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arXiv · 2407.15960

The CSS Hamiltonian: high energy evolution of rapidity dependent observables

Haowu Duan·Alex Kovner·Michael Lublinsky
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Abstract

We consider evolution of observables which depend on a small but fixed value of longitudinal momentum fraction $x$, to high rapidity, such that $\eta>\ln 1/x$. 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.

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Haowu Duan, Alex Kovner, Michael Lublinsky. 2024-07-22. The CSS Hamiltonian: high energy evolution of rapidity dependent observables. https://arxiv.org/abs/2407.15960

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