[Paper Review] Sivers distribution functions and the latest SIDIS data

M. Anselmino, M. Boglione+4 more|arXiv (Cornell University)|Jul 22, 2011

Particle physics theoretical and experimental studies13 citations

TL;DR

This paper presents a phenomenological fit of Sivers distribution functions using the latest HERMES and COMPASS SIDIS data, assuming only valence quark contributions (u and d) and neglecting sea quark Sivers functions. The fit achieves a good description of the data with a reduced chi-squared value of 1.06, indicating that the enhanced kaon asymmetry previously attributed to sea quarks can be consistently explained by valence quark Sivers functions alone.

ABSTRACT

We present an extraction of the Sivers distribution functions from the most recent experimental data of the HERMES and COMPASS experiments, assuming a negligible contribution of sea quark Sivers functions.

Motivation & Objective

• To re-evaluate the Sivers distribution functions using the most recent SIDIS data from HERMES and COMPASS.
• To test whether the previously observed large kaon Sivers asymmetry can be explained without contributions from sea quark Sivers functions.
• To perform a global fit of HERMES and COMPASS data using only u and d valence quark Sivers functions, assuming a factorized parametrization.
• To assess the constraints on the Sivers function parameters and their correlations using a systematic error analysis.

Proposed method

• A factorized parametrization of the Sivers function is used, with form Δᴺf_q/p↑(x,k⊥) = 2N_q(x)h(k⊥)f_q/p(x,k⊥), where N_q(x) is a polynomial and h(k⊥) is a Gaussian in transverse momentum.
• The unpolarized distribution and fragmentation functions are fixed using GRV98 and DSS sets, with Gaussian widths ⟨k⊥²⟩ = 0.25 (GeV/c)² and ⟨p⊥²⟩ = 0.20 (GeV/c)².
• A global fit is performed on 209 data points from HERMES (proton target) and COMPASS (deuteron target), using only u and d quark Sivers functions as free parameters.
• The fit minimizes χ²/dof with seven free parameters: Nu, αu, βu, Nd, αd, βd, and M₁², with M₁² controlling the k⊥ width of the Sivers function.
• Parameter uncertainties are extracted via a Monte Carlo sampling method, generating parameter sets that correspond to a 95.45% confidence level in Δχ².
• Correlations between parameters are analyzed, particularly between Nu and M₁², which show strong interdependence.

Experimental results

Research questions

• RQ1 Can the latest HERMES and COMPASS SIDIS data be consistently described without including sea quark Sivers functions?
• RQ2 Is the large Sivers asymmetry observed in K⁺ production at HERMES explainable by valence quark contributions alone?
• RQ3 What are the constraints on the Sivers function parameters, particularly the transverse momentum width M₁², when fitting only valence quark distributions?
• RQ4 How do the extracted Sivers functions for u and d quarks compare to previous fits that included sea quark contributions?
• RQ5 What is the significance of the correlation between Nu and M₁² in the context of Sivers function shape and data constraints?

Key findings

• The fit achieves a reduced chi-squared value of χ²/dof = 1.06, indicating a good agreement with the experimental data.
• The Sivers function parameters are constrained with M₁² = 0.19 GeV², which is approximately 60% of the unpolarized distribution's k⊥ width (0.25 GeV²).
• The u-quark Sivers function has a positive normalization (Nu = 0.40), while the d-quark function is negative (Nd = -0.97), consistent with the expected sign structure.
• The strongest parameter correlation is found between Nu and M₁², indicating that the amplitude and width of the Sivers function are not independently determined.
• The model predicts a Sivers asymmetry for proton targets at COMPASS kinematics that is compatible with data, despite a reported ±0.01 scale uncertainty in the COMPASS measurements.
• The inclusion of sea quark Sivers functions slightly improves χ²/dof, but is not necessary to describe the data, suggesting valence quark contributions are sufficient.