Positronium Decay : Gauge Invariance and Analyticity

Abstract

The construction of positronium decay amplitudes is handled through the use of dispersion relations. In this way, emphasis is put on basic QED principles: gauge invariance and soft-photon limits (analyticity). A firm grounding is given to the factorization approaches, and some ambiguities in the spin and energy structures of the positronium wavefunction are removed. Non-factorizable amplitudes are naturally introduced. Their dynamics is described, especially regarding the enforcement of gauge invariance and analyticity through delicate interferences. The important question of the completeness of the present theoretical predictions for the decay rates is then addressed. Indeed, some of those non-factorizable contributions are unaccounted for by NRQED analyses. However, it is shown that such new contributions are highly suppressed, being of order alpha^3. Finally, a particular effective form factor formalism is constructed for parapositronium, allowing a thorough analysis of binding energy effects and analyticity implementation.

34 pages, 13 figures

References in corpus (2)

• The bound mu+ mu- system
• alpha^2 corrections to parapositronium decay

Cited by in corpus (6)

• Two-photon decays of hadronic molecules
• Two-photon decay of P-wave positronium: a tutorial
• Stokes Vector of Photon in the Decays B^0 -> rho^0 gamma and B^0 -> K^* gamma
• Gauge invariant formulation of 3$\gamma$ decay of particle-antiparticle bound states
• A New Basis for QED Bound State Computations
• Thermal corrections for positronium