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Bessel-Weighted Asymmetries in Semi Inclusive Deep Inelastic Scattering

Daniel Boer, Leonard Gamberg, Bernhard Musch, Alexei Prokudin

TL;DR

This paper reframes the SIDIS cross section in Fourier (${\bm b}_T$) space, where convolutions of TMD PDFs and TMD FFs become simple products, enabling direct, model-independent access to spin–momentum correlations via Bessel-weighted asymmetries. By introducing generalized weights based on Bessel functions, the authors project Fourier-transformed TMDs, achieve explicit soft-factor cancellation, and connect the observables to TMD evolution and lattice QCD computations. They provide explicit constructions for the Sivers case and outline how these methods extend to other leading-twist asymmetries, while addressing high transverse momentum tails and the Y-term. The work argues that Bessel-weighted asymmetries offer clean, scalable observables for studying TMD dynamics across current and future experimental facilities, with broad applicability to related processes like Drell–Yan and $e^+e^-$ annihilation.

Abstract

The concept of weighted asymmetries is revisited for semi-inclusive deep inelastic scattering. We consider the cross section in Fourier space, conjugate to the outgoing hadron's transverse momentum, where convolutions of transverse momentum dependent parton distribution functions and fragmentation functions become simple products. Individual asymmetric terms in the cross section can be projected out by means of a generalized set of weights involving Bessel functions. Advantages of employing these Bessel weights are that they suppress (divergent) contributions from high transverse momentum and that soft factors cancel in (Bessel-) weighted asymmetries. Also, the resulting compact expressions immediately connect to previous work on evolution equations for transverse momentum dependent parton distribution and fragmentation functions and to quantities accessible in lattice QCD. Bessel weighted asymmetries are thus model independent observables that augment the description and our understanding of correlations of spin and momentum in nucleon structure.

Bessel-Weighted Asymmetries in Semi Inclusive Deep Inelastic Scattering

TL;DR

This paper reframes the SIDIS cross section in Fourier () space, where convolutions of TMD PDFs and TMD FFs become simple products, enabling direct, model-independent access to spin–momentum correlations via Bessel-weighted asymmetries. By introducing generalized weights based on Bessel functions, the authors project Fourier-transformed TMDs, achieve explicit soft-factor cancellation, and connect the observables to TMD evolution and lattice QCD computations. They provide explicit constructions for the Sivers case and outline how these methods extend to other leading-twist asymmetries, while addressing high transverse momentum tails and the Y-term. The work argues that Bessel-weighted asymmetries offer clean, scalable observables for studying TMD dynamics across current and future experimental facilities, with broad applicability to related processes like Drell–Yan and annihilation.

Abstract

The concept of weighted asymmetries is revisited for semi-inclusive deep inelastic scattering. We consider the cross section in Fourier space, conjugate to the outgoing hadron's transverse momentum, where convolutions of transverse momentum dependent parton distribution functions and fragmentation functions become simple products. Individual asymmetric terms in the cross section can be projected out by means of a generalized set of weights involving Bessel functions. Advantages of employing these Bessel weights are that they suppress (divergent) contributions from high transverse momentum and that soft factors cancel in (Bessel-) weighted asymmetries. Also, the resulting compact expressions immediately connect to previous work on evolution equations for transverse momentum dependent parton distribution and fragmentation functions and to quantities accessible in lattice QCD. Bessel weighted asymmetries are thus model independent observables that augment the description and our understanding of correlations of spin and momentum in nucleon structure.

Paper Structure

This paper contains 21 sections, 91 equations, 2 figures.

Table of Contents

  1. Introduction
  2. Overview on weighted asymmetries
  3. The SIDIS cross section in Fourier space at tree level
  4. Elements of the SIDIS cross section
  5. Representation in Fourier space
  6. Beyond tree level
  7. TMD PDFs at the level of matrix elements
  8. Bessel-weighted asymmetries
  9. Average transverse momentum shift and Bessel-weighted counterpart
  10. Conclusions
  11. Acknowledgments
  12. Conventions and useful relations
  13. Multipole expansion and Fourier transform
  14. Parameterization of the correlator in $b$-space
  15. Structure functions in terms of Fourier transformed TMD PDFs and FFs
  16. ...and 6 more sections

Figures (2)

  • Figure 1: Kinematics of the SIDIS process, compare Refs. Bacchetta:2004jzBacchetta:2006tn.
  • Figure 2: Schematic illustration of important scales for Bessel-weighted asymmetries before and after the Fourier-transform.