arXiv2024
The subject of this thesis is the construction of an approximation for the next-to-next-to-next-to leading order (N^3LO) deep inelastic scattering (DIS) massive coefficient function of the gluon for F2 in heavy quark pair production. Indeed, this object is one of the ingredients needed for the construction of any variable flavour number (factorization) scheme at O(alphas^3). The construction of such scheme is crucial for the improvement of the accuracy of the extraction of the parton distribution functions from the experimental data, that in turn will provide an improvement of the accuracy of all the theoretical predictions in high energy physics. Despite the function we are interested in is not known exactly, its expansion in some kinematic limits is available. In particular the high-scale limit (Q^2 >> m^2), high-energy limit (z->0, where z is the argument of the coefficient function) and threshold limit (z->zmax=1/(1+4m^2/Q^2)) of the exact coefficient function are all known, with the exception of some terms that we will provide in approximate form. Therefore, combining these limits in a proper way, we will construct an approximation for the unknown term of the N^3LO gluon coefficient function, that describes the exact curve in the whole range of z. Since other approximations for the N^3LO gluon coefficient functions are present in the literature, we will conclude by comparing our final approximate coefficient functions with such approximations. We will show a comparison both for the NNLO, whose exact function is known, and for the N^3LO. With our approach, we expect our results to be more accurate than previous approximations, thus providing a sufficient precision for a complete description of DIS at N^3LO and the consequent determination of N^3LO PDFs.