Some Inequalities for the Generalized Parton Distribution E(x,0,t)

TL;DR

This paper derives positivity-based constraints on the generalized parton distribution $E(x,0,t)$ by working in impact parameter space and relating $E$ to forward PDFs. The main results are inequalities that bound integrals and the value of $E$ in terms of $q_\pm(x)$ and the slope of $H_+(x,0,t)$ at $t=0$, making the constraints more directly usable with data. In the $x\to1$ limit, $E(x,0,0)$ is shown to vanish faster than the unpolarized distribution, and the authors provide a bound on the second moment of $E$, offering a practical way to limit $E$'s contribution to the quark angular momentum sum rule. Overall, these momentum-space inequalities enhance model-independent constraints on $E$ and its role in nucleon spin structure.

Abstract

We discuss some constraints on the $x$ and $t$-dependence of $E(x,0,t)$ that arise from positivity bounds in the impact parameter representation. In addition, we show that $E(x,0,0)$ for the nucleon vanishes for $x\to 1$ at least as rapidly as $(1-x)^4$. Finally we provide an inequality that limits the contribution from $E$ to the angular momentum sum rule.