Sivers effect at Hermes, Compass and Clas12

TL;DR

This work analyzes the Sivers function through SIDIS measurements by HERMES and COMPASS, emphasizing the role of sea-quark contributions and testing the SIDIS–DY universality prediction. It introduces a flavor-dependent Gaussian Ansatz for the Sivers distributions, performing a multi-flavor fit that reveals opposite signs for u and d, as well as notable sea-quark components, with s and s̄ near positivity bounds. The study provides predictions for CLAS12 and COMPASS to probe the kaon sector and refine flavor decompositions, and discusses potential power corrections and their experimental signatures. Overall, the results support a nonzero, flavor-asymmetric Sivers function with significant sea-quark contributions and highlight future measurements as critical for resolving tensions in kaon data and validating universality with Drell–Yan.

Abstract

Single spin asymmetries in semi-inclusive deep-inelastic scattering off transversely polarized targets give information on, among other fascinating effects, a pseudo time-reversal odd parton distribution function, the 'Sivers function'. In this proceeding we review the extractions of this function from HERMES and COMPASS data. In particular, the HERMES pion and kaon data suggest significant sea-quarks contributions at $x \simeq 0.15$ to the Sivers effect. We present a new fit that includes all relevant sea quark distributions and gives a statistically satisfactory overall description of the data, but does not describe ideally the $K^+$ data from HERMES. We argue that measurements of the pion- and kaon Sivers effect at CLAS12, and COMPASS, will clarify the situation.

Figures (8)

• Figure 1: The SSA due to Sivers effect arises in SIDIS from final state interactions Brodsky:2002cx (upper part), and in DY from initial state interactions Brodsky:2002rv (lower part). Both types of interactions are encoded appropriately defined Wilson lines that are connected to each other by time reversal Collins:2002kn. In the Figure the respective interactions are sketched in the one-gluon-exchange approximation, see text.
• Figure 2: Left panel: The kinematics of the SIDIS process $lN\rightarrow l^\prime h X$. The nucleon is polarized transversely with respect to the beam. However, up to power corrections the polarization is transverse also with respect to the momentum of the virtual photon: $\sin\Theta_S\sim M_N/Q\ll 1$. Right panel: Tree-level diagram for the hadronic tensor in leading order in $1/Q$ in the parton model.
• Figure 3: (a) Sivers function of $u$-quarks vs. $x$ at a scale of $2.5\,{\rm GeV}^2$, as obtained from HERMES data Airapetian:2004tw. Shown are the best fit and its 1-$\sigma$ uncertainty. (b + c) The Sivers SSA, Eqs. (\ref{['Eq:SSA-in-SIDIS-unweighted']}, \ref{['Eq:AUT-SIDIS-Gauss']}), for $\pi^+$ from proton as function of $x$ and $z$ as obtained from the fit in Figure \ref{['Fig5-compare-to-data']}a in comparison to the data Airapetian:2004tw. The $\pi^-$ data from Airapetian:2004tw are compatible with zero, and are equally well described (not shown here).
• Figure 4: (a) The Sivers SSA for $K^+$ as function of $x$. The preliminary HERMES data is from Diefenthaler:2006vn. The solid line is the $K^+$ SSA obtained from the best fit to pion data Airapetian:2004tw (see Sec. \ref{['Sec:Sivers-effect-in-SIDIS-first-insights']}). The dashed lines display the effect of adding on top of that Sivers sea quarks saturating $\pm$ the positivity bounds (see Sec. \ref{['Sec:Sivers-effect-in-SIDIS-further-developments']}). It seems that sea quarks could explain the effect, but at the same time one overshoots $\pi^+$ data (see next figure). (b) Sivers SSA for $\pi^+$ as function of $x$. The published HERMES data are from Airapetian:2004tw, and the theoretical curves as in Fig. \ref{['Fig4-new-kaon-data']}b (but for $\pi^+$). (c) Comparison of the first (lower statistics, boxes) Diefenthaler:2006vn and the most recent (higher statistics, circles) Diefenthaler:2007rj data from HERMES on the $K^+$ Sivers SSA as function of $x$. It seems unlikely that the effect could be due to statistical fluctuation, especially in the region of $x\sim 0.1$.
• Figure 5: The Sivers SSA for various hadrons from different targets vs. $x$. Left panel: HERMES data (proton target) Diefenthaler:2007rj. Right panel: COMPASS data (deuteron target) Martin:2007au. The theoretical curves are the best fit (solid line) and its 1-$\sigma$-region (shaded area) as obtained from the Ansatz and best fit in Eqs. (\ref{['Eq:f1Tperp-ansatz']}, \ref{['Eq:best-fit']}). These data served as INPUT for the fit (\ref{['Eq:f1Tperp-ansatz']}, \ref{['Eq:best-fit']}).