Exact kinematics in the small x evolution of the color dipole and gluon cascade

TL;DR

This paper investigates the exact kinematic effects in gluon and color dipole cascades at large N_c, deriving recurrence relations, proposing an improved evolution kernel, and analyzing scattering amplitudes with implications for small x physics.

Contribution

It introduces an exact treatment of gluon emission kinematics, derives recurrence relations for gluon wave functions, and proposes a new evolution kernel that incorporates kinematic effects in dipole evolution.

Findings

Derived recurrence relations for gluon wave functions.

Obtained an exact form of multi-gluon wave function when gluon virtuality is neglected.

Proposed an approximate scheme for kinematic effects in the dipole evolution kernel.

Abstract

The problem of kinematic effects in the gluon and color dipole cascades is addressed in the large N_c limit of SU(N_c) Yang--Mills theory. We investigate the tree level multi-gluon components of the gluon light cone wave functions in the light cone gauge keeping the exact kinematics of the gluon emissions. We focus on the components with all helicities identical to the helicity of the incoming gluon. The recurrence relations for the gluon wave functions are derived. In the case when the virtuality of the incoming gluon is neglected the exact form of the multi-gluon wave function is obtained. Furthermore, we propose an approximate scheme to treat the kinematic effects in the color dipole evolution kernel. The new kernel entangles longitudinal and transverse degrees of freedom and leads to a reduced diffusion in the impact parameter. When evaluated in the next-to-leading logarithmic (NLL) accuracy, the kernel reproduces the correct form of the double logarithmic terms of the dipole size ratios present in the exact NLL dipole kernel. Finally, we analyze the scattering of the incoming gluon light cone components off a gluon target and the fragmentation of the scattered state into the final state. The equivalence of the resulting amplitudes and the maximally-helicity-violating amplitudes is demonstrated in the special case when the target gluon is far in rapidity from the evolved gluon wave function.