Bethe phase including proton excitations

TL;DR

This paper assesses the impact of proton excitations on the phase difference in high-energy proton-proton scattering, finding the effect negligible for current experimental precision.

Contribution

It provides a quantitative evaluation of inelastic intermediate states' contribution to the scattering phase, showing it is minimal.

Findings

Inelastic proton excitations have a negligible effect on the scattering phase.

The contribution is much smaller than experimental uncertainties in measuring .

The phase correction due to multiphoton diagrams is insignificant.

Abstract

We evaluate the contribution of inelastic intermediate states (such as $p\to N^*$ excitations) to the phase between the one-photon-exchange and the `nuclear' high energy $pp$ scattering amplitudes as $t\to 0$, caused by multiphoton diagrams. It turns out to be rather small - much smaller than to have any influence on the experimental accuracy of the measurements of $\rho$, defined to be the ratio of the real to imaginary parts of the forward `nuclear' amplitude.