Implications of unitarity and analyticity for the D\pi form factors

TL;DR

This paper uses dispersion relations, unitarity, and QCD calculations to constrain the shape of D to pi form factors, providing new analytic parametrizations useful for semileptonic decay analysis.

Contribution

It introduces new constraints on Dπ form factors based on unitarity and analyticity, including O(α_s^2) corrections, and proposes improved analytic parametrizations.

Findings

Constraints on form factor shape parameters

Exclusion regions for zeros in the complex plane

New analytic expressions for Dπ form factors

Abstract

We consider the vector and scalar form factors of the charm-changing current responsible for the semileptonic decay D\rightarrow \pi l \nu. 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, we constrain the shape parameters of the form factors and find exclusion regions for zeros on the real axis and in the complex plane. For the scalar form factor, a low energy theorem and phase information on the unitarity cut are also implemented to further constrain the shape parameters. We finally propose new analytic expressions for the $D\pi$ form factors, derive constraints on the relevant coefficients from unitarity and analyticity, and briefly discuss the usefulness of the new parametrizations for describing semileptonic data.