Title:

New thirdorder corrections and largex resummation in perturbative QCD

In this thesis we present thirdorder corrections to perturbative quantities in inclusive leptonhadron and leptonphoton deepinelastic scattering (DIS) and study the resummation of leading contributions to quantities at large values of the scaling variable x. We provide up to thirdorder 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 doublelogarithmic enhancement in the largex limit, with a similar enhancement of leading contributions in the smallx region unlike for the smallx behaviour of the Higgs boson. Consequently in the smallx region, the scalarphi� probe no longer represents the Higgs boson in the heavytop limit. The thirdorder corrections to the photonparton 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 nonperturbative initial distributions beyond the leading order. They are shown to exhibit a doublelogarithmic enhancement in the largex region. The thirdorder contributions to the coefficient functions for the photon structure functions F2^gamma and FL^gamma are presented along with the contributions to the scalarphi 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 doublelogarithmic enhancement in the largex region. Our results presented for leptonphoton 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 nexttonexttoleading order (NNLO) accuracy in both the MS_bar and DIS_gamma factorization schemes. The twoloop results for the coefficient functions for F�phi are used to construct the physical evolution kernels for the system (F2, F�phi) of flavoursinglet structure functions, and are shown to be singlelogarithmically enhanced at largex. The conjecture that this feature persists, in conjunction with the largex behaviour of the participating splitting and coefficient functions, allows for the prediction of the doublelogarithmic contributions to the fourthorder singlet splitting functions. These predictions, when used in the construction of the analogous singlelogarithmically enhanced physical evolution kernels for the system (F2, FL), yield analogous predictions of the doublelogarithmic contributions to the fourthorder 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 fourthorder photonparton splitting functions and the coefficient function for FLns^gamma respectively. Finally, we turn our attention to the largex resummation of the doublelogarithmic contributions to some of the perturbative quantities in leptonhadron and leptonphoton 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 nexttoleading logarithmic (NLL) accuracy and for the quantities in leptonhadron DIS. The second method uses the functional forms in dimensional regularization of the real and virtualemission contributions to the unfactorized partonic structure functions together with the KinoshitaLeeNauenberg (KLN) cancellations required by the massfactorization theorem, and allows for resummation to nexttonexttoleading logarithmic (NNLL) accuracy. The second method was applied to quantities in both leptonhadron and leptonphoton 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.
