Abstract
In this work a method for calculating radiative corrections to positronium decay is presented that is direct, and allows for a systematic extension applicable to the calculation of corrections beyond the first [ o( α)] correction. An expression for the decay amplitude in terms of the Bethe-Salpeter wavefunction is employed. The Bethe-Salpeter wavefunction is evaluated perturbatively in a scheme having a lowest-order bound state equation that is exactly soluble. The decay amplitude is evaluated in Coulomb gauge, without the introduction of a photon mass. One-loop renormalization in Coulomb gauge is shown to be consistent. Using this method the known analytic result for the o( α) correction to the parapositronium decay rate is obtained. The same method is applied to orthopositronium, and the existing theoretical discrepancy in the value of the o( α) correction to the decay rate is resolved. This o( α) correction is obtained with an error which corresponds to an uncertainty in the total rate much smaller than α 2 Γ LO (where Γ LO is the lowest-order rate). Also, the o( α) correction to the differential decay rate is computed for the first time.
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