Structure of the nucleon at leading and subleading twist in the covariant parton model

The covariant parton model is generalized to describe quark correlators in a systematic way. Previous results are reproduced for the T-even leading-twist transverse momentum dependent parton distribution functions (TMDs), and for the first time all T-even twist-3 TMDs are evaluated in this model. We apply the approach to evaluate the fully unintegrated quark correlator which allows us to understand the model-specific relations between different TMDs. We verify the consistency of the approach, present numerical results and compare to available TMD parametrizations.

Figure 1

The input PDFs used in this work for the model calculations as functions of $x$ at the scale $2.5{\mathrm{GeV}}^2$. (a) LO parametrizations of the unpolarized PDFs $x{f}_1^q(x)$ from GRV’98 [160], MRST’98 [161], MSTW’09 [162]. (b) LO parametrizations of the helicity PDFs $x{g}_1^q(x)$ from GRSV’00 standard and valence scenario (see text) [163], and LSS’05 [164].

Figure 2

Predictions for (a) $x{f}^{\perp (1)q}(x)$ and (b) $x{e}^q(x)$ as functions of $x$ at the scale $2.5{\mathrm{GeV}}^2$ from the CPM according to Eqs. (29a) and (29b) using the unpolarized LO input PDFs shown in Fig. 1.

Figure 3

Model predictions for $x{h}_1^q(x)$, (a) and (b), and $x{h}_{1T}^{\perp (1)q}(x)$, (c) and (d), as functions of $x$ at the scale $2.5{\mathrm{GeV}}^2$ obtained using the helicity LO input PDFs from Fig. 1 in comparison to, respectively, the JAM’20 [45] and LP’15 [46] parametrizations.

Figure 4

Model predictions for (a) $x{g}_{1T}^{\perp (1)q}(x)$ and (b) $x{h}_{1L}^{\perp (1)q}(x)$ for $q=u$, $d$ as functions of $x$ at the scale $2.5{\mathrm{GeV}}^2$ obtained using the helicity LO input PDFs from Fig. 1. For comparison we show in (b) the estimate for $x{h}_{1L}^{\perp (1)q}(x)$ from [156] based on the WW-type approximation and JAM’20 transversity parametrization [45].

Figure 5

Model predictions for the twist-3 PDFs (a) $x{g}_T^q(x)$ and (b) $x{h}_L^q(x)$ as functions of $x$ at the scale $2.5{\mathrm{GeV}}^2$ obtained using the helicity LO input PDFs from Fig. 1.

Figure 6

Model predictions for the twist-3 polarized TMDs (a) $x{g}_L^{\perp (1)q}(x)$, (b) $x{g}_T^{\perp (2)q}(x)$, (c) $x{h}_T^{(1)q}(x)$, (d) $x{h}_T^{\perp (1)q}(x)$ as functions of $x$ at the scale $2.5{\mathrm{GeV}}^2$ obtained using the helicity LO input PDFs from Fig. 1.