Simultaneous extraction of transversity and Collins functions from new SIDIS and e+e- data

TL;DR

This work performs a global, leading-twist analysis of SIDIS and $e^+e^-$ data to simultaneously extract the nucleon transversity distributions $\Delta_T q(x)$ and the Collins fragmentation functions $\Delta^N D_{h/q^\uparrow}(z,p_\perp)$. Using a Gaussian TMD factorisation and two Collins parameterisations, the authors fit recent HERMES, COMPASS, and Belle data, confirming earlier transversity and Collins extractions while exploring a more flexible Collins form that better accommodates large-$z$ behavior. The results yield transversity for $u$ and $d$ quarks and the corresponding Collins moments, with tensor charges $\delta q$ and uncertainty bands, and provide predictions for upcoming $e^+e^-$ measurements. They also highlight the need for incorporating TMD evolution in future analyses to refine the $k_\perp$ and $p_\perp$ dependences and to improve cross-process consistency.

Abstract

We present a global re-analysis of the most recent experimental data on azimuthal asymmetries in semi-inclusive deep inelastic scattering, from the HERMES and COMPASS Collaborations, and in e+e- --> h_1 h_2 X processes, from the Belle Collaboration. The transversity and the Collins functions are extracted simultaneously, in the framework of a revised analysis in which a new parameterisation of the Collins functions is also tested.

Figures (10)

• Figure 1: The experimental data on $A_{12}^{UL}$, $A_{12}^{UC}$ (upper plots) and $A_{0}^{UL}$ and $A_{0}^{UC}$ (lower plots), as measured by the Belle Collaboration Seidl:2012er in unpolarized $e^+e^- \to h_1 \, h_2 \, X$ processes, are compared to the curves obtained from our global fit. The solid lines correspond to the parameters given in Table \ref{['fitpar']}, obtained by fitting the SIDIS and the $A_{12}$ asymmetries with the standard parameterisation; the shaded areas correspond to the statistical uncertainty on the parameters, as explained in the text and in Ref. Anselmino:2008sga. Notice that the $A_{0}^{UL}$ and $A_{0}^{UC}$ data are not included in the fit and our curves, with the corresponding uncertainties, are simply computed using the parameters of Table \ref{['fitpar']}.
• Figure 2: The experimental data on the SIDIS azimuthal moment $A_{UT}^{\sin(\phi_h + \phi_S)}$ as measured by the COMPASS Collaboration Martin:2013eja on proton (upper plots) and deuteron (lower plots) targets, are compared to the curves obtained from our global fit. The solid lines correspond to the parameters given in Table \ref{['fitpar']}, obtained by fitting the SIDIS and the $A_{12}$ asymmetries with standard parameterisation; the shaded areas correspond to the statistical uncertainty on the parameters, as explained in the text and in Ref. Anselmino:2008sga.
• Figure 3: The experimental data on the SIDIS azimuthal moment $A_{UT}^{\sin(\phi_h + \phi_S)}$ as measured by the HERMES Collaboration Airapetian:2010ds, are compared to the curves obtained from our global fit. The solid lines correspond to the parameters given in Table \ref{['fitpar']}, obtained by fitting the SIDIS and the $A_{12}$ asymmetries with standard parameterisation; the shaded areas correspond to the statistical uncertainty on the parameters, as explained in the text and in Ref. Anselmino:2008sga.
• Figure 4: Plots of the functions ${\cal N}^{_{_C}}_{\rm fav}(z)$ and ${\cal N}^{_{_C}}_{\rm dis}(z)$ for the favoured and disfavoured Collins functions as obtained by using the standard, Eq. (\ref{['NC-coll']}), and polynomial, Eq. (\ref{['coll-2']}), parameterisations. On the left panel we show the results obtained by fitting the SIDIS data together with the $A_{12}$ Belle asymmetries (both with standard and polynomial parameterisation), while on the right panel we show the corresponding results obtained by fitting the SIDIS data together with the $A_{0}$ Belle asymmetries.
• Figure 5: The experimental data on $A_{0}^{UL}$, $A_{0}^{UC}$ (upper plots) and $A_{12}^{UL}$ and $A_{12}^{UC}$ (lower plots), as measured by the Belle Collaboration Seidl:2012er in unpolarized $e^+e^- \to h_1 \, h_2 \, X$ processes, are compared to the curves obtained from our global fit. The solid lines correspond to the parameters given in Table \ref{['fitpar-poly']}, obtained by fitting the SIDIS and the $A_{0}$ asymmetries with polynomial parameterisation; the shaded areas correspond to the statistical uncertainty on the parameters, as explained in the text and in Ref. Anselmino:2008sga. Notice that the $A_{12}^{UL}$ and $A_{12}^{UC}$ data are not included in the fit and our curves, with the corresponding uncertainties, are simply computed using the parameters of Table \ref{['fitpar-poly']}.