The Hydrogen Lamb Shift and the Proton Radius

The Lamb shift measurement and theory are now both a dynamically developing field and we give a review of the current data. Critical comparison of theory and experiment can be done using a value of the proton charge radius and we pay attention to several results of its determination. The talk is devoted to the Lamb shift in the hydrogen atom. The workshop is for exotic atoms and first of all I would like to say that to my mind the hydrogen is one of them. The possibility both to calculate and to measure different energy intervals with extremely high accuracy make hydrogen a quite exotic system. Next, one has to remember that there is actually no special separate theory of the positronium or muonium atom, investigations of which were discussed here in detail. The same expression can be of use in a number of calculations for several atomic systems (see e. g. Refs. 1, 2. One more point which is quite similar to the pionium and pionic hydrogen is that we investigate an atomic system but after all the result is important for particle physics, namely for the proton charge radius. All of these reasons show that hydrogen atomic properties are to be discussed among exotic ones. The workshop talk is based on a Max-Planck-Institut für Quantenoptik report 3 and all references can be found there. The hydrogen atom is one of the most important QED systems. In contrast to muonium and positronium the nucleus is a proton and hence the energy of the level is influenced by the proton structure, i. e. by the strong interaction. The knowledge of the proton radius leads now to a limit of the theoretical value for the Lamb shift. We discuss here the problem of the radius determination, the most popular values of which are summarized in Table 1. We give a critical review of all of these values, as well as of the theory and the experiment on the Lamb shift. Let us briefly describe all items of the Table 1. The elastic electron-proton scattering data were obtained with small momentum transfer and were extrapolated to zero momentum. The other way to extract the radius from such data is based on a dispersion relation approach which allows to involve data from other kinematic areas into fitting. The numerical calculation within the chiral limit of the lattice QCD can be corrected due to the chiral perturbative theory . And indeed one of the ways to determine the radius is based on the hydrogen Lamb shift investigation. First we mention that we expect that the uncertainties presented in Table 1 accordingly to the original works 4, 6, 7 are significant underestimations and we will not consider those anymore here. The details can be found in our review 3. E-mail: [email protected]; [email protected]