Transverse momentum distributions of quarks in the nucleon from the chiral quark soliton model

Abstract

We report the first calculation of the simplest but most fundamental transverse-momentum-dependent distribution of quarks in the nucleon, i.e. the time-reversal-even unpolarized transverse-momentumdependent quark and antiquark distribution with isoscalar combination, within the framework of the chiral quark soliton model. The nonperturbative account of the deformed Dirac-sea quarks within the theoretical scheme enables us to make reliable predictions not only for the quark distribution but also for the antiquark distribution. We found that the predicted average transverse momentum square hk 2 ? i of quarks and antiquarks depends strongly on their longitudinal momentum fraction x, which means that the frequently used assumption of factorization in x and k ? is significantly violated. It is also found, somewhat unexpectedly, that the average transverse momentum square of antiquarks is considerably larger than that of quarks.

Relation between transverse momentum dependent distribution functions and parton distribution functions in the covariant parton model approach

“…Moreover, it was also shown that the 3D picture of parton momenta inside the nucleon provides a basis for a consistent description of quark orbital angular momentum [21], which is related to pretzelosity [26]. It should be remarked that some of the relations among different TMDs were found (sometimes before) also in other models [27][28][29][30][31][32][33][34][35].…”

Modelling the nucleon structure

“…Notice that the terms valence and sea have a dynamical meaning in the context of this model, which is not equivalent to the usual meaning of valence distributions as the difference q −q and of sea asq. The χQSM has been applied to describe unpolarized [46,47] and helicity [47] TMDs. It predicts significantly broader k ⊥ -distributions for sea-quark TMDs than for valence quarks, due to non-perturbative shortrange correlations caused by chiral symmetry breaking effects [47].…”

“…The former can be studied in models with only quark degrees of freedom, while T-odd TMDs require explicit gauge degrees of freedom. Models for T-even TMDs can be grouped in the following categories: (a) light-front quark models [35][36][37][38][39]; (b) spectator models [40][41][42][43][44][45]; (c) chiral quark soliton models [7,46,47]; (d) bag models [48,49]; (e) covariant parton models [13,50]; (f) quark-target model [51][52][53][54]. All these models, with the exception of the covariant parton model and the applications with phenomenological LFWFs of ref.…”

“…A different approach consists in a direct calculation of GPDs using effective quark models. After the first calculation within the MIT bag model [103], GPDs were calculated in the χQSM [104][105][106][107][108][109][110], using covariant BetheSalpeter approaches [111][112][113][114][115][116][117][118], in the quark-target model [51,119,120], in nonrelativistic quark models [121][122][123], in light-front quark models [7,[124][125][126][127][128], in meson-cloud models [129,130], and from LFWFs inspired by AdS/QCD [131][132][133]. Although these models single out only a few features of the QCD dynamics in hadrons, they may provide some guidance on the functional dependence of GPDs, particularly if a model is constrained to reproduce electromagnetic form factors and ordinary parton distributions.…”

On chiral-odd Generalized Parton Distributions

“…Not much is known about them, but model calculations have been developed in Refs. [5,[8][9][10] and a few moments have been computed on the lattice [11]. To factorize the amplitude of this process we use the now classical proof of the factorization of exclusive scattering at fixed angle and large energy [12].…”