Boost operators in Coulomb-gauge QCD: the pion form factor and Fock expansions in phi radiative decays

TL;DR

This paper rederives boost operators in Coulomb-gauge QCD, revealing that traditional interpretations of pion charge radii are obscured by relativistic effects, and discusses implications for meson wavefunction decompositions in radiative decays.

Contribution

It provides a complete formulation of boost operators in Coulomb-gauge QCD and analyzes their impact on interpreting pion form factors and meson wavefunction decompositions.

Findings

Pion charge radii are blurred by relativistic and interaction corrections.

The pion form factor measures matrix elements of boost operators, not charge distribution.

Velocity corrections are crucial for meson wavefunction analyses in radiative decays.

Abstract

In this article we rederive the Boost operators in Coulomb-Gauge Yang-Mills theory employing the path-integral formalism and write down the complete operators for QCD. We immediately apply them to note that what are usually called the pion square, quartic... charge radii, defined from derivatives of the pion form factor at zero squared momentum transfer, are completely blurred out by relativistic and interaction corrections, so that it is not clear at all how to interpret these quantities in terms of the pion charge distribution. The form factor therefore measures matrix elements of powers of the QCD boost and Moeller operators, weighted by the charge density in the target's rest frame. In addition we remark that the decomposition of the eta' wavefunction in quarkonium, gluonium, ... components attempted by the KLOE collaboration combining data from phi radiative decays, requires corrections due to the velocity of the final state meson recoiling against a photon. This will be especially important if such decompositions are to be attempted with data from J/psi decays.