Probing the phase of the elastic $pp$ scattering amplitude with vortex proton beams

We show that colliding vortex proton beams instead of (approximate) plane waves
can lead to a direct measurement of how the overall phase of the scattering amplitude
changes with the scattering angle.
In elastic $pp$ scattering, this will open a novel way to measure the parameter $\rho(t)$
and probe the real part of the Pomeron.