The Color Glass Condensate formalism, Balitsky-JIMWLK evolution and Lipatov's high energy effective action

TL;DR

The paper shows that Lipatov's high-energy effective action can reproduce quark and gluon propagators resumming interactions with a strong reggeized-gluon background, a key feature of CGC approaches. By employing a special parametrization of the gluonic field, it derives these propagators and demonstrates that LO Balitsky-JIMWLK evolution follows from the action, effectively linking high-energy factorization formalisms. It also confirms the reggeized gluon corresponds to the logarithm of an adjoint Wilson line, aligning with Caron-Huot's proposal, and establishes the equivalence of the Lipatov action with CGC in this context, while outlining paths to NLO extensions and central production.

Abstract

We investigate the question whether Lipatov's high energy effective action is capable to reproduce quark and gluon propagators which resum interaction with a strong background field within high energy factorization. Such propagators are frequently employed in calculations within the Color Glass Condensate formalism, in particular when considering scattering of a dilute projectile on a dense target nucleus or nucleon. We find that such propagators can be obtained from the high energy effective action, if a special parametrization of the gluonic field is used, first proposed by Lipatov in the original publication on the high energy effective action. The obtained propagators are used to rederive from the high energy effective action the leading order Balitsky-JIMWLK evolution equation in covariant gauge. As an aside, our result confirms the definition of the reggeized gluon as the logarithm of an adjoint Wilson lines, proposed in the literature.

Figures (4)

• Figure 1: Feynman rules for the lowest-order effective vertices of the effective action. Wavy lines denote reggeized fields and curly lines gluons. Note that in comparison with the Feynman rules used in quarkjetgluonjetHentschinski:2014esatraject we absorbe a factor $1/2$ into the vertices which is compensated by changing the residue of the reggeized gluon propagator from $1/2$ to $2$.
• Figure 2: Feynman rules for the calculation of quadratic fluctuations of the Wilson lines for covariant or $v_-=0$ gauge. Note that the the Wilson-line-gluon vertex (d) conserves momentum as usually, while four momenta are not conserved at the vertices (a) and (c). Momenta which are not fixed by external momenta are understood to be integrated over with the measure $d^4 p/(2 \pi)^4$
• Figure 3: Left: 2 gluon exchange within QCD. Right: The corresponding decomposition within the high energy effective action in symmetric (2 reggeized gluon exchange) and anti-symmetric contribution
• Figure 4: Three gluon exchange within the high energy effective action. Left: The anti-symmetric contribution. Center: The contribution with mixed symmetry. Right: The symmetric contribution.