Collins fragmentation function from gluon rescattering

TL;DR

The paper investigates the Collins fragmentation function $H_1^{\perp}$ by incorporating gluon rescattering to generate the necessary T-odd phase within a chiral-invariant fragmentation framework. All one-loop gluon corrections, including gauge-link contributions, are computed, and the resulting imaginary parts are assembled to yield $H_1^{\perp}$ and its first two moments. Three of the four gluon-loop diagrams contribute with magnitudes comparable to the pion-rescattering mechanism but with opposite sign, leading to a sign reversal relative to the pion-loop result and implying potential cancellations in observed asymmetries. While the findings highlight the significant role of gluon dynamics in shaping $H_1^{\perp}$, they are model-dependent and rely on a perturbative expansion at relatively low $Q^2$, warranting cautious interpretation for phenomenology in SIDIS and $e^+e^-$ processes.

Abstract

We estimate the Collins fragmentation function by introducing the effect of gluon rescattering in a model calculation of the fragmentation process. We include all necessary diagrams to the one-loop level and compute the nontrivial phases giving rise to the Collins function. We compare our results to the ones obtained from pion rescattering. We conclude that three out of four one-loop diagrams give sizeable contributions to the Collins function, and that the effect of gluon rescattering has a magnitude comparable to that of pion rescattering, but has opposite sign.

Figures (5)

• Figure 1: Single gluon-loop corrections to the fragmentation of a quark into a pion contributing to the Collins function. The Hermitian conjugate diagrams (H. c.) are not shown explicitly.
• Figure 2: One-loop self-energy, pion vertex, box, and photon vertex corrections.
• Figure 3: Result for $H_1^{\perp (1/2)}/D_1$ including only the self-energy and vertex gluon-loop corrections (solid line) and comparison with the result of the pion-loop model (dashed line) from Ref. Bacchetta:2002tk.
• Figure 4: Result for $H_1^{\perp (1/2)}/D_1$ including all gluon-loop contributions (solid line) and comparison with the result of the pion-loop model (dashed line) from Ref. Bacchetta:2002tk.
• Figure 5: Result for $H_1^{\perp (1)}/D_1$ including all gluon-loop contributions (solid line) and comparison with the result of the pion-loop model (dashed line) from Ref. Bacchetta:2002tk.