Unpolarized 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.

Transverse pion structure beyond leading twist in constituent models

“…2 in comparison to the results from the nucleon in this model [25, 55]. For the results are qualitatively similar in shape and magnitude to those from the LFCM.…”

“…(3c) and (3d) are valid with the proofs analog to the nucleon case [25]. The sum rule (3d) also follows directly from Eq.…”

“…Since owing to the Gell-Mann–Oakes–Renner relation, the sum rule (3c) for the pion diverges like in the chiral limit. The Jaffe–Ji sum rule (3d) connects the first moment of to the current quark mass in QCD, or the constituent (or effective) mass in models [25, 33]. In the chiral limit this sum rule goes to zero like .…”

“…[25], with an explicit application to the nucleon. The same approach is adopted here in the case of pion.…”

Semi-inclusive deep inelastic scattering in Wandzura-Wilczek-type approximation

“…In general, the model predicts non-zero tilde-terms, for instanceẽ a (x) = 0 [99][100][101]. However, despite strong interactions in this effective theory, the tilde termf ⊥q (x, k 2 ⊥ ) vanishes exactly in this model [94] and the WW-type approximation (3.3b) becomes exact at the low initial scale of this model of µ 0 ∼ 0.6 GeV.…”