An $α^{2}(Z α)^{5}m$ Contribution to the Hydrogen Lamb Shift from Virtual Light by Light Scattering

Abstract

The radiative correction to the Lamb shift of order $α^{2}(Zα)^5m$ induced by the light by light scattering insertion in external photons is obtained. The new contribution turns out to be equal to $-0.122(2)α^2(Zα)^5/(πn^3)(m_r/m)^3m$. Combining this contribution with our previous results we obtain the complete correction of order $α^{2}(Zα)^5m$ induced by all diagrams with closed electron loops. This correction is $37.3(1)$ kHz and $4.67(1)$ kHz for the $1S$- and $2S$-states in hydrogen, respectively.