Gluon Regge trajectory at two loops from Lipatovʼs high energy effective action

Abstract

We present the derivation of the two-loop gluon Regge trajectory using Lipatov's high energy effective action and a direct evaluation of Feynman diagrams. Using a gauge invariant regularization of high energy divergences by deforming the light-cone vectors of the effective action, we determine the two-loop self-energy of the reggeized gluon, after computing the master integrals involved using the Mellin-Barnes representations technique. The self-energy is further matched to QCD through a recently proposed subtraction prescription. The Regge trajectory of the gluon is then defined through renormalization of the reggeized gluon propagator with respect to high energy divergences. Our result is in agreement with previous computations in the literature, providing a non-trivial test of the effective action and the proposed subtraction and renormalization framework. I IntroductionCurrent applications of high energy factorization to QCD phenomenology range from the analysis of perturbative observables, such as dijets widely separated in rapidity [1], over transverse momentum dependent parton distribution functions in the low x region [2], up to the study of phenomena in heavy ion collisions [3]. Their common base is the factorization of QCD scattering amplitudes in the limit of asymptotically large center of mass energy, together with the resummation of large logarithmic contributions using the Balitsky-Fadin-KuraevLipatov (BFKL) equation [4,5]. Recent phenomenological use of the BFKL resummation can be found in the analysis of the combined HERA data on the structure function F 2 and F L [6,7], the study of di-hadron spectra in high multiplicity distributions at the Large Hadron Collider [8] or the production of high p T dijets [9,10,11] , widely separated in rapidity.In the present work we discuss Lipatov's high energy effective action [12] and show that it can serve as a useful tool to reformulate the high energy limit of QCD as an effective field theory of reggeized gluons. While the determination of the high energy limit of tree-level 1 arXiv:1307.2591v1 [hep-ph]

The quark induced Mueller–Tang jet impact factor at next-to-leading order

“…2. Determination of NLO corrections using this effective action approach has been addressed recently to a certain extent, through the explicit calculation of the NLO corrections to both quark [16] and gluon [17] induced forward jets (with associated radiation) as well as the determination of the gluon Regge trajectory up to 2 loops [18]. These previous applications have all in common that they are, at amplitude level, restricted to a color octet projection and, therefore, single reggeized gluon exchange.…”

“…The calculation of higher order corrections from the effective action approach [14] has been successfully explored by our group in recent years. In particular, both NLO impact factors for quark [16] and gluon induced forward jets [17] and the gluon Regge trajectory up to two loops [18] have been obtained making use of Lipatov's effective action and a set of supplementary calculational rules. In the following we will use this framework for the determination of the missing real NLO corrections which will be then combined at partonic level with the already known virtual corrections.…”

Color glass condensate formalism, Balitsky-JIMWLK evolution, and Lipatov’s high energy effective action

“…One of the main advantages of Lipatov's high energy effective action is that it provides a gauge invariant factorization of QCD amplitudes in the high energy limit through introducing a new type of field, i.e., the Reggeized gluon. Using this effective action it has been possible to both reproduce and derive a number of next-to-leading order (NLO) results, most notable the calculation of NLO correction to forward jet production without [13,14] and with rapidity gap [15], the gluon Regge trajectory up to two loops [16], and the NLO kernel of the Bartels-KwiecinskiPraszalowicz evolution equation [17] (see also the review [18]); for the determination of NLO corrections for Reggeized quarks, see [19]. The description of scattering amplitudes for multiple Reggeized gluon exchange has also been studied by a number of authors; see, e.g., [20][21][22].…”

On the application of the effective action approach to amplitudes with reggeon splitting

“…He found that after this projection the dependence on the sign of vanishes and the vertices satisfy the desired properties of Bose symmetry and negative signature of the reggeon. It was checked that his recipe reproduced the QCD results for the gluon trajectory with one and two loops [14][15][16]. However, his prescription refers only to the induced vertices themselves and consequently to the amplitude with a single interaction of colliding particles and not to the one with several interactions as in our case.…”