Quantum structure of the non-Abelian Weizsacker-Williams field for a very large nucleus

TL;DR

Problem: small-x gluon distributions in very large nuclei within the MV model. Approach: map the classical non-Abelian Weizsäcker-Williams field to a set of light-cone gauge Feynman diagrams and analyze its quantum structure order by order, using Ward identities and color averaging. Findings: the classical field reproduces the field up to order g^5, but higher orders (g^7 and beyond) require quantum corrections, diagnosing a limit of two gluons per nucleon. Implications: for nucleus-onium scattering at higher orders, the dominant diagrams are classical, enabling practical calculations of charm production and dijet production in heavy-ion collisions, and clarifying the regime where a semiclassical description is valid.

Abstract

We consider the McLerran-Venugopalan model for calculation of the small-$x$ part of the gluon distribution function for a very large ultrarelativistic nucleus at weak coupling. We construct the Feynman diagrams which correspond to the classical Weizsäcker-Williams field found previously [Yu. V. Kovchegov, Phys. Rev. D 54, 5463 (1996)] as a solution of the classical equations of motion for the gluon field in the light-cone gauge. Analyzing these diagrams we obtain a limit for the McLerran-Venugopalan model. We show that as long as this limit is not violated a classical field can be used for calculation of scattering amplitudes.

Figures (9)

• Figure 1: Gluon propagator in the light-cone gauge (see text).
• Figure 2: Diagram giving the classical field in the light-cone gauge at lowest order.
• Figure 3: Diagrams giving the classical field in the light-cone gauge at order $g^3$. The intersection of two gluon lines in C is not a vertex.
• Figure 4: Application of the Ward identity at order $g^3$.
• Figure 5: The diagrams at order $g^5$.