The higher-order perturbative corrections, beyond leading logarithmic accuracy, to the BFKL evolution in QCD at high energy are well known to suffer from a severe lack-of-convergence problem, due to radiative corrections enhanced by double collinear logarithms. Via an explicit calculation of Feynman graphs in light cone (time-ordered) perturbation theory, we show that the corrections enhanced by double logarithms (either energy-collinear, or double collinear) are associated with soft gluon emissions which are strictly ordered in lifetime. These corrections can be resummed to all orders by solving an evolution equation which is non-local in rapidity. This equation can be equivalently rewritten in local form, but with modified kernel and initial conditions, which resum double collinear logs to all orders. We extend this resummation to the next-to-leading order BFKL and BK equations. The first numerical studies of the collinearly-improved BK equation demonstrate the essential role of the resummation in both stabilizing and slowing down the evolution.Comment: 16 pages, 5 figure

In a previous publication, we have established a collinearly-improved version of the Balitsky-Kovchegov (BK) equation, which resums to all orders the radiative corrections enhanced by large double transverse logarithms. Here, we study the relevance of this equation as a tool for phenomenology, by confronting it to the HERA data. To that aim, we first improve the perturbative accuracy of our resummation, by including two classes of single-logarithmic corrections: those generated by the first non-singular terms in the DGLAP splitting functions and those expressing the one-loop running of the QCD coupling. The equation thus obtained includes all the next-to-leading order corrections to the BK equation which are enhanced by (single or double) collinear logarithms. We then use numerical solutions to this equation to fit the HERA data for the electron-proton reduced cross-section at small Bjorken x. We obtain good quality fits for physically acceptable initial conditions. Our best fit, which shows a good stability up to virtualities as large as Q^2=400 GeV^2 for the exchanged photon, uses as an initial condition the running-coupling version of the McLerran-Venugopalan model, with the QCD coupling running according to the smallest dipole prescription.Comment: 15 pages, 3 figures; minor corrections to fit results and few comments adde

20 pagesInternational audienceWe provide a concise overview on transverse momentum dependent (TMD) parton distribution functions, their application to topical issues in high-energy physics phenomenology, and their theoretical connections with QCD resummation, evolution and factorization theorems. We illustrate the use of TMDs via examples of multi-scale problems in hadronic collisions. These include transverse momentum q_T spectra of Higgs and vector bosons for low q_T, and azimuthal correlations in the production of multiple jets associated with heavy bosons at large jet masses. We discuss computational tools for TMDs, and present an application of a new tool, TMDlib, to parton density fits and parameterizations

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We determine both real and virtual next-to-leading order corrections to the gluon induced forward jet vertex, from the high energy effective action proposed by Lipatov. For these calculations we employ the same regularization and subtraction formalism developed in our previous work on the quark-initiated vertex. We find agreement with previous results in the literature.

Ratios of azimuthal angle correlations between two jets produced at large rapidity separation are studied in the N = 4 maximally supersymmetric Yang-Mills (MSYM) theory. It is shown that these observables, which directly prove the SL(2,C) symmetry present in gauge theories in the Regge limit, exhibit an excellent perturbative convergence. They are compared to those calculated in QCD for different renormalization schemes concluding that the momentum-substraction scheme with the Brodsky-Lepage-Mackenzie scale-fixing procedure captures the bulk of the MSYM results.

The two loop (NLO) diagrams with quark content contributing to the gluon Regge trajectory are computed within the framework of Lipatov's effective action for QCD, using the regularization procedure for longitudinal divergencies recently proposed by two of us in [1]. Perfect agreement with previous results in the literature is found, providing a robust check of the regularization prescription and showing that the high energy effective action is a very useful computational tool in the quasi-multi-Regge limit.

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]