Abstract
The effective action for reggeized gluons is based on the gluodynamic Yang–Mills Lagrangian with external current for longitudinal gluons added, see 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). On the base of classical solutions, obtained in Bondarenko et al. (Eur Phys J C 77(8):527, 2017), the one-loop corrections to this effective action in light-cone gauge are calculated. The RFT calculus for reggeized gluons similarly to the RFT introduced in Gribov (Sov Phys JETP 26:414, 1968) is proposed and discussed. The correctness of the results is verified by calculation of the propagators of A_{+} and A_{-} reggeized gluons fields and application of the obtained results is discussed as well.
Highlights
The construction of an RFT based on a QCD Lagrangian requires the knowledge of solutions of classical equations of motion in terms of reggeon fields A+ and A−
From the QFT point of view, the problem of interest is the calculation of the one-loop effective action for gluon QCD Lagrangian with added external current by use of the non-trivial classical solutions expressed in terms of new degrees of freedom; see [7]
This effective action can be considered as the one-loop effective action for gluodynamics with added gauge invariant source of longitudinal gluons, calculated on the base of non-trivial classical solutions for gluon fields
Summary
The construction of an RFT based on a QCD Lagrangian requires the knowledge of solutions of classical equations of motion in terms of reggeon fields A+ and A−. From the QFT point of view, the problem of interest is the calculation of the one-loop effective action for gluon QCD Lagrangian with added external current by use of the non-trivial classical solutions expressed in terms of new degrees of freedom; see [7]. There are other possibilities to verify the self-consistency of the approach It might be a calculation of the BFKL kernel, which is an effective vertex of interactions of four reggeons, or a calculation of the triple Pomeron vertex, see [39,40,41], which is the interaction vertex of six reggeon fields.
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