Collinear Singularities and Running Coupling Corrections to Gluon Production in CGC

Abstract

We analyze the structure of running coupling corrections to the gluon production cross section in the projectile-nucleus collisions calculated in the Color Glass Condensate (CGC) framework. We argue that for the gluon production cross section (and for gluon transverse momentum spectra and multiplicity) the inclusion of running coupling corrections brings in collinear singularities due to final state splittings completely unaffected by CGC resummations. Hence, despite the saturation/CGC dynamics, the gluon production cross section is not infrared-safe. As usual, regularizing the singularities requires an infrared cutoff Lambda_coll that defines a resolution scale for gluons. We specifically show that the cutoff enters the gluon production cross section in the argument of the strong coupling constant alpha_s(Lambda_coll^2). We argue that for hadron production calculations one should be able to absorb the collinear divergence into a fragmentation function. The singular collinear terms in the gluon production cross section are shown not to contribute to the energy density of the produced matter, which is indeed an infrared-finite quantity.

35 pages, 16 figures; v2: minor corrections, references and figures added

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• Decoherence and Entropy Production in Relativistic Nuclear Collisions
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• Time-Dependent Observables in Heavy Ion Collisions I: Setting up the Formalism
• Thermal radiation and inclusive production in the running coupling $k_T$ -- factorization approach
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• Properties of inclusive hadron production in Deep Inelastic Scattering on heavy nuclei at low x
• Universality aspects of quantum corrections to transverse momentum broadening in QCD media