Shape of Proton and the Pion Cloud

TL;DR

This paper investigates the proton shape and the 'break' in diffraction cone behavior observed at different energies, attributing it to two-pion loop contributions and analyzing their impact through a Regge-pole model.

Contribution

It demonstrates that the diffraction cone 'break' results from two-pion loop effects and provides a model to compare the phenomenon across ISR and LHC energies.

Findings

The 'break' is due to two-pion loop contributions affecting both the Regge residue and propagator.

The effect shows universality between ISR and LHC energies.

The balance between proton-pomeron coupling and size expansion explains the 'break'.

Abstract

Proton-proton differential and total cross sections provide information on the energy dependence of proton shape and size. We show that the deviation from exponential behavior of the diffraction cone observed near $t=-0.1$ GeV$^2$, (so-called break), both at the ISR and the LHC follows from the $t$-channel two-pion loop contributions, imposed by unitarity. By using a simple Regge-pole model, we extrapolate the "break" from the ISR energy region to that of the LHC. This allows us to answer two important questions: 1) To what extent is the "break" observed recently at the LHC a "recurrence" of that seen at the ISR (universality)? 2) What is the relative weight of two-pion effect to the vertex coupling (Regge residue) compared to expanding size (pomeron propagator) in producing the "break"? We find that the effect comes both from the Regge residue (proton-pomeron coupling) and from the Regge propagator. A detail analyses of their balance, including the correlation between the relevant parameters is presented.