Pretzelosity distribution function h_1T^perp and the single spin asymmetry A_UT^sin(3phi-phi_S)

TL;DR

The paper investigates the pretzelosity distribution h1T^⊥, a leading-twist, chirally-odd TMD, and its connection to the SIDIS single-spin asymmetry A_UT^{sin(3φ-φ_S)}. It reviews theoretical properties and computes h1T^⊥ in relativistic quark models—the MIT bag model and Jakob's spectator model—highlighting a relation where helicity minus transversity equals pretzelosity in these frameworks. The work discusses positivity bounds, large-Nc flavor patterns, and the scale-dependence of proposed relations, noting that the relation is not exact in QCD with gluons and may hold only approximately in no-gluon models. Using this foundation, the authors estimate the magnitude of the A_UT^{sin(3φ-φ_S)} asymmetry for current and future experiments, compare with preliminary COMPASS data, and provide predictions for JLab, COMPASS, and HERMES to map the pretzelosity distribution.

Abstract

The leading twist transverse momentum dependent parton distribution function h_1T^perp, which is sometimes called ``pretzelosity,'' is studied. We review the theoretical properties of this function, and present bag model predictions. We observe an interesting relation valid in a large class of relativistic models: The difference between helicity and transversity distributions, which is often said to be a 'measure of relativistic effects' in nucleon, is nothing but the pretzelosity distribution. Pretzelosity is chirally odd and can be accessed in combination with the Collins effect in semi-inclusive deep inelastic scattering, where it gives rise to an azimuthal single spin asymmetry proportional to sin(3phi-phi_S). We discuss the preliminary deuteron target data from COMPASS, on that observable and make predictions for future experiments on various targets at JLab, COMPASS and HERMES.

Figures (7)

• Figure 1: Kinematics of the SIDIS process $lN\to l^\prime h X$ and the definitions of azimuthal angles in the lab frame.
• Figure 2: The parton distribution function $h_{1T}^{\perp q}(x)$ vs. $x$ from the bag model (results obtained here) in comparison to $f_1^q(x)$ and $h_1^q(x)$ from the same model. The functions $h_{1T}^{\perp q}(x)$ are rather large, even larger than $f_1^q(x)$. Notice, however, that $h_{1T}^{\perp q}(x)$ itself, as defined in (\ref{['Eq:def-h1Tperp-of-x']}), is not constrained by positivity bounds. All results refer to the low scale of the bag model.
• Figure 4: The parton distribution function $h_{1T}^{\perp q}(x)$ vs. $x$ from the spectator model of Ref. Jakob:1997wg in comparison to $f_1^q(x)$ and $h_1^q(x)$ from the same model. The functions $h_{1T}^{\perp q}(x)$ are rather large, even larger than $f_1^q(x)$. Notice, however, that $h_{1T}^{\perp q}(x)$ itself, as defined in (\ref{['Eq:def-h1Tperp-of-x']}), is not constrained by positivity bounds. All results refer to the low scale of the model Jakob:1997wg.
• Figure 6: Comparison of results from bag model (computed here, cf. Sec. \ref{['Sec-4:pretzelosity-in-bag']}) and spectator model, Ref. Jakob:1997wg. (a) $h_{1T}^{\perp q}(x)$ vs. $x$. (b) $h_{1T}^{\perp (1)q}(x)$ vs. $x$. (c) The ratio of $h_{1T}^{\perp (1)q}(x)$ to $h_1^a(x)$ vs. $x$. (d) The flavor combinations $(h_{1T}^{\perp (1)u}\pm h_{1T}^{\perp (1)d})(x)$ vs. $x$. All results refer to the low scales of these models.
• Figure 7: The transverse target SSA $A_{UT,\,\pi}^{\sin(3\phi-\phi_S)}$ for deuteron estimated on the basis of the positivity bound vs. preliminary COMPASS data Kotzinian:2007uv.