solutions of the corresponding wave equation with a helicoidal wave front - open new opportunities for particle physics, unavailable in plane wave scattering. Here we demonstrate that $p\bar{p}$ annihilation with a vortex proton and antiproton provides access to the phase of proton electromagnetic form factors even in unpolarized scattering.