Collins Asymmetry at Hadron Colliders

TL;DR

This paper investigates the universality of the Collins fragmentation function in hadron production within jets from single-transverse-polarized proton-proton collisions. By analyzing one-gluon and two-gluon exchange diagrams and employing the eikonal approximation plus Ward identity arguments, it shows that the Collins function extracted in pp scattering coincides with that from SIDIS and e^+e^- processes, enabling a factorized spin-dependent cross section as a hard Collins channel times the fragmentation function. The findings indicate that eikonal propagators do not contribute the phase needed for Collins SSAs in fragmentation, in contrast to Sivers-type SSAs, and thus support a model-independent, universal Collins function tied to the gauge link in fragmentation. The work also discusses broader implications for TMD factorization, potential issues in dijet production, and the relevance of twist-three fragmentation contributions for a complete understanding of SSAs in hadronic processes.

Abstract

We study the Collins effect in the azimuthal asymmetric distribution of hadrons inside a high energy jet in the single transverse polarized proton proton scattering. From the detailed analysis of one-gluon and two-gluon exchange diagrams contributions, the Collins function is found the same as that in the semi-inclusive deep inelastic scattering and e^+e^- annihilations. The eikonal propagators in these diagrams do not contribute to the phase needed for the Collins-type single spin asymmetry, and the universality is derived as a result of the Ward identity. We argue that this conclusion depends on the momentum flow of the exchanged gluon and the kinematic constraints in the fragmentation process, and is generic and model-independent.

Figures (6)

• Figure 1: Illustration of the kinematics for the azimuthal distribution of hadrons inside a jet in $pp$ scattering.
• Figure 2: Quark fragmentation to pion production (a), and in $pp$ scattering in a model described in Manohar:1983md (b).
• Figure 3: Universality of the Collins function in $e^+e^-$ (a), deep inelastic scattering (b), and $pp$ scattering (c), when we have dressed quark propagator associated with the fragmenting quark in these processes. The universal Collins function can be calculated from the diagram in (d). The blobs in the diagrams represent the dressed quark propagator in this model.
• Figure 4: Gluon exchange diagrams contributions to the Collins asymmetry in $pp$ collisions. The short bars indicate the pole contributions to the phase needed for a non-vanishing SSA. The additional two cuts in (d) cancel out each other.
• Figure 5: Factorize the contributions from Fig. \ref{['fig2']} into the hard partonic cross section multiplied by the universal Collins fragmentation function. The short bars indicate the pole contribution to the Collins function.