Boost operators in Coulomb gauge QCD: The pion form factor and Fock expansions in $\phi$ radiative decays

Abstract

In this article we re-derive 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 Mœller operators, weighted by the charge density in the target’s rest frame. In addition we remark that the decomposition of the $\eta{^\prime}$ wave function 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.