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

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 canceled 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.