Collins effect in semi-inclusive deeply inelastic scattering and in electron positron annihilation

TL;DR

This work analyzes Collins effect data from SIDIS (HERMES/COMPASS) and $e^+e^-$ annihilation (BELLE) to extract the Collins fragmentation function using a Gaussian transverse-momentum model and transversity predictions from a chiral quark-soliton model. By focusing on ratios like $H_1^ot/D_1$, the authors find a coherent picture across experiments: favoured and unfavoured Collins functions have opposite signs with comparable magnitudes, and the $u$-quark transversity is positive and near the Soffer bound while $h_1^d(x)$ remains largely unconstrained. BELLE data are well described by $H_1^{ot(1/2)a}(z) \,\propto\, z D_1^a(z)$, yielding two symmetric fits for favoured/unfavoured fragmentation and consistent with DELPHI within uncertainties. The article also provides predictions for future SIDIS and $e^+e^-$ measurements and discusses model dependencies, emphasizing the value of complementary data (e.g., Drell–Yan) to fully map Collins fragmentation and transversity.

Abstract

The Collins fragmentation function is extracted from HERMES data on azimuthal single spin asymmetries in semi-inclusive deeply inelastic scattering, and BELLE data on azimuthal asymmetries in electron positron annihilations. A Gaussian model is assumed for the distribution of transverse parton momenta and predictions are used from the chiral quark-soliton model for the transversity distribution function. We find that the HERMES and BELLE data yield a consistent picture of the Collins fragmentation function which is compatible with COMPASS data and the information previously obtained from an analysis of DELPHI data. Estimates for future experiments are made.

Figures (12)

• Figure 1: Kinematics of the SIDIS process $lp\to l^\prime h X$ and the definitions of azimuthal angles in the lab frame. The target polarization vector is transverse with respect to the beam.
• Figure 2: The quantity $2B_{\rm Gauss}H_1^{\perp(1/2)a}$ averaged over $z$, i.e. practically the weight of $h_1^a(x)$ in the Collins SSA $A_{UT}^{\sin(\phi+\phi_S)}(x)$ in Eq. (\ref{['Eq:AUT-Collins-1']}), vs. $x$ as extracted from the preliminary HERMES data Diefenthaler:2005gx. This quantity does not show any significant $x$-dependence --- as expected, see text.
• Figure 3: The Collins SSA $A_{UT}^{\sin(\phi+\phi_S)}(x)$ as function of $x$. The preliminary HERMES data are from Diefenthaler:2005gx, the COMPASS data are from Alexakhin:2005iw. The theoretical curves are based on the fit in Eqs. (\ref{['Eq:B-Gauss-H1perp12-fav']}, \ref{['Eq:B-Gauss-H1perp12-unf']}) and predictions for the transversity distribution from the chiral quark-soliton model Schweitzer:2001sr. Notice that different sign conventions are used in Diefenthaler:2005gxAlexakhin:2005iw: $A_{UT}^{\sin\phi_C}(x)=-A_{UT}^{\sin(\phi+\phi_S)}(x)$.
• Figure 4: Kinematics of the process $e^+e^-\to h_1 h_2 X$ and the definitions of azimuthal angles in the $e^+e^-$ rest frame.
• Figure 5: a. The two best fit solutions for the parameters $C_i$ in the Ansatz (\ref{['Eq:ansatz-BELLE']}) (indicated as discrete points) and their respective 1-$\sigma$ regions as obtained from a fit to the BELLE data Abe:2005zx. The solutions are symmetric with respect to the line $C_{\rm fav}=C_{\rm unf}$ indicated by a dashed line. b. The best fit for $H_1^{\perp(1/2)a}(z)$ resulting from Fig. \ref{['Fig5:BELLE-best-fit']} with the choice $H_1^{\perp\rm fav}>0$ and $H_1^{\perp\rm unf}<0$ as suggested by the analysis of the HERMES experiment, see Sec. \ref{['Sec-2:Collins-effect-in-SIDIS']}.