The $D\pi$ form factors from analyticity and unitarity

TL;DR

This paper employs dispersion relations and unitarity, combined with Operator Product Expansions including higher-order QCD corrections, to analyze the shape parameters of $D\pi$ scalar and vector form factors, constraining their behavior and zero locations.

Contribution

It introduces a novel approach combining dispersion relations, unitarity, and high-order QCD calculations to determine $D\pi$ form factor parameters and zero exclusion regions.

Findings

Determined shape parameters of $D\pi$ form factors.

Identified regions in the complex plane where zeros are excluded.

Enhanced constraints on form factor behavior using phase and low energy theorems.

Abstract

We study the shape parameters of the $D\pi$ scalar and vector form factors using as input dispersion relations and unitarity for the moments of suitable heavy-light correlators evaluated with Operator Product Expansions, including $O(\alpha_s^2)$ terms in perturbative QCD. For the scalar form factor, a low energy theorem and phase information on the unitarity cut are implemented to further constrain the shape parameters. We finally determine points on the real axis and isolate regions in the complex energy plane where zeros of the form factors are excluded.