Production of a gluon with the exchange of three reggeized gluons in the Lipatov effective action approach

Abstract

In the Regge kinematics the amplitude for gluon production off three scattering centers is found in the Lipatov effective action technique. The vertex for gluon emission with the reggeon splitting in three reggeons is calculated and its transversality is demonstrated. It is shown that in the sum of all contributions terms containing principal value singularities are cancelled and substituted by the standard Feynman poles. These results may be used for calculation of the inclusive cross-section for gluon production on two nucleons in the nucleus.

One-loop light-cone QCD, effective action for reggeized gluons and QCD RFT calculus

“…The action for the interaction of reggeized gluons was introduced in the series of papers [1][2][3][4][5][6] and describes multi-Regge processes at high energies; see [9][10][11][12][13][14][15][16][17][18][19][20][21][22]. There are the following important applications of this action: it can be used for the calculation of production amplitudes in different scattering processes and calculation of sub-leading, unitarizing corrections to the amplitudes and production vertices; see [1][2][3][4][5][6].…”

Off-shell gluon production in interaction of a projectile with 2 or 3 targets

“…The crucial point is that the same Bartels vertex B( p, q 3 , q 2 ) appears in the vertex amplitude A V Q and rescattering amplitude A R 1 , exactly as happens in the on-mass-shell case. As a result cancellation of non-Feynman singularities and restoration of Feynman propagators for the rescattering projectile proceeds in the same manner as in the on-mass-shell case [9]. So we only briefly comment on the derivation.…”

“…The first term in (6) may be used as the definition of the off-mass-shell Bartels vertex (9) so that the vertex V as a whole can be rewritten in the same form as on the mass shell in the gauge (el) = 0 [8]…”

“…In applications to the amplitudes with many in-coming or outgoing reggeons these integrations are not trivial, since the induced vertices contain singularities in longitudinal varia e-mail: salykinmisha@yandex.ru; m.salykin@spbu.ru ables different from the standard Feynman ones. In earlier papers [8,9] it was shown, however, that the amplitudes for emission of a real gluon in transition of a reggeon into two or three reggeons in fact can be rewritten in the purely transverse form with the standard transversal vertices connected with Feynman propagators. The contribution from induced vertices becomes substituted by the one from the Feynman propagators of the rescattering projectile.…”

Effective action for reggeized gluons, classical gluon field of relativistic color charge and color glass condensate approach

“…The effective action approach of [2][3][4][5][6][7] can be considered as some generalization of Gribov's Regge calculus, [1], for the case of QCD degrees of freedom. Besides the usual gluon field, it includes two additional reggeon fields and widely used for the calculations of different quasi-elastic LO and NLO production amplitudes in the multi-Regge kinematics, see [51][52][53][54][55][56][57][58][59][60], or calculation of NLO corrections to the BKP, [61,62], kernel, see [63].…”