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

Abstract

We derive relations between transverse momentum dependent distribution functions (TMDs) and the usual parton distribution functions (PDFs) in the 3D covariant parton model, which follow from Lorentz invariance and the assumption of a rotationally symmetric distribution of parton momenta in the nucleon rest frame. Using the known PDFs f a 1 (x) and g a 1 (x) as input we predict the x-and pT -dependence of all twist-2 T-even TMDs.

Publisher’s Note: Kinematics of deep inelastic scattering in leading order of the covariant approach [Phys. Rev. D85, 037501 (2012)]

“…We have discussed the available data in [1,2] and apparently relation (21) is compatible with the set of lower values p T corresponding to the 'leptonic data'. On the other hand the second set giving substantially greater p T and denoted as the 'hadronic data', seems to contradict this relation.…”

“…These variables were used in our recent papers on TMDs [1,2]. Simply the value of invariant variable x does not depend on the reference frame, but its interpretation e.g.…”

“…That is a complementary task to the study of above mentioned relations between distribution functions, which depend on these variables. So, the report can be considered as an addendum to our former papers related to the covariant QPM [1][2][3][4][5][6][7][8][9].…”

“…We have paid attention to these topics in our recent studies, see [1][2][3][4][5] and citations therein. In particular we have shown that the requirements of Lorentz invariance (LI) and the nucleon rotational symmetry in its rest frame (RS), if applied in the framework of the 3-D covariant quark-parton model (QPM), generate a set of relations between parton distribution functions.…”

Naive time-reversal odd phenomena in semi-inclusive deep-inelastic scattering from light-cone constituent quark models

“…For polarized TMDs it is supported approximately by some models [58,59,65,66]. A rigorous description of p Teffects would require methods along the QCD-based formalism of [67], as implemented in [68,69], but for our purposes the Ansatz (6) will be sufficient.…”