Multiplet bases, recursion relations and full color parton showers

Abstract: The papers in this thesis all concern the treatment of colors in perturbative QCD, both in the context of hard scattering cross sections and for parton showers. The complexity of the color structure of QCD increases quickly with the number of external partons. One way of tackling this issue is by using an orthogonal, group theory based, type of bases, called multiplet bases. This is the topic of papers I, II and IV. In paper III the inclusion of full color treatment in parton showers is addressed. Paper I concerns the decomposition of QCD color structures into multiplet bases, using Wigner 3j and 6j coefficients. A strong constraint is put on the required Wigner coefficients for leading order and next-to-leading order QCD amplitudes. The required Wigner coefficients for up to six external gluons were calculated by the method described in the paper. In paper II the results of paper I is applied to maximally helicity violating amplitude recursion relations, to investigate the viability of multiplet bases in this context. The result is a shift in the computational bottleneck of recursion, from the squaring of amplitudes to the recursion step, but yielding an overall better scaling for the total number of terms encountered. In paper IV a more general method of constructing multiplet bases is presented, which improves the decomposition of paper I for amplitudes with quarks. New basis vectors are constructed by the presented method and from them Wigner 6j cofficients are calculated. Paper III concerns the implementation of an Nc=3 parton shower in the event generator Herwig. In the implementation, the trace basis has been used, but it could, in a straight-forward way, be extended to other color space bases. The implementation has been used to study the effects of subleading color corrections, for both LEP and LHC events. The effects on observables are comparable to earlier findings for LEP, up to ~10% differences, compared to a leading color shower. For LHC the differences are often of the order of a few percent, but in some cases differences of up to 20% were found.