Lorentz invariance relations between parton distributions and the Wandzura-Wilczek approximation

TL;DR

The paper investigates Lorentz invariance relations (LIRs) between forward parton distributions and their possible violation due to gauge-link effects. It shows, in a model-independent way, that LIRs are not violated within a generalized Wandzura-Wilczek (WW) approximation which neglects certain quark-gluon-quark correlations and current-quark masses. The authors derive explicit WW-type relations such as $g^{(1)}_{1T}(x) \approx x \int_x^1 \frac{dy}{y} g_1(y)$ and $h^{\perp(1)}_{1L}(x) \approx -x^2 \int_x^1 \frac{dy}{y^2} h_1(y)$, and show that the LIR violations vanish ($\Delta_g(x)\approx 0$, $\Delta_h(x)\approx 0$) in this framework. These findings suggest LIRs can serve as useful approximations in phenomenology of SIDIS and Drell-Yan processes, though experimental tests and process dependence remain essential for validation.

Abstract

The violation of the so-called Lorentz invariance relations between parton distribution functions is considered in a model independent way. It is shown that these relations are not violated in a generalized Wandzura-Wilczek approximation, indicating that numerically their violation may be small.