Nonradiative ${\alpha }^{7}m$ QED effects in the Lamb shift of helium triplet states

Theoretical predictions for the Lamb shift in helium are limited by unknown quantum electrodynamic effects of the order ${\alpha }^{7}m$, where $\alpha$ is the fine-structure constant and $m$ is the electron mass. We make an important step towards the complete calculation of these effects by deriving the most challenging part, which is induced by the virtual photon exchange between all three helium particles, the two electrons and the nucleus. The complete calculation of the ${\alpha }^{7}m$ effect including the radiative corrections will allow comparing of the nuclear charge radii determined from the electronic and muonic helium atoms and thus provide a stringent test of the standard model of fundamental interactions.

Figure 1

Individual time-ordered diagrams contributing to the middle-energy contribution. We note that $E_{10}$ and $E_{15}$ were calculated from Feynman diagrams. The large dot denotes a correction to the vertex according to ${\delta }_{\mathrm{ST}}{H}_{\mathrm{FW}}$ and ${\delta }_{\mathrm{DT}}{H}_{\mathrm{FW}}$, as explicitly shown in Table 1.

Figure 2

Two-photon exchange scattering amplitude.