Lipatov's QCD high energy effective action: past and future

Abstract

In this contribution we briefly review some aspects of Lipatov's gauge invariant QCD high energy effective action. The high energy effective provides a field theory framework to systematically factorize QCD scattering amplitudes and related theories in the limit of high center of mass energies. After a short review of the underlying concepts, we address the question how the high energy effective action can be used for actual calculations. As an explicit example we review the derivation of the gluon Regge trajectory up to 2 loop. We then review two topics of current interest: automatic amplitude generation of high energy effective action amplitudes and a discussion of the relation between the so-called Color-Glass-Condensate framework and the high energy effective action.

Dijet impact factor in DIS at next-to-leading order in the Color Glass Condensate

“…Even though the wrong lightcone gauge, in contrast to the lightcone gauge A + cl = 0, does not provide a simple partonic interpretation of the target wavefunction, it simplifies tremendously the form of the propagators inside the background field for a fast moving projectile in the "minus" lightcone direction. These propagators were computed previously in [9,15,[60][61][62][63]; the corresponding effective quark and gluon propagators are identical [64,65] to the quark-quark-reggeon and gluon-gluon-reggeon propagators in Lipatov's reggeon effective field theory [66,67].…”

Transverse Momentum Dependent Gluon Distribution within High Energy Factorization at Next-to-Leading Order

“…As for the real part of the 1-loop BFKL kernel within the high energy effective action, see [34,36,41] for an explicit construction, the above expression is proportional to an integral which extends over the entire range of rapidity. In contrast to the derivation of the BFKL kernel, the above integral is now being divided into a 'soft' and a 'hard' part,…”

“…For a more in depth discussion of the effective action we refer to the reviews [40,41]. Due to the induced term in Eq.…”

“…The parameters η a,b as well as the function f are at first arbitrary; the former define through the combination η a −η b the evolution parameter of the 2 reggeized gluon Green's function G R , see also the related discussion in [41,50]. As usually, it is necessary to chose these parameters such that the next-to-leading order corrections to impact factors are under perturbative control and that large logarithms in the center of mass energy are resumed through the 2 reggeized gluon Green's function.…”

“…While a related study has been already presented in [18] within the Color-Glass-Condensate approach, we will investigate this problem within the context of Lipatov's high energy effective action [32,33]. Starting with [34][35][36][37][38] the systematic determination of perturbative higher order corrections has been worked out for this framework, while in [39] equivalence with the Color-Glass-Condensate formalism has been demonstrated, including an re-derivation of the Balitsky-JIMWLK evolution, see also [40,41] for reviews; for further recent studies based on this framework see also [42][43][44][45][46][47][48][49]. In [50] a systematic framework for the determination of next-to-leading order corrections at cross-section level has been worked out.…”