Pion electromagnetic form factor at spacelike momenta

TL;DR

This paper introduces a new Dyson-Schwinger equation method to compute the pion electromagnetic form factor across all spacelike momenta, revealing the significant role of dynamical chiral symmetry breaking in QCD.

Contribution

The work presents a unified DSE-based approach to predict the pion form factor and parton distribution amplitude, improving understanding of QCD dynamics at high momentum transfers.

Findings

Q^2 F_(Q^2) is underestimated by 15% using leading-order perturbative QCD at Q^2>8 GeV^2

Hard contributions dominate for Q^2>8 GeV^2, but the form factor still reflects dynamical chiral symmetry breaking

The DSE framework unifies predictions of the pion form factor and parton distribution amplitude

Abstract

A novel method is employed to compute the pion electromagnetic form factor, F_\pi(Q^2), on the entire domain of spacelike momentum transfer using the Dyson-Schwinger equation (DSE) framework in quantum chromodynamics (QCD). The DSE architecture unifies this prediction with that of the pion's valence-quark parton distribution amplitude (PDA). Using this PDA, the leading-order, leading-twist perturbative QCD result for Q^2 F_\pi(Q^2) underestimates the full computation by just 15% on Q^2>~8GeV^2, in stark contrast with the result obtained using the asymptotic PDA. The analysis shows that hard contributions to the pion form factor dominate for Q^2>~8GeV^2 but, even so, the magnitude of Q^2 F_\pi(Q^2) reflects the scale of dynamical chiral symmetry breaking, a pivotal emergent phenomenon in the Standard Model.