High Energy Resummation in Quantum Chromo–Dynamics
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In this thesis I discuss different aspects of high energy resummation in Quantum Chromo-Dynamics and its relevance for precision physics at hadron colliders. The high energy factorisation theorem is presented and discussed in detail, emphasizing its connections with standard factorisation of collinear singularities. The DGLAP and the BFKL equations are presented and leading twist duality relations between the evolution kernels are discussed. High energy factorisation is used to compute resummed coefficient functions for hadronic processes relevant for LHC phenomenology. The case of heavy flavour production is analysed in some detail and results already present in the literature are confirmed. High energy effects can play an important role for such cross sections which are to be used as standard candles at the LHC, such as W/Z production. To this purpose Drell-Yan processes are studied in high energy factorisation. The inclusive cross section for Higgs boson production via gluon-gluon fusion is analysed both in the heavy top limit and for finite values of the top mass. The different high energy behaviour of the two cases is studied, showing explicitly that the full theory exhibits single high energy logarithms in contrast to the infinite top mass limit. The correct high energy behaviour of the partonic cross section is then combined to the NNLO calculation performed in the heavy top limit, in order to obtain an improved coefficient function. Finite top mass effects at high energy on the hadronic cross section are moderate. As far as parton evolution is concerned, an approximate expression for the NNLO contribution to the kernel of the BFKL equation is computed exploiting running coupling duality relations between DGLAP and BFKL. This result includes all collinear and anticollinear singular contributions and it is computed in various factorisation schemes. The collinear approximation is tested against the known LO and NLO kernels with the discrepancy being at the percent level. Therefore the approximate NNLO contribution is likely to be close to the as yet unknown complete result in the region relevant at leading twist.