NNLO classical solution for Lipatov's effective action for reggeized gluons

Abstract

We consider the formalism of small-x effective action for reggeized gluons, Gribov (Sov Phys JETP 26:414, 1968), Lipatov (Nucl Phys B 452:369, 1995; Phys Rep 286:131, 1997; Subnucl Ser 49:131, 2013, Int J Mod Phys Conf Ser 39:1560082, 2015; Int J Mod Phys A 31(28/29):1645011, 2016; EPJ Web Conf 125:01010, 2016) and Lipatov et al. (Sov J Nucl Phys 23:338, 1976; Sov Phys JETP 45:199, 1977; Sov J Nucl Phys 28:822, 1978), and, following to the approach developed in Bondarenko et al. (Eur Phys J C 77(8):527, 2017, Eur Phys J C 77(9):630, 2017), calculate the classical gluon field to NNLO precision with fermion loops included. It is demonstrated, that the the self-consistency of the equations of motion in each perturbatie order in the approach is equivalent to the transversality conditions applied to the solutions of the equations in the lower orders, that allows to construct the solutions with the help of some recursive scheme. Applications of the obtained results are also discussed.

arXiv comment12 pages; submitted to Eur.Phys.Jour. C

References in corpus (39)

• Computing Quark and Gluon Distribution Functions for Very Large Nuclei
• Gluon Distribution Functions for Very Large Nuclei at Small Transverse Momentum
• Nonlinear Gluon Evolution in the Color Glass Condensate: I
• The Wilson renormalization group for low x physics: towards the high density regime
• The BFKL Equation from the Wilson Renormalization Group
• Nonlinear Gluon Evolution in the Color Glass Condensate: II
• The Renormalization Group Equation for the Color Glass Condensate
• The Intrinsic Glue Distribution at Very Small x
• The Wilson renormalization group for low x physics: Gluon evolution at finite parton density
• Small-x physics in perturbative QCD
• Gauge invariant effective action for high-energy processes in QCD
• Feynman rules for effective Regge action
• Quark contribution to the reggeon-reggeon-gluon vertex in QCD
• Helicity amplitudes for high-energy scattering
• NLO jet vertex from Lipatov's QCD effective action
• Quark-antiquark contribution to the BFKL kernel
• Radiative corrections to quark-quark-reggeon vertex in QCD
• On the one-loop calculations with Reggeized quarks
• The BFKL Pomeron Calculus in zero transverse dimensions: summation of Pomeron loops and generating functional for the multiparticle production processes
• NLO Corrections to the kernel of the BKP-equations
• Gluon production on two centers and the effective action approach
• The Reggeon $\to$ 2 Reggeons $+$ Particle vertex in the Lipatov effective action formalism
• Effective action for reggeized gluons, classical gluon field of relativistic color charge and color glass condensate approach
• Production of a gluon with the exchange of three reggeized gluons in the Lipatov effective action approach
• Ward Identities for Amplitudes with Reggeized Gluons
• One loop light-cone QCD, effective action for reggeized gluons and QCD RFT calculus
• On the inclusive gluon production in the Lipatov effective action formalism
• TMD gluon distributions for multiparton processes
• Regge Field Theory in zero transverse dimensions: loops versus "net" diagrams
• The dimensionally reduced description of the high energy scattering and the effective action for the reggeized gluons
• Production of two gluons in the Lipatov effective action formalism
• S-matrix and productions amplitudes in high energy QCD
• Off-shell gluon production in interaction of a projectile with 2 or 3 targets
• Gluon production in the Lipatov effective action formalism
• Reggeon-gluon vertices with Ward identities
• Diffractive scattering on the deuteron
• On correlators of Reggeon fields and operators of Wilson lines in high energy QCD
• On asymptotic solutions of RFT in zero transverse dimensions
• On the application of the effective action approach to amplitudes with reggeon splitting