Twist-3 T-odd fragmentation functions $G^\perp$ and $\tilde{G}^\perp$ in a spectator model

TL;DR

This paper calculates twist-3 T-odd fragmentation functions $G^ot$ and $ ilde{G}^ot$ within a spectator model, incorporating gluon exchange effects to understand their contributions and relations to the Collins function.

Contribution

It introduces a calculation of twist-3 T-odd fragmentation functions including gluon exchange effects, and verifies their relation to the Collins function within a spectator model.

Findings

Gluon loops generate non-zero contributions to $G^ot$ and $ ilde{G}^ot$.

Numerical half-$k_T$ moments of the functions are obtained.

The equation of motion relation among the functions and the Collins function is verified.

Abstract

We present a calculation of the twist-3 T-odd chiral-even fragmentation functions $G^{\perp}$ and $\tilde{G}^{\perp}$ using a spectator model. We consider the effect gluon exchange to calculate all necessary one-loop diagrams for the quark-quark and quark-gluon-quark correlation functions. We find that the gluon loops corrections generate non-zero contribution to these two fragmentation function. We numerically calculate their half-$k_T$ moments by integrating over the transverse momentum and also verify the equation of motion relation among $G^{\perp}$, $\tilde{G}^{\perp}$ and the Collins function.