The CSS Hamiltonian: high energy evolution of rapidity dependent observables

2024/07/22 by Duan, Haowu, Kovner, Alex, Lublinsky, Michael
#FOS: Physical sciences #High Energy Physics - Phenomenology (hep-ph) #High Energy Physics - Theory (hep-th) #Nuclear Theory (nucl-th)

paper · doi:10.48550/arxiv.2407.15960

Abstract

We consider evolution of observables which depend on a small but fixed value of longitudinal momentum fraction x, to high rapidity, such that η>ln 1/x. We show that this evolution is not given by the JIMWLK (or BK) equation. We derive the evolution Hamiltonian - H_CSS-JIMWLK which generates this evolution in the cases of dilute and dense projectile wave function. The two limits yield identical results for H_CSS-JIMWLK. We show that the resulting evolution for the gluon TMD is identical to the (double logarithmic) perturbative Collins-Soper-Sterman evolution equation in the longitudinal resolution parameter at a fixed and very large transverse resolution.

Related

• Rapidity factorization and evolution of gluon TMDs
• Rapidity evolution of gluon TMD from low to moderate x
• Evolution of the transverse-momentum dependent gluon distribution at small x
• Born-Oppenheimer Renormalization group for High Energy Scattering: CSS, DGLAP and all that
• Reconciling the kinematical constraint with the JIMWLK evolution equation: correlation functions non-local in rapidity