The two-loop Lamb shift

As can be seen from Table 1, the CH result for the transition, 2787.997 eV, is consistent with all other potentials within 0.01 eV. Adding in small three-photon and recoil corrections of -0.033 eV gives a final theoretical prediction of 2787.964 eV for the CH potential. As this disagrees with experiment, new physics must be present. The source of this physics is well known from the hydrogen Lamb shift, where two-loop effects are known to be quite important, and in fact are at present the dominant source of uncertainty, with the only other major unknown in the calculation being the precise size of the proton. We infer, then, 

The two-loop diagrams, two of which are shown in Fig. 4, are by far the most difficult to evaluate. They were first treated for the high-Z case in some detail in Ref. [35], which however presented only a partial result. Certain terms were of the form of the one-loop Lamb shift, but with one 

The purpose of the preceding discussion of this particular transition in lithiumlike Bismuth was to show that use of the Furry representation firstly allows a consistent implementation of QED for the many-electron problem, with both correlation and radiative effects treated as Feynman diagrams, and secondly to show that when the extra expansion parameter 1/Z is present that extremely precise predictions result that agree well with experiment. There is no reason in principle, therefore, that QED cannot be applied to all atoms and molecules. In practice, however, without the rapid convergence provided by factors of 1/Z, the utility of this approach for neutral systems can be questioned. The best way to combine many-body methods and QED in this case is one of the forefront problems of the field. We now turn to a neutral system, the cesium atom, and describe the progress that has been made in the search for new physics in this much more challenging case. 

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