Gluon production on two centers and the effective action approach

Abstract

Application of the effective action formalism is studied for processes in which the reggeons may split. It is shown that the gluon production on two centers is described by the contribution of the Reggeon-to-two-Reggeons-plus-Particle vertex supplemented by certain singular contributions from the double gluon exchange. The rules for longitudinal integrations are established from the comparison to perturbative QCD amplitude. Convenient expressions for application to the inclusive gluon production are derived.

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

“…As it was discussed in [8] due to locality in quark rapidity v.p. poles of quark propagators should be dropped.…”

“…As was discussed in [8], in the contribution from rescattering one has to keep only the part of the projectile propagator containing the δ-function. The part containing the principal value should be dropped.…”

“…The three-reggeon vertex R→RR was calculated in [8] to be with signs − for the first diagram and + for the second. Taking into account that we have to leave only delta-functional parts we finally get the rescattering amplitude for Fig.…”

“…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].…”