QED calculation of the dipole polarizability of helium atom

The QED contribution to the dipole polarizability of the He-4 atom was computed, including the effect of finite nuclear mass. The computationally most challenging contribution of the second electric-field derivative of the Bethe logarithm was obtained using two different methods: the integral representation method of Schwartz and the sum-over-states approach of Goldman and Drake. The results of both calculations are consistent, although the former method turned out to be much more accurate. The obtained value of the electric-field derivative of the Bethe logarithm, equal to 0.048 557 2(14) in atomic units, confirms the small magnitude of this quantity found in the only previous calculation [G. Lach, B. Jeziorski, and K. Szalewicz, Phys. Rev. Lett. 92, 233001 (2004)], but differs from it by about 5%. The origin of this difference is explained. The total QED correction of the order of alpha(3) in the fine-structure constant alpha amounts to 30.6671(1) x 10(-6), including the 0.1822 x 10(-6) contribution from the electric-field derivative of the Bethe logarithm and the 0.011 12(1) x 10(-6) correction for the finite nuclear mass, with all values in atomic units. The resulting theoretical value of the molar polarizability of helium-4 is 0.517 254 08(5) cm(3)/mol with the error estimate dominated by the uncertainty of the QED corrections of order alpha(4) and higher. Our value is in agreement with but an order of magnitude more accurate than the result 0.517 254 4(10) cm(3)/mol of the most recent experimental determination [C. Gaiser and B. Fellmuth, Phys. Rev. Lett. 120, 123203 (2018)].