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Off-shell helicity amplitudes in high-energy factorization

In the Catani-Ciafaloni-Hautmann high-energy factorization approach a cross section is expressed as a convolution of unintegrated gluon densities and a gauge-invariant hard process, in which two incoming gluons are off-shell with momenta satisfying certain high-energy kinematics. We present two methods of evaluating the tree-level hard process with multiple final states. The first one assumes that only one of the gluons is off-shell and relies on the Slavnov-Taylor identities. Such asymmetric configuration of incoming gluons is phenomenologically important in small x probing by forward processes. The second method deals also with two off-shell gluons and is based on the analytic continuation of the off-shell gluons momenta to the complex space. The methods were implemented into Monte Carlo computer programs and used in phenomenological applications. The results of both methods are straightforwardly related to Lipatov's effective vertices in quasi-multi-regge kinematics.