Sivers effect in semi-inclusive deeply inelastic scattering

TL;DR

This work extracts the Sivers function's first transverse moment from HERMES SIDIS data by employing a Gaussian model for intrinsic parton transverse momentum and enforcing large-$N_c$ relations that tie the up and down quark Sivers distributions. It demonstrates that the Gaussian approach, with antiquark Sivers distributions neglected, provides a consistent description of the observed asymmetries and passes cross-checks with z-dependence data and COMPASS results. The authors quantify the moment $f_{1T}^{\uparrow(1)a}$ as $x f_{1T}^{6(1)u}(x)=-x f_{1T}^{6(1)d}(x)=-(0.17 ext{--}0.18) imes x^{0.66}(1-x)^5$ (at $Q^2 oughly 2.5$ GeV$^2$) with $p_{ m Siv}^2$ in $[0.10,0.32]$ GeV$^2$, and finds consistency with positivity bounds and limited sensitivity to $1/N_c$ corrections given current uncertainties. The analysis also outlines robust cross-checks using the $z$-dependence and discusses how future data, including Drell-Yan measurements, could test the predicted sign change and further validate the Gaussian TMD framework. Overall, the study supports the large-$N_c$ expectations for the Sivers effect and provides a pathway for more precise flavor-separated extractions as data improve.

Abstract

The Sivers function is extracted from HERMES data on single spin asymmetries in semi-inclusive deeply inelastic scattering. Our analysis use a simple Gaussian model for the distribution of transverse parton momenta, together with the flavor dependence given by the leading 1/Nc approximation and a neglect of the Sivers antiquark distribution. We find that within the errors of the data these approximations are sufficient.

Figures (12)

• Figure 1: Kinematics of the SIDIS process $lp\to l^\prime h X$ and the definitions of the azimuthal angles in the lab frame.
• Figure 2: The average transverse momentum $\langle P_{h\perp}(z)\rangle$ of pions produced in SIDIS as measured by HERMES from a deuterium target Airapetian:2002mf vs. $z$. The dashed curve is the $\langle P_{h\perp}(z)\rangle$ in the Gaussian model (\ref{['Eq:Phperp-av']}) with the parameters as fixed here, see Eq. (\ref{['Eq:fit-pT2-KT2']}). The dotted curve is the $\langle P_{h\perp}(z)\rangle$ Gaussian model with the parameters as obtained from a study of data on the Cahn effect Anselmino:2005nn.
• Figure 3: a. The best fit and the respectively 1- and 2-$\sigma$ range for the parameters $A$ and $b$ in the ansatz (\ref{['Eq:ansatz']}) for the Sivers function. b. The dependence of the parameter $A$ on the Gaussian width $p_{\rm Siv}^2$ characterizing the transverse momentum distribution in the Sivers function in the Gaussian model (\ref{['Eq:Gauss-ansatz']}). The parameter $b$ is practically $p_{\rm Siv}^2$-independent.
• Figure 4: a. The $u$-quark Sivers function $xf_{1T}^{\perp (1)u}(x)$ as function of $x$, as extracted from the HERMES data Airapetian:2004tw. Shown are the best fit, and its 1- and 2-$\sigma$ regions. b. Here it is shown that the absolute value of the extracted Sivers function does not exceed half of the positivity bound in the Gaussian model in Eq. (\ref{['Eq:positivity-bound-2use']}).
• Figure 5: The azimuthal SSA $A_{UT}^{\sin(\phi_h-\phi_S)}$ as function of $x$ for charged pions as obtained from the fit (\ref{['Eq:2nd-fit']}) in comparison to the final HERMES data Airapetian:2004tw.