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Title: NNNLO and all-order corrections to splitting and coefficient functions in deep-inelastic scattering
Author: Davies, Joshua
Awarding Body: University of Liverpool
Current Institution: University of Liverpool
Date of Award: 2016
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This thesis describes several calculations of quantities describing the deep-inelastic scattering (DIS) of leptons and hadrons, within the framework of massless perturbative quantum chromodynamics. The third order (NNNLO) contributions to the coefficient functions C⁻ 2,ns, C⁻ L,ns and C⁻ 3,ns, which describe charged-current (W±-exchange) DIS in the linear combination W⁺-W⁻ are presented. Complementing existing results for the W⁺+W⁻ combination, these new results complete the third-order description of charged-current DIS. The results are presented both as compact parametrizations and exact expressions. The corrections are found to be small for experimentally relevant values of the Bjorken-x variable. The behaviour of the DIS structure functions in the small-x limit is considered. By finding a suitable functional form with which to describe them, it is possible to use the results of existing fixed-order perturbative calculations to resum the leading small-x double logarithms of the coefficient functions and splitting functions to all orders in the strong coupling constant αs. All-order descriptions of the leading three double logarithms are discussed and presented for both coefficient functions and splitting functions. Finally, the results of recent advances in the fourth-order computation of the Mellin moments of structure functions are used to reconstruct expressions for the general Mellin-N dependence of the large-nf parts of the fourth-order contributions to the splitting functions. The software package FORCER is able to compute a sufficient number of Mellin moments to determine the N dependence of the n²f terms of the non-singlet splitting functions, and the n³f terms of the singlet splitting functions. The resulting expressions are in agreement with, and extend, various existing computations found in the literature.
Supervisor: Vogt, A. Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral