Gluon-gluon elastic scattering amplitude in classical color field of colliding protons

TL;DR

This paper develops a formalism for gluon-gluon elastic scattering in the presence of classical color fields in high-energy proton collisions, modifying the gluon propagator and providing a basis for a model that fits experimental cross section data.

Contribution

It introduces a new formalism for gluon scattering in classical color fields, incorporating the classical Yang-Mills solution and modifying the gluon propagator within the Color Glass Condensate framework.

Findings

Successfully fits $pp$ and $ar{p}p$ cross section data from 5 GeV to 30 TeV.

Predicts a $( ext{ln } s)^2$ growth for cross sections at high energies.

Saturates the Froissart bound at asymptotic energies.

Abstract

We present a formalism for gluon-gluon elastic scattering in the presence of the classical color field of the protons in high energy collision. The classical field is obtained by solving the classical Yang-Mills equation in the covariant gauge and treated as a prescribed background for the quantum gluons involved in the scattering process. The interaction between the classical field and the quantum gluon modifies the gluon propagator, and, in turn, the $gg\rightarrow gg$ amplitude. The modified gluon propagator is derived to the first non-zero order of the classical field using the Gaussian approximation in Color Glass Condensate and shown to satisfy the generalized Slavnov-Taylor identity. This formalism is the theoretical basis for our recently proposed classical color field modified minijet model where we show that the $pp$ and $\pbar p$ cross section data from $\sqrt{s}=5$ GeV to 30 TeV can be satisfactorily fitted and the model predicts a $(\ln s)^2$ behavior for large $s$, which saturates the asymptotic behaviour of Froissart bound.