Positivity bounds on generalized parton distributions in impact parameter representation

TL;DR

The paper derives an infinite set of positivity bounds for generalized parton distributions (GPDs) using the impact parameter representation. By formulating the bounds from the positive semidefinite norm of hadronic states, it shows these inequalities are preserved under one-loop evolution to higher scales. Specializing to nucleon GPDs $H$ and $E$, the authors obtain explicit constraints that connect GPDs to forward parton distributions and reproduce several known bounds (e.g., Burkardt, Diehl, PST, Pobylitsa) as special cases, while also yielding new relations. The work also addresses renormalization considerations, arguing that positivity can be maintained with suitable regularizations, making these bounds a practical tool for modeling GPDs in hard exclusive processes.

Abstract

New positivity bounds are derived for generalized (off-forward) parton distributions using the impact parameter representation. These inequalities are stable under the evolution to higher normalization points. The full set of inequalities is infinite. Several particular cases are considered explicitly.

Figures (2)

• Figure 1: Longitudinal momentum flow corresponding to variables $x,\xi$ [in units of $(P_{1}^{+}+P_{2}^{+})/2$ ].
• Figure 2: Diagram representing the evolution kernel $K_{\beta_{1}\beta_{2}}^{\alpha_{1}\alpha_{2}}(x_{1},y_{1};x_{2},y_{2})$ at $0<x_{k}<y_{k}$.