DSE Perspective on QCD Modeling, Distribution Amplitudes, and Form Factors

TL;DR

This paper uses Dyson-Schwinger equations to analyze the pion distribution amplitude and electromagnetic form factor, revealing non-perturbative effects and the transition from constituent to partonic quark behavior in QCD.

Contribution

It provides a non-perturbative calculation of the pion distribution amplitude and form factor, highlighting the impact of dynamical chiral symmetry breaking on light-front distributions.

Findings

PDA shows significant dilation due to DCSB

Perturbative QCD underestimates form factor by 15% at high Q^2

Transition from non-perturbative to perturbative behavior identified

Abstract

We describe results for the pion distribution amplitude (PDA) at the non-perturbative scale $\mu=~$2GeV by projecting the Poincar\'e-covariant Bethe-Salpeter wave-function onto the light-front and use it to investigate the ultraviolet behavior of the electromagnetic form factor, $F_\pi(Q^2)$, on the entire domain of spacelike $Q^2$. The significant dilation of this PDA compared to the known asymptotic PDA is a signature of dynamical chiral symmetry breaking (DCSB) on the light front. We investigate the transition region of $Q^2$ where non-perturbative behavior of constituent-like quarks gives way to the partonic-like behavior of quantum chromodynamics (QCD). The non-perturbative approach is based on the Dyson-Schwinger equation (DSE) framework for continuum investigations in QCD. The leading-order, leading-twist perturbative QCD result for $Q^2 F_\pi(Q^2)$ underestimates the new DSE computation by just 15\% on $Q^2\gtrsim 8\,$GeV$^2$, in stark contrast with the result obtained using the asymptotic PDA.