Higher-order calculations and collider analyses with Mellin-space techniques

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The proposed research focuses on higher-order calculations in perturbative quantum field theory, in particular quantum chromodynamics (QCD, the theory of the interactions of quarks and gluons), and the efficient application of such calculations to analyses of experimental data, especially from present and forthcoming high energy electron-proton and proton-proton colliders. Quantum field theory, the merger of quantum mechanics and the theory of special relativity for pointlike fundamental objects, is the mathematical framework for particle physics phenomenology, the theoretical research with direct relevance to experimental investigations. Even for simple processes, the predictions of phenomenologically relevant quantum field theories cannot be calculated exactly by present or foreseeable mathematical methods. Lattice theory offers a way out by discretizing space-time and numerically solving the resulting equations on supercomputers. This method, however, is not applicable to a large amount of scattering observables, thus leaving perturbation theory, i.e., the evaluation of the predictions in terms of a series expansion in a small parameter (coupling constant) such as the fine-structure constant of quantum electrodynamics. In order to derive quantitatively reliable predictions, this expansion has to be extended beyond the first term (the leading order). In fact, for many important processes even contributions beyond the second term (the next-to-leading order) need to be computed. Such higher-order calculations also help to uncover general structural features of the theory under consideration, thus stimulating also research in formal quantum field theory and, via `duality' relations, even string theory. During the time span of the proposed research, particle physics will take the next big step by starting experimentation at the Large Hadron Collider (LHC) at CERN, a proton-proton accelerator with an unprecedented collision energy of 14 TeV. Research at this facility will shed light on fundamental questions like the mechanism of electroweak symmetry breaking and the realization of supersymmetry, or other `new physics', at the TeV scale. At a proton collider, perturbation theory can be applied only after factorizing the non-perturbative structure of the protons encoded in the momentum distributions of the quarks and gluons (`partons') in the proton. These universal quantities cannot be obtained from lattice theory either, but have to be fitted from experimental data, including results from the 320 GeV electron-proton collider HERA at DESY which is now in its final phase of high-luminosity data taking. Hence it is vital to perform sufficiently accurate calculations not only for proton-proton cross sections, but also the electron-proton observables employed for the determination of the parton distributions. Furthermore the resulting, usually very complex higher-order results need to be included in a highly efficient numerical setup, improving on codes so far used for the determination of parton distributions and collider cross sections. The proposed research will address these issues by 1. performing higher-order QCD calculations relevant to collider processes. These calculations will be performed via an integral transform (leading to integer Mellin-moments), a technique already used in the past years for pioneering third-order calculations by the applicant and his collaborators. 2. setting up, applying and publicizing an efficient platform for the numerical analysis of proton collider data which incorporates the above calculations and relevant results by other groups. This platform will be based on a technique using complex Mellin moments, for which the applicant is one of the leading international experts. This project is a novel initiative at Liverpool University which will considerably strengthen the synergy between the theory group in Mathematical Sciences and the experimental group in the Physics Department.