# Violation of Positivity Bounds in Models of Generalized Parton Distributions

## TL;DR

This paper demonstrates that common modeling approaches for generalized parton distributions, specifically the impulse approximation, can violate fundamental positivity bounds, highlighting the need for more complete models.

## Contribution

It shows that impulse approximation models of GPDs can violate positivity bounds, emphasizing limitations of Lorentz covariant models in describing pion GPDs.

## Key findings

- Impulse approximation can violate GPD positivity bounds.
- Violation linked to endpoint behavior mismatch.
- Lorentz covariance alone does not ensure positivity.

## Abstract

As with parton distributions, flexible phenomenological parameterizations of generalized parton distributions (GPDs) are essential for their extraction from data. The large number of constraints imposed on GPDs make simple Lorentz covariant models viable; but, such models are often incomplete in that they employ the impulse approximation. Using the GPD of the pion as a test case, we show that the impulse approximation can lead to violation of the positivity bound required of GPDs. We focus on a particular model of the pion bound-state vertex that was recently proposed and demonstrate that satisfying the bound is not guaranteed by Lorentz covariance. Violation of the positivity bound is tied to a problematic mismatch between the behavior of the quark distribution at the endpoint and the crossover value of the GPD.