On the factorisation theorem in boson-gluon fusion at hadron colliders

An 'improved' tree level description of the calculation of the O(alpha squared (alpha(sub s))) boson gluon fusion processes is presented focusing on heavy fermions in the final state, and the singular structure of the expression for the matrix elements squared is analyzed in detail. At lowest order, that is O(alpha squared), contributions from for instance W bottom scattering, where the bottom quark flux is taken from the bottom quark distribution function in the proton, are deemed to give non negligible contributions to the heavy flavor cross sections. Adding O(alpha squared) and O(alpha squared (alpha(sub s))) cross sections will lead to a typical double counting of Feynman graphs and a solution to this problem by subtracting the collinear singularity in the W gluon fusion process is presented. The results obtained are finite and, although virtual corrections were not explicitly taken into account, are expected to be valid for almost full phase space. Similar conclusions can be drawn in the case where the charged weak current is replaced by the neutral weak current.