Collins functions for pions from SIDIS and new e+e- data: a first glance at their transverse momentum dependence

TL;DR

The paper tackles the transverse momentum dependence of Collins fragmentation functions and transversity by performing a global analysis of SIDIS and $e^+e^-$ data within a Generalized Parton Model using a Gaussian TMD ansatz. It tests different $Q^2$ evolution schemes for the Collins function and finds that the data can be described with mild or negligible evolution effects due to cancellations in asymmetries. The fit yields a well-constrained $u_v$ transversity distribution and a refined determination of the Collins function width $M_C$, while the disfavoured component remains loosely constrained. BESIII data at low $Q^2$ provide an important cross-check and indicate nonzero Collins effects, reinforcing the need for properly normalised cross sections to disentangle TMD evolution in azimuthal asymmetries.

Abstract

New data from Belle and BaBar Collaborations on azimuthal asymmetries, measured in e+e- annihilations into pion pairs at Q^2=112 GeV^2, allow to take the first, direct glance at the transverse momentum dependence of the Collins functions, in addition to their z dependence. These data, together with available Semi-Inclusive Deep Inelastic Scattering (SIDIS) data on the Collins asymmetry, are simultaneously analysed in the framework of the generalised parton model assuming two alternative Q^2 evolution schemes and exploiting two different parameterisations for the Collins functions. The corresponding results for the transversity distributions are presented. Analogous data, newly released by the BESIII Collaboration, on e+e- annihilations into pion pairs at the lower Q^2 of 13 GeV^2, offer the possibility to explore the sensitivity of these azimuthal correlations on transverse momentum dependent evolution effects.

Figures (15)

• Figure 1: 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 reference fit. The solid lines correspond to the parameters given in Table \ref{['tab:fitpar']}, while the shaded areas correspond to the statistical uncertainty on these parameters, as explained in the text. Notice that, at order $k_\perp/Q$ and $p_\perp/Q$, $x_B=x$ and $z_h=z$.
• Figure 2: The experimental data on the SIDIS azimuthal moment $A_{UT}^{\sin(\phi_h+\phi_S)}$ as measured by the COMPASS Collaboration on proton (upper panel) and deuteron (lower panel) targets Martin:2013ejaAdolph:2014zba, are compared to the curves obtained from our global reference fit. The solid lines correspond to the parameters given in Table \ref{['tab:fitpar']}, while the shaded areas correspond to the statistical uncertainty on these parameters, as explained in the text. Notice that, at order $k_\perp/Q$ and $p_\perp/Q$, $x_B=x$ and $z_h=z$.
• Figure 3: The experimental data on the azimuthal correlations $A_{0}^{UC}$ (left panel) and $A_{0}^{UL}$ (right panel) as functions of $z_1$ and $z_2$ in unpolarised $e^+e^- \to h_1 \, h_2 \, X$ processes, as measured by the Belle Collaboration Seidl:2008xcSeidl:2012er, are compared to the curves obtained from our global reference fit. The solid lines correspond to the parameters given in Table \ref{['tab:fitpar']}, while the shaded areas correspond to the statistical uncertainty on these parameters, as explained in the text.
• Figure 4: The experimental data on the azimuthal correlations $A_{0}^{UC}$ (upper panel) and $A_{0}^{UL}$ (lower panel) as functions of $z_1$ and $z_2$ in unpolarised $e^+e^- \to h_1 \, h_2 \, X$ processes, as measured by the BaBar Collaboration TheBABAR:2013yha, are compared to the curves obtained from our global reference fit. The solid lines correspond to the parameters given in Table \ref{['tab:fitpar']}, while the shaded areas correspond to the statistical uncertainty on these parameters, as explained in the text.
• Figure 5: The experimental data on the azimuthal correlations $A_{0}^{UC}$ (left panel) and $A_{0}^{UL}$ (right panel) as functions of $P_{1T}$ in unpolarised $e^+e^- \to h_1 \, h_2 \, X$ processes, as measured by the BaBar Collaboration TheBABAR:2013yha, are compared to the curves obtained from our global reference fit. The solid lines correspond to the parameters given in Table \ref{['tab:fitpar']}, while the shaded areas correspond to the statistical uncertainty on these parameters, as explained in the text.