Orderα3ln(1/α)Corrections to Positronium Decays

The logarithmically enhanced ${\alpha }^3\ln \left(1/\alpha \right)$ corrections to the para- and 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 ${\alpha }^3{ln}^2\left(1/\alpha \right)$ one, and is comparable to the nonlogarithmic $O\left({\alpha }^2\right)$ one. As for orthopositronium, the correction is positive and almost cancels the ${\alpha }^3{ln}^2\left(1/\alpha \right)$ one. The uncertainty in the theoretical prediction for the parapositronium decay width is reduced to ${10}^{-2\mathrm{}}\mu {\mathrm{s}}^{-1\mathrm{}}$.