Higher order and heavy quark mass effects in the determination of parton distribution functions

The present thesis was devoted to the study of the inclusion of higher-order corrections and heavy quark mass effects in a PDF determination. This has been carried out in the NNPDF framework resulting originally in the NNPDF2.1 sets, which were at a later stage supplemented by the first LHC data leading to the most recent NNPDF2.3 sets. In Chapter 1 the concept of Parton Distribution Function (PDF) was introduced. We have shown how the analytical computation of the Deep-Inelastic-Scattering (DIS) process at order α_s in QCD leads to initial-stale collinear divergences which, using the factorization theorem, can be reabsorbed into the PDFs. The energy dependence of PDFs is fully determined and the task is then reduced to the determination of the x (Bjorken variable) dependence. In Chapter 2 a detailed discussion of the factorization schemes presently available to include heavy quark mass effects into DIS structure functions has been given. It emerged that there are two possible basic approaches to the calculation of the DIS structure functions. In the first approach, the so-called Fixed-Flavour-Number Scheme (FFNS), the calculation is performed retaining the quark mass of the heavy flavours which provide a ''natural'' regulator for the infrared divergences. In the second approach, called Zero-Mass Variable-Flavour-Number Scheme (ZM-VFNS), the heavy quark masses are instead set to zero and this gives rise to the usual final-state collinear divergences that are absorbed into the PDFs. In addition, in the ZM-VFNS, the number of active flavours is assumed to increase by one unity as the energy of the process crosses the energy threshold of a given heavy quark. In order to obtain a factorization scheme that is accurate both at large and low energies, several prescriptions that interpolate between FFNS at low energy and ZM-VFNS at large energy have been proposed and implemented in as many PDF fits. In Chapter 2 they have been described showing how they behave for different energy regimes. They are: the ACOT, the TR, the FONLL and the BMSN schemes, more generally called General-Mass Variable-Flavour-Number Schemes (GM-VFNS). The topic of Chapter 3 was the implementation of the FONLL scheme, which is the scheme adopted by the NNPDF collaboration. All the relevant formulas have been derived up to order α_s², discussing how a suitable definition of heavy quark structure functions for both Neutral-Current (NC) and Charged-Current (CC) processes emerges from the requirement of infrared safety in the limit of vanishing heavy quark mass. In a second stage the formalism of the Mellin transformation has been introduced showing how it provides a more analytical approach to the implementation of the structure functions. Finally, the heavy quark structure functions have been benchmarked. In Chapter 4 the implementation of the MS heavy quark masses in the DIS structure functions has been worked out. All the relevant formulas for PDF, α_s and mass evolution in the presence of MS heavy quark masses have been derived and benchmarked against publicly available codes. In addition, the heavy quark coefficient functions, which are commonly given in terms of pole masses, have been adapted to the MS and benchmarked. All the expressions presented in the previous chapters for the inclusion of the heavy quark mass effects into a PDF determination have been implemented in the NNPDF framework which thus needs to be properly introduced. Chapter 5 was then devoted to the description of the NNPDF methodology. The PDF sets resulting from the implementation of the FONLL method up to order α_s² in the NNPDF framework have been finally presented in Chapter 6. In the first place, a description of the dataset included in the fits has been given. Secondly, the impact of the inclusion of the order α_s² corrections has been assessed comparing the NNPDF2.3 NLO set, obtained using the FONLL-A scheme, to the NNPDF2.3 NNLO set, obtained using the NNLO. We then turned to the impact of the heavy quark mass effects in a PDF determination. After having ascertained that the implementation of the FONLL scheme in a PDF fit leads to an improvement in the accuracy, we turned to study some phenomenological implications of such a determination. The theoretical predictions for some of the standard candles at the LHC 8 TeV, that is electro-weak vector boson production, top-pair production and Higgs production via gluon-gluon fusion, have been evaluated using the most up to date public codes using the NNPDF2.3 NNLO fits and compared, when possible, to the most recent experimental measurements.