Transverse Momentum Dependent Parton Distribution Functions from Twisted Mass Lattice QCD

Abstract

The aim of this thesis is the theoretical calculation of the unpolarized transverse momentum dependent parton distribution function (TMDPDF) from first principles using lattice QCD. TMDPDFs are important quantities that provide information about the three-dimensional structure of the nucleon. Experimentally, they can be accessed through the Drell-Yan and the semi-inclusive deep inelastic scattering processes. Presently, this way of extracting TMDPDFs, through global fits to experimental data, lacks in precision. This is expected to improve with more data from future experiments and in particular from the planned Electron-Ion Collider (EIC). A theoretical computation of TMDPDFs can serve as an input to future phenomenological studies and also as a guideline for observations at EIC. <br> The lattice QCD calculation of TMDPDFs is challenging due to partonic observables being defined on the light-cone. The development of the large momentum effective theory (LaMET) has been one of the most successful approaches to tackle this problem. In this thesis, we present an exploratory study of the calculation of the unpolarized TMDPDF in the LaMET framework using the twisted mass fermion action. We use two lattice ensembles at same lattice spacing, {F_DISS_ABSTRACT}.09$ fm, but at volumes ^3 times 48$ and ^3 times 64$ with pion masses 0$ MeV and 0$ MeV respectively. We calculate the three quantities necessary for the extraction of the TMDPDF, namely the quasi-TMDPDF, the Collins-Soper kernel and the reduced soft function. We also study the renormalization of the underlying staple-shaped Wilson line operator using regularization independent momentum subtraction (RI/MOM) scheme. We find a vanishingly small contribution from mixing and study alternate multiplicative renormalization methods such as the short distance ratio and the RI-short. We finally perform a consistent matching up to 1-loop in perturbation theory to obtain the physical TMDPDF. We find our results to be comparable to previous calculations on the lattice and also to the phenomenological fits.