QED calculation of the dipole polarizability of helium atom

The QED contribution to the dipole polarizability of the $^4$He atom was\ncomputed, including the effect of finite nuclear mass. The computationally most\nchallenging contribution of the second electric-field derivative of the Bethe\nlogarithm was obtained using two different methods: the integral representation\nmethod of Schwartz and the sum-over-states approach of Goldman and Drake. The\nresults of both calculations are consistent, although the former method turned\nout to be much more accurate. The obtained value of the electric-field\nderivative of the Bethe logarithm, equal to $0.048\\,557\\,2(14)$ in atomic\nunits, confirms the small magnitude of this quantity found in the only previous\ncalculation [G. {\\L}ach, B. Jeziorski, and K. Szalewicz, Phys. Rev. Lett. 92,\n233001 (2004)], but differs from it by about 5\\%. The origin of this difference\nis explained. The total QED correction of the order of {\\alpha} 3 in the\nfine-structure constant {\\alpha} amounts to 30.6671(1)$\\cdot 10^{-6}$,\nincluding the 0.1822$\\cdot 10^{-6}$ contribution from the electric-field\nderivative of the Bethe logarithm and the 0.01112(1)$\\cdot 10^{-6}$ correction\nfor the finite nuclear mass, with all values in atomic units. The resulting\ntheoretical value of the molar polarizability of helium-4 is\n$0.517\\,254\\,08(5)\\,$cm$^3$/mol with the error estimate dominated by the\nuncertainty of the QED corrections of order $\\alpha^4$ and higher. Our value is\nin agreement with but an order of magnitude more accurate than the result\n$0.517\\, 254\\, 4(10)\\,$cm$^3$/mol of the most recent experimental determination\n[C. Gaiser and B. Fellmuth, Phys. Rev. Lett. 120, 123203 (2018)].\n