QED calculation of the dipole polarizability of helium atom

The QED contribution to the dipole polarizability of the ⁴He 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. {}ach, 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 α³ in the fine-structure constant α amounts to 30.6671(1)×10^-6, including the 0.1822×10^-6 contribution from the electric-field derivative of the Bethe logarithm and the 0.0110.16em0ex12(1)×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 0.5170.16em0ex2540.16em0ex08(5)4pt0excm³/mol with the error estimate dominated by the uncertainty of the QED corrections of order α⁴ and higher. Our value is in agreement with but an order of magnitude more accurate than the result 0.5170.16em0ex2540.16em0ex4(10)0.28em0excm³/mol of the most recent experimental determination [C. Gaiser and B. Fellmuth, Phys. Rev. Lett. 120, 123203 (2018)].