Order α ln(1/α) Corrections to Positronium Decays

The logarithmically enhanced α3 ln(1/α) corrections to the paraand orthopositronium decay widths are calculated in the framework of dimensionally regularized nonrelativistic quantum electrodynamics. In the case of parapositronium, the correction is negative, approximately doubles the effect of the leading logarithmic α3 ln(1/α) one, and is comparable to the nonlogarithmic O(α2) one. As for orthopositronium, the correction is positive and almost cancels the α3 ln(1/α) one. The uncertainties in the theoretical predictions for the decay widths are reduced to 10−2μs−1 for parapositronium and to 10−5μs−1 for orthopositronium. PACS numbers: 12.20.Ds, 31.30.Jv, 36.10.Dr ∗Permanent address: Institute for Nuclear Research, Russian Academy of Sciences, 60th October Anniversary Prospect 7a, Moscow 117312, Russia. Positronium (Ps), which is an electromagnetic bound state of the electron e and the positron e, is the lightest known atom. Since its theoretical description is not plagued by strong-interaction uncertainties, thanks to the smallness of the electron mass me relative to typical hadronic mass scales, its properties can be calculated perturbatively in quantum electrodynamics (QED), as an expansion in Sommerfeld’s fine-structure constant α, with very high precision. Ps is thus a unique laboratory for testing the QED theory of weakly bound systems. The decay widths of the S0 parapositronium (p-Ps) and S1 orthopositronium (oPs) ground states to two and three photons, respectively, have been the subject of a vast number of theoretical and experimental investigations. The present theoretical knowledge may be summarized as: