Orderα7ln(1/α)Contribution to Positronium Hyperfine Splitting

The logarithmically enhanced ${\alpha }^7\ln \left(1/\alpha \right)$ contribution to the hyperfine splitting of the positronium ground-state energy levels is calculated in the framework of dimensionally regularized nonrelativistic quantum electrodynamics. The correction is negative and amounts to about 1/3 of the leading logarithmic ${\alpha }^7{ln}^2\left(1/\alpha \right)$ one. The discrepancy between the experimental measurements and the theoretical prediction is reduced.