Hadron collisions and the fifth form factor

TL;DR

The paper develops a formalism to resum soft, large-angle gluon radiation in 2→2 hadronic QCD scattering by introducing a cross-channel fifth form factor $F_X(\tau)$ that multiplies the four Sudakov factors associated with the external partons. By decomposing the soft radiation in terms of cross-channel color charges and an $s$-channel color basis, it constructs a soft anomalous dimension ${\cal Q}$ whose eigenvalues dictate the scale-dependent suppression through $F_X(\tau)$. The approach is applied to gluon–gluon scattering, revealing a rich eigenstructure that simplifies in important limits: at 90° scattering, in the $N\to\infty$ limit, and in the Regge limit, where the soft factor reduces to a gluon Regge trajectory. A striking symmetry between internal color degrees of freedom and external kinematic variables is uncovered in the cubic equation for the $N$-dependent energies, hinting at a deeper underlying framework. These results provide a compact, gauge-invariant description of global soft gluon effects in hadron collisions with potential connections to broader theoretical structures.

Abstract

Logarithmically enhanced effects due to radiation of soft gluons at large angles in $2\to 2$ QCD scattering processes are treated in terms of the "fifth form factor" that accompanies the four collinear singular Sudakov form factors attached to incoming and outgoing hard partons. Unexpected symmetry under exchange of internal and external variables of the problem is pointed out for the anomalous dimension that governs soft gluon effects in hard gluon--gluon scattering.