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Insights on non-perturbative aspects of TMDs from models

H. Avakian, A. V. Efremov, P. Schweitzer, O. V. Teryaev, F. Yuan, P. Zavada

TL;DR

This paper surveys non-perturbative insights into transverse-momentum dependent parton distributions (TMDs) from quark-model perspectives, highlighting how Lorentz invariance in relativistic quark models yields specific LIRs and how additional model-dependent relations emerge across approaches. It clarifies that QCD does not impose exact general relations among TMDs, while WW-type approximations and quark-gluon effects can provide useful, though limited, structure at low scales. The authors illustrate these concepts with general model results, detailed bag-model relations, and discussions of pretzelosity and other relativistic effects, emphasizing the caution required when extrapolating to full QCD. Overall, quark models remain valuable tools for interpreting non-perturbative features of TMDs and guiding phenomenology ahead of comprehensive experimental validation.

Abstract

Transverse momentum dependent parton distribution functions are a key ingredient in the description of spin and azimuthal asymmetries in deep-inelastic scattering processes. Recent results from non-perturbative calculations in effective approaches are reviewed, with focus on relations among different parton distribution functions in QCD and models.

Insights on non-perturbative aspects of TMDs from models

TL;DR

This paper surveys non-perturbative insights into transverse-momentum dependent parton distributions (TMDs) from quark-model perspectives, highlighting how Lorentz invariance in relativistic quark models yields specific LIRs and how additional model-dependent relations emerge across approaches. It clarifies that QCD does not impose exact general relations among TMDs, while WW-type approximations and quark-gluon effects can provide useful, though limited, structure at low scales. The authors illustrate these concepts with general model results, detailed bag-model relations, and discussions of pretzelosity and other relativistic effects, emphasizing the caution required when extrapolating to full QCD. Overall, quark models remain valuable tools for interpreting non-perturbative features of TMDs and guiding phenomenology ahead of comprehensive experimental validation.

Abstract

Transverse momentum dependent parton distribution functions are a key ingredient in the description of spin and azimuthal asymmetries in deep-inelastic scattering processes. Recent results from non-perturbative calculations in effective approaches are reviewed, with focus on relations among different parton distribution functions in QCD and models.

Paper Structure

This paper contains 7 sections, 7 equations, 3 figures.

Table of Contents

  1. Introduction
  2. Relations among TMDs in QCD
  3. Model-independent relations among TMDs in quark models
  4. Relations among TMDs in quark models
  5. Relations among TMDs in bag model
  6. Conclusions
  7. The earlier analogs of LIRs

Figures (3)

  • Figure 1: The SSA $A_{LU}^{\sin\phi}$ vs. $x$. The data are from CLAS Avakian:2003pk, and the shaded area is the contribution due to the chirally odd twist-3 distribution function Schweitzer:2003uy$e^q(x)$ and the Collins fragmentation function Efremov:2006qm$H_1^\perp$.
  • Figure 2: (a) The unpolarized functions $f^{\perp u}(x)$, $f_1^u(x)$, $e^u(x)$ vs. $x$ from the bag model at low scale. (b) The polarized functions $g_T^{\perp u}(x)=-h_{1T}^{\perp u}(x)$, $g_{1T}^{\perp u}(x)=-h_{1L}^{\perp u}(x)$, $h_1^u(x)$, $g_1^u(x)$ plotted vs. $x$. (c) The polarized functions $h_T^{\perp u}(x)$, $g_L^{\perp u}(x)=-h_T^u(x)$, $g_T^u(x)$, $h_L^u(x)$ as functions of $x$. Distribution functions of $d$-quarks are related to those of $u$-quarks by SU(6) spin-flavour symmetry.
  • Figure 3: $xf^{\perp u}(x)$ and $f_1^u(x)$ vs. $x$. These functions would be equal in a WW-type approximation.