Transverse-momentum dependent parton distribution functions beyond leading twist in quark models

Abstract: Higher-twist transverse momentum dependent parton distribution functions (TMDs) are a valuable probe of the quark-gluon dynamics in the nucleon, and play a vital role for the explanation of sizable azimuthal asymmetries in hadron production from unpolarized and polarized deep-inelastic lepton-nucleon scattering observed in experiments at CERN, DESY and Jefferson Lab. The associated observables are challenging to interpret, and still await a complete theoretical explanation, which makes guidance from models valuable. In this work we establish the formalism to describe unpolarized higher-twist TMDs in the light-front framework based on a Fock-space expansion of the nucleon state in terms of free on-shell parton states. We derive general expressions and present numerical results in a practical realization of this picture provided by the light-front constituent quark model. We review several other popular quark model approaches including free quark ensemble, bag, spectator and chiral quark-soliton model. We discuss how higher-twist TMDs are described in these models, and obtain results for several TMDs not discussed previously in literature. This study contributes to the understanding of non-perturbative properties of subleading twist TMDs. The results from the light-front constituent quark model are also compared to available phenomenological information, showing a satisfactory agreement.