Improved theory of helium fine structure

Improved theoretical predictions for the helium fine-structure splitting of $2^3P_J$ levels are obtained by the calculation of the higher order $\alpha^5 $Ry contribution. New results for transition frequencies: $\nu_{01} = 29 616 943.01(17)$ kHz and $\nu_{12} = 2 291 161.13(30)$ kHz significantly disagree with experimental values, thus question the possibility of the determination of the fine structure constant $\alpha$ from a recent series of highly accurate helium measurements.