Assessing signals of TMD physics in SIDIS azimuthal asymmetries and in the extraction of the Sivers function

TL;DR

The paper presents a data-driven extraction of the Sivers function from SIDIS azimuthal asymmetries using a simple Gaussian TMD parameterization, incorporating COMPASS, HERMES, and JLab data. It systematically investigates uncertainties, explores low-x and large-x behavior, and compares three scale-dependence scenarios (no evolution, twist-3, and TMD). The analysis finds that the u-flavor Sivers contribution is robustly constrained while sea and d-quark components remain uncertain, with deuteron-target data and future facilities like the EIC poised to greatly improve flavor separation and low-x coverage. While collinear twist-3 evolution hints at possible Q^2-dependent effects, current TMD-evolution signals remain inconclusive due to large uncertainties in the nonperturbative width evolution.

Abstract

New data on the Sivers azimuthal asymmetry measured in semi-inclusive deep-inelastic scattering processes have recently been released by the COMPASS Collaboration at CERN. Their increased precision and their particular binning, in terms of $Q^2$ as well as $x$, motivates a new extraction of the Sivers function, within the framework of a simple and transparent parametrization. Signals of TMD effects visible in the Sivers asymmetries are critically assessed. A thorough study of the uncertainties affecting the extracted Sivers function is presented, including the low-$x$ and large-$x$ regions.

Figures (12)

• Figure 1: Compatibility tests on $\pi^+$ production from a proton target using only the $u$-contribution (all others flavours being set to zero) of the Sivers function, as described in the text. In each panel, we show the scatter plot of the allowed values of $\beta_u$ and $N_u$, corresponding to a $2\sigma$ C.L., for three cases: HERMES data(red), COMPASS data(blue), HERMES+COMPASS(black). Left panel: same unpolarized widths ($\langle k_\perp ^2 \rangle =0.57$ GeV$^2$ and $\langle p_\perp ^2 \rangle=0.12$ GeV$^2$ as obtained from HERMES multiplicities). Right panel: different unpolarized widths for each experiment ($\langle k_\perp ^2 \rangle =0.57$ GeV$^2$ and $\langle p_\perp ^2 \rangle=0.12$ GeV$^2$ for HERMES data, $\langle k_\perp ^2 \rangle =0.60$ GeV$^2$ and $\langle p_\perp ^2 \rangle=0.20$ GeV$^2$ for COMPASS data).
• Figure 2: Scatter plots representing the parameter space of the reference best fit. The shaded regions correspond to our estimate of $2\sigma$ C.L. error band.
• Figure 4: Parameter space scatter plots for the $\alpha$-fit, which includes the $\alpha_u$ and $\alpha_d$ free parameters. The regions displayed correspond to our estimate of $2\sigma$ C.L. error band. Notice that the uncertainties on the parameters which can be inferred from the scatter plots are much larger than the errors reported in Table \ref{['tab:ref-alpha']}.
• Figure 5: The extracted Sivers distributions for $u = u_v + \bar{u}$ and $d = d_v + \bar{d}$. Upper panels: the first moments of the Sivers function, Eqs. \ref{['eq:first-mom-ref']} and \ref{['eq:first-mom-alpha']}, are shown versus $x$. Middle panel: relative uncertainties, given by the ratio between the upper/lower border of the uncertainty bands and the best-fit curve for the reference fit. Lower panel: the Sivers functions, Eqs. (\ref{['eq:siv']}), is shown versus $k_\perp$, at $x=0.1$. Here we have no $Q^2$ dependence. The shaded bands correspond to our estimate of $2\sigma$ C.L. In all panels, the light blue bands correspond to the uncertainties of the reference fit (only $N_{u(d)}$ and $\beta_{u(d)}$ free parameters), while the large grey bands correspond to the uncertainties for the fit which includes also the $\alpha_u$ and $\alpha_d$ parameters.
• Figure 6: The results obtained from the reference fit and the $\alpha$-fit are compared to the HERMES measurements of the SIDIS Sivers asymmetry for $\pi^\pm$ production off a proton target Airapetian:2009ae (upper panels), to the COMPASS measurements of the SIDIS Sivers asymmetry on a LiD target Alekseev:2008aa for $\pi^\pm$ production (middle panels), and to the JLab data for $\pi^\pm$ production on a $^3$He target Qian:2011py (bottom panel). Here we show the $x$ dependence only. The shaded region corresponds to our estimate of $2\sigma$ C.L. error band. The light-blue bands correspond to the uncertainties of the reference fit (only $N_{u(d)}$ and $\beta_{u(d)}$ free parameters), while the (larger) gray bands correspond to the uncertainties of the $\alpha$-fit, which includes also the $\alpha_{u(d)}$ parameters.