Higher order QCD corrections and resummation effects to the Drell-Yan process in the Standard Model and Beyond[HBNI Th136]

Abstract

Computation of higher order quantum chromodynamics (QCD) corrections play an important role to constrain different model parameters as well as for precise phenomenological predictions at the Large Hadron Collider. The first part of the thesis contains a detailed phenomenological study on the second order QCD corrections to the production of di-leptons through the Drell-Yan process, in large extra dimension models where a generic spin-2 particle can be produced in the intermediate stages. We have studied both the scenarios where the spin-2 particle couples universally as well as non-universally to the Standard Model particles. For the universal scenario, we find that the two loop corrections increase the cross section by about 10%. The two loop corrections are large and also important to make the predictions stable under renormalization and factorization scale variations. For the non-universal scenario the spin-2 fields couple to two sets of gauge invariant tensorial operators with different coupling strengths. This non-universality introduces interesting consequences like additional ultraviolet divergences, which needs to be renormalized by multiplying overall operator renormalization constants. These renormalization constants satisfy renormalization group equation, whose solution at each order in perturbative expansion, can be written down in terms of anomalous dimensions. We have computed the three loop form factors and used the universal nature of infrared divergences to extract the anomalous dimensions up to three loop order in perturbative QCD. Using such a non-universal model we have also studied the phenomenological impact of the two loop QCD corrections. The impact of these higher order corrections can be quantified through K factor. We find through our detailed analysis that the K factors depend on the particular value of the non-universal couplings that is chosen. The second part of the thesis deals with resummation, that is needed to make reliable predictions at the colliders. Often the fixed order corrections are not reliable in some regions of the phase space, where large logarithms of some kinematic variables can appear. In such boundaries of the phase space, these large logarithms can spoil the reliability of the perturbative expansion. The resolution to this problem is to systematically resum these large contributions to all orders in the perturbation theory. In this thesis, we have presented a general framework to the resum threshold logarithms that appear in the rapidity distribution for the Drell-Yan production of lepton pairs. We have derived an all order compact formula in two dimensional Mellin space and then presented its phenomenological impact up to next-to-next-to-leading logarithmic accuracy. Although the dependence of rapidity distribution on the renormalization and factorization scale does not get better with the inclusion of resummed results, the perturbative convergence of the resummed result is better compared to the fixed order counterpart. In addition we compare our resummed result with the Tevatron data and find good agreement.