Simplification of Flavour Combinatorics in the Evaluation of Hadronic Processes

Abstract

A serious computational problem in the evaluation of hadronic collision processes is connected with the large number of partonic subprocesses included in the calculation. These are from the quark and gluon content of the initial hadrons, and from CKM quark mixing. For example, there are 180 subprocesses which contribute to the $W$+2jets process, and 292 subprocesses in $W$+3jets production at the LHC, even when quarks from only the first two generations are taken into account. We propose a simple modification of the rules for evaluation of cross sections and distributions, which avoids multiplication of channels from the mixture of quark states. The method is based on a unitary rotation of down quarks, thus, transporting the mixing matrix elements from vertices of Feynman diagrams to the parton distribution functions (PDF). As a result, one can calculate cross sections with significantly fewer subprocesses. For the example mentioned above, with the new rules, one need evaluate only 21 and 33 subprocesses respectively. The matrix elements of the subprocesses are calculated without quark mixing but with a modified PDF convolution which depends on the quark mixing angle, and on the topologies of gauge invariant classes of diagrams. The proposed method has been incorporated into the CompHEP program and checked with various examples.