Gauge invariant formulation of 3$\gamma$ decay of particle-antiparticle bound states

Abstract

We construct the gauge invariant three-photon decay amplitude of particle-antiparticle bound states modeled by the Dyson-Schwinger and Bethe-Salpeter equations. Application to the quark-antiquark ($q\bar{q}$) bound states is emphasized. An essential aspect of our formulation is that it applies to any underlying quantum field theoretic model of the $q\bar{q}$ system, and not just to models, like exact QCD, where the quark self-energy $\Sigma$ couples to the electromagnetic field solely via dressed quark propagators. In this way, applications to effective field theories and other QCD motivated models are envisioned. The three-photon decay amplitude is constructed by attaching currents to all possible places in the Feynman diagrams contributing to the dressed quark propagator. The gauge invariance of our construction is thus a direct consequence of respecting the underlying structure of the quantum field theory determining the dynamics. In the resultant expression for the three-photon decay amplitude, all the basic ingredients consisting of the bound state wave function, the final-state interaction $q\bar{q}$ $t$ matrix, the dressed quark propagator, and dressed quark currents, are determined by a universal Bethe-Salpeter kernel.

33 pages, 11 figures, version accepted for publication in Phys Rev D

References in corpus (15)

• Heavy quarkonium: progress, puzzles, and opportunities
• Infrared Properties of QCD from Dyson-Schwinger equations
• Charmonium
• Precision Study of Positronium: Testing Bound State QED Theory
• Two-photon decays of hadronic molecules
• On covariant nonlocal chiral quark models with separable interactions
• Pion pole light-by-light contribution to g-2 of the muon in a nonlocal chiral quark model
• Beyond Rainbow-Ladder in bound state equations
• The light-by-light contribution to the muon (g-2) from lightest pseudoscalar and scalar mesons within nonlocal chiral quark model
• Nucleon Compton scattering in the Dyson-Schwinger approach
• The role of momentum dependent dressing functions and vector meson dominance in hadronic light-by-light contributions to the muon g-2
• Status of the lepton g-2 and effects of hadronic corrections
• Covariant equations for the tetraquark and more
• Reconciling the nonrelativistic QCD prediction and the $J/\psi \to 3\gamma$ data
• Precision measurements of positronium decay rate and energy level