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The CSS Hamiltonian: high energy evolution of rapidity dependent observables
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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.
Forward citations
Cited by 2 Pith papers
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Running coupling effects in the anti-collinear resummation in high energy evolution
Running coupling plus anti-collinear resummation in BFKL/JIMWLK slows evolution and cuts the anti-collinear Pomeron intercept, while χ(γ=1) is protected by a cancellation between kernel and DGLAP running.
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One-loop renormalization of quark TMD in the light-cone gauge: CSS evolution
One-loop renormalization of the quark TMD in the target light-cone gauge with the Mandelstam-Leibbrandt prescription reproduces the CSS evolution equations, with the double log traced to the ML zero-mode in diagrams e...
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