Determination of pion distribution amplitudes from the electromagnetic form factor with the data-driven dispersion relation

TL;DR

This paper employs a data-driven dispersion relation approach to extract nonperturbative parameters of the pion's light-cone distribution amplitude from electromagnetic form factor data, improving understanding of pion structure.

Contribution

It introduces a model-independent method using dispersion relations combined with QCD calculations to determine pion distribution amplitude parameters from experimental data.

Findings

Chiral mass of pion meson estimated as 1.31 GeV with uncertainties.

Highlights the need for more precise timelike form factor measurements.

Provides a new approach to extract distribution amplitude moments from experimental data.

Abstract

We study the pion electromagnetic form factor in the modulus squared dispersion relation, and do the model independent extraction of the most important nonperturbative parameters in pion light-cone distribution amplitude. The motivation of this work is the recent measurement of timelike form factor in the resonant regions, which makes up the piece lacking solid QCD-based calculation. With the perturbative QCD calculation up to next-to-leading-order QCD corrections and twist four level of meson distribution amplitudes, we obtain the chiral mass of pion meson as $m_0^\pi(1 \, {\rm GeV}) = 1.31^{+0.27}_{-0.30} \, {\rm GeV}$. More accuracy measurement of the timelike form factor are desirable to help us to determine the lowest gegenbauer moments in pion distribution amplitudes with the data-driven dispersion relation method developed in this work.