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Register a new userNNLO classical solution for Lipatovs effective action for reggeized gluons
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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.
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We discuss application of formalism of small-$x$ effective action for reggeized gluons, cite{Gribov,LipatovEff,BFKL}, for the calculation of classical gluon field of relativistic color charge, similarly to that done in CGC approach of cite{Venug,Kovner}. The equations of motion with the reggeon fields are solved in LO and NLO approximations and new solutions are found. The results are compared to the calculations performed in the CGC framework and it is demonstrated that the LO CGC results for the classical field are reproduced in our calculations. Possible applications of the NLO solution in the effective action and CGC frameworks are discussed as well.
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