Soar, Gary (2011) *New third-order corrections and large-x resummation in perturbative QCD.* Doctoral thesis, University of Liverpool.

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## Abstract

In this thesis we present third-order corrections to perturbative quantities in inclusive lepton-hadron and lepton-photon deep-inelastic scattering (DIS) and study the resummation of leading contributions to quantities at large values of the scaling variable x. We provide up to third-order the coefficient functions for DIS via the exchange of a scalar-�phi directly coupling only to gluons, realised effectively in the Standard Model by the Higgs boson in the heavy top quark limit, and N_f effectively massless flavours. The functions are shown to exhibit a double-logarithmic enhancement in the large-x limit, with a similar enhancement of leading contributions in the small-x region unlike for the small-x behaviour of the Higgs boson. Consequently in the small-x region, the scalar-phi� probe no longer represents the Higgs boson in the heavy-top limit. The third-order corrections to the photon-parton splitting functions are presented in the MS_bar factorization scheme and the results are also transformed to the DIS_gamma scheme to allow for a physical form of the non-perturbative initial distributions beyond the leading order. They are shown to exhibit a double-logarithmic enhancement in the large-x region. The third-order contributions to the coefficient functions for the photon structure functions F2^gamma and FL^gamma are presented along with the contributions to the scalar-phi counterpart F�phi^gamma up to O(�alpha_em alpha_s^2 ) for electromagnetic and strong coupling constants �alpha_em and �alpha_s respectively. In each case, the expressions also display a double-logarithmic enhancement in the large-x region. Our results presented for lepton-photon DIS then facilitate the evolution of parton densities within the photon allowing us to obtain the inhomogeneous contributions to the photon structure function F2^gamma up to next-to-next-to-leading order (NNLO) accuracy in both the MS_bar and DIS_gamma factorization schemes. The two-loop results for the coefficient functions for F�phi are used to construct the physical evolution kernels for the system (F2, F�phi) of flavour-singlet structure functions, and are shown to be single-logarithmically enhanced at large-x. The conjecture that this feature persists, in conjunction with the large-x behaviour of the participating splitting and coefficient functions, allows for the prediction of the double-logarithmic contributions to the fourth-order singlet splitting functions. These predictions, when used in the construction of the analogous single-logarithmically enhanced physical evolution kernels for the system (F2, FL), yield analogous predictions of the double-logarithmic contributions to the fourth-order longitudinal coefficient functions. The corresponding photonic physical kernels for (F2^gamma , Fphi^gamma) and FLns^gamma are constructed and lead to predictions of the leading contributions to the fourth-order photon-parton splitting functions and the coefficient function for FLns^gamma respectively. Finally, we turn our attention to the large-x resummation of the double-logarithmic contributions to some of the perturbative quantities in lepton-hadron and lepton-photon DIS via two separate methods. The first method, namely using the iterative structure of the unfactorized partonic structure functions, was only employed for resummation to next-to-leading logarithmic (NLL) accuracy and for the quantities in lepton-hadron DIS. The second method uses the functional forms in dimensional regularization of the real- and virtual-emission contributions to the unfactorized partonic structure functions together with the Kinoshita-Lee-Nauenberg (KLN) cancellations required by the mass-factorization theorem, and allows for resummation to next-to-next-to-leading logarithmic (NNLL) accuracy. The second method was applied to quantities in both lepton-hadron and lepton-photon DIS resulting in new resummations to NNLL for the following quantities: P_qg, P_gq, C_2,g, C_phi�,q, C_L,g, P_qgamma and C_2,gamma.

Item Type: | Thesis (Doctoral) |
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Uncontrolled Keywords: | Phenomenology; Resummation; Perturbative QCD; Third-order corrections; large-x; DIS; Deep Inelastic Scattering |

Subjects: | Q Science > QC Physics |

Departments, Research Centres and Related Units: | Academic Faculties, Institutes and Research Centres > Faculty of Science > Department of Mathematical Sciences |

Status: | Unpublished |

ID Code: | 4413 |

Deposited On: | 08 Feb 2012 11:56 |

Last Modified: | 08 Feb 2012 11:56 |

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