Interaction of Two Reggeized Gluons: 2nd Order Corrections and the Bootstrap

Our aim is to show how the reggeization of the gluon, encoded in the bootstrap property of the BFKL kernel, permits to calculate the interaction kernel in the octet colour channel in the forward and non forward direction, for the quark contribution, starting from the known gluon trajectory up to 2nd order. To this end an ansatz to solve the bootstrap equation is used. The obtained result, for what regard the quark contribution, has been verified by direct Feynman diagram calculations.