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Sivers effect in semi-inclusive DIS and in the Drell-Yan process

A. V. Efremov, K. Goeke, S. Menzel, A. Metz, P. Schweitzer

TL;DR

The paper tests the QCD-predicted sign change of the Sivers function between SIDIS and Drell-Yan by parameterizing $f_{1T}^{\perp}$ from HERMES SIDIS data under large-$N_c$ constraints and then predicting Drell-Yan single-spin asymmetries for PAX and COMPASS. It demonstrates that the SIDIS data can be described with a flavor structure $f_{1T}^{\perp u} = -f_{1T}^{\perp d}$ and provides two viable fits, which in turn yield distinct predictions in DY due to the universal sign reversal. The work argues that upcoming PAX and COMPASS measurements could decisively confirm or refute the SIDIS–DY universality and thereby test the underlying factorization framework for transverse-momentum dependent distributions. It also discusses theoretical bounds, connections to generalized parton distributions, and the role of gauge links in generating T-odd effects.

Abstract

The Sivers parton distribution has been predicted to obey a particular ``universality relation'', namely to have opposite sign in semi-inclusive deeply inelastic scattering (SIDIS) and the Drell-Yan process. We discuss how, on the basis of present HERMES data, this remarkable prediction of the QCD factorization approach to the description of single spin asymmetries related to the Sivers effect could be checked experimentally in future experiments at PAX and COMPASS.

Sivers effect in semi-inclusive DIS and in the Drell-Yan process

TL;DR

The paper tests the QCD-predicted sign change of the Sivers function between SIDIS and Drell-Yan by parameterizing from HERMES SIDIS data under large- constraints and then predicting Drell-Yan single-spin asymmetries for PAX and COMPASS. It demonstrates that the SIDIS data can be described with a flavor structure and provides two viable fits, which in turn yield distinct predictions in DY due to the universal sign reversal. The work argues that upcoming PAX and COMPASS measurements could decisively confirm or refute the SIDIS–DY universality and thereby test the underlying factorization framework for transverse-momentum dependent distributions. It also discusses theoretical bounds, connections to generalized parton distributions, and the role of gauge links in generating T-odd effects.

Abstract

The Sivers parton distribution has been predicted to obey a particular ``universality relation'', namely to have opposite sign in semi-inclusive deeply inelastic scattering (SIDIS) and the Drell-Yan process. We discuss how, on the basis of present HERMES data, this remarkable prediction of the QCD factorization approach to the description of single spin asymmetries related to the Sivers effect could be checked experimentally in future experiments at PAX and COMPASS.

Paper Structure

This paper contains 7 sections, 16 equations, 5 figures.

Table of Contents

  1. Introduction
  2. The Sivers function
  3. Sivers effect in SIDIS
  4. Sivers effect in the Drell-Yan process
  5. Conclusions
  6. Acknowledgement.
  7. Note added:

Figures (5)

  • Figure 1: The path of the process-dependent gauge link ${\cal W}[0,\xi;\hbox{process}]$ which enters the definition of the Sivers function in SIDIS and DY.
  • Figure 2: Kinematics of the SIDIS process $lp\rightarrow l^\prime h X$ (left), and the Drell-Yan process $p^{\uparrow}h \to l^{+}l^{-} X$ (right) in the lab frame.
  • Figure 3: Sivers function according to Eqs. (\ref{['Eq:sidis-ansatz']}, \ref{['Eq:sidis-fit']}) as obtained from a fit to the HERMES data HERMES-new, see Figs. \ref{['Fig4-Sivers-vs-HERMES']}a-c. The unpolarized quark distributions $xf_1^q(x)$ at $Q^2=2.5\,{\rm GeV}^2$, rescaled by the factor $(-1)/10$, are shown for the sake of comparison.
  • Figure 4: (a,b,c) The azimuthal SSA $A_{UT}^{\sin(\phi_h-\phi_S)P_{h\perp}/M_N}$ as function of $x$. The preliminary data are from the HERMES experiment HERMES-new. The curves are obtained from the large-$N_c$ constrained fits I and II (denoted as in Fig. \ref{['Fig3-Sivers-fit']}) of the Sivers function. (d,e,f) $A_{UT}^{\sin(\phi_h-\phi_S)P_{h\perp}/M_N}$ as function of $z$, with the preliminary data from HERMES-new, and the theoretical curves from the fits I and II of the Sivers function. The z-dependent data were not used for the fit, and serve as a cross check of our results.
  • Figure 5: The azimuthal SSA $A_{UT}^{\sin(\phi_h-\phi_S)q_\perp/M_N}$ in Drell-Yan lepton pair production, $p^\uparrow h\to\mu^+\mu^- X$, as function of $y$: (a) for the kinematics of the PAX experiment where the hadron $h=\bar{p}$, (b) for the kinematics of the COMPASS experiment where $h=\pi^-$. The different curves correspond to the fits I and II (see Eq. (\ref{['Eq:sidis-fit']})), including the sign-reversal in (\ref{['Eq:01']}).