Helium fine structure theory for determination of α

We present recent progress in the calculation of the helium fine-structure splitting of the 2^3P_J states, based on the quantum electrodynamic theory. Apart from the complete evaluation of m\alpha^7 and m^2/M\alpha^6 corrections, we have performed extensive tests by comparison with all experimental results for light helium-like ions and with the known large nuclear charge asymptotics of individual corrections. Our theoretical predictions are still limited by the unknown m\alpha^8 term, which is conservatively estimated to be 1.7 kHz. However, comparison with the latest experimental result for the 2^3P_0 - 2^3P_2 transition [M. Smiciklas and T. Shiner, Phys. Rev. Lett. 105, 123001 (2010)] suggests that the higher-order contribution is in fact much smaller than the theoretical estimate. This means that the spectroscopic determination of \alpha can be significantly improved if another measurement of the 2^3P_0 - 2^3P_2 transition in helium-like Li^+ or Be^{2+} ion is performed.