A Study Of The Transverse Momentum Dependent Parton Distribution Functions Within The Basis Light-front Quantization Framework

As the composite state of quarks and gluons,the internal structures of the hadron have always been one of the central topics of high-energy physics research.Among them,transverse momentum dependent distribution functions(TMD PDFs,or simply TMDs in the following)introduce the transverse-momentum dependence to extend the collinear parton distribution functions(PDFs).They can not only reveal the threedimensional internal structures of the hadron,but also contain information for studying the spin decomposition of the hadron.Via TMD factorization and scale evolution,TMDs also contribute to the non-perturbative parts of the cross sections of processes like semi-inclusive deep inelastic scatterings(SIDIS),Drell-Yan processes,and the annihilation of electron-positron pair into two hadrons,making it one of the major physical objectives of the future electron-ion colliders.As one of the light-front Hamiltonian methods,Basis Light-front Quantization(BLFQ)framework provides the probability to calculate TMDs directly from the first principle of Quantum Chromodynamics(QCD).In this research we study the leadingtwist quark TMDs of the proton under the truncation up to the leading Fock sector.We calculate all 8 leading-twist,T-even and T-odd,TMDs using the zeroth order expansion of the gauge link and the one-gluon exchange(OGE)approximation,respectively.We obtain real and angular-independent TMDs which satisfy the Soffer-type positivity constraints.Those conditions validate our calculations.We further calculate the average transverse momenta of those TMDs and find that they are strongly dependent on x and flavour.These results suggest that it may not be a good approximation to use x-k⊥ factorization while doing global fitting of the TMDs.Next,we investigate the behaviour of TMDs in different momentum regions,finding that BLFQ agree with the expected behaviours of TMDs in both perturbative and nonperturbative regions.We consider this as an advantage of the BLFQ framework.Starting from TMDs,we also calculate the Sivers asymmetry of the SIDIS,ie,the difference in cross sections when a lepton collides with a transversely polarized proton with opposite polarizations.Comparison with the experimental data reveals good consistency,at least for the overall behaviour.The importance of this research is twofold.First,we extend the applications of the BLFQ framework to studying the hadron structures in the three-dimensional momentum space.Even though we still need to use an effective Hamiltonian in this study due to our restriction to the leading Fock sector,we still think that this work lays down a firm ground for our future endeavours of studying the hadron structure in the threedimensional momentum space from the first-principle.Second,the theoretical calculations of the three-dimensional structure of the proton provide guidances and references for the future experimental investigations of TMDs.