Twist-3 transverse momentum dependent gluon distributions in a spectator model

We study the twist-3 transverse momentum dependent distributions of gluons in a nucleon within a spectator model framework. In this model, the nucleon is described as emitting a virtual (time-like) gluon and an on-shell spectator particle, with the spectator mass treated continuously via a spectral function. The twist-3 gluon-gluon correlators, $\Phi^{+i;+-}$ and $\Phi^{ij;l+}$, are parameterized by a set of complex functions, whose real and imaginary parts correspond to T-even and T-odd components, respectively. We numerically check the equation of motion relation for these distributions and find that relation holds fairly well in the spectator model.