Theory of Loosely Bound Composite Systems: Multiloop Corrections to Lamb Shift, Hyperfine Splitting, and g-Factors

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High precision experiments with two-body bound systems have achieved a new level of accuracy in recent years and further progress is expected. The experimental errors of measurements of energy shifts in hydrogen, muonium and other simple hydrogenlike ions were reduced by orders of magnitude. These recent developments opened new perspectives for precise determination of many fundamental constants (the Rydberg constant, electron-muon mass ratio, electron mass in atomic units, proton charge radius,deuteron structure radius, etc.), and for comparison of the experimental and theoretical results on the Lamb shifts and hyperfinne splitting.The experimental progress poses new theoretical challenges. Reduction of the theoretical error of the value of the 1S Lamb shift in hydrogen to the level below 1 kHz (and, respectively, of the 2S Lamb shift to below several tenth of kHz) should be considered as a next stage of the theory. The theoretical error of the hyperfine splitting in muonium should be reduced to about 10 Hz. The theoretical error of the 2S 2P Lamb shift in muonic hydrogen should be reduced below 0:001 meV. The problem of the spin dependence of the bound state corrections to g factors should be resolved.The following major problems in the theory of low Z systems will be addressed in the proposed research: Three-loop nonrecoil corrections to the Lamb shift and hyperfine splitting in hydrogen and muoinium. Three-loop radiative-recoil corrections to hyperfine splitting in muonium. Nonrecoil high-order corrections to the Lamb shift in muonic hydrogen and the binding and recoil corrections to the bound g factor in systems including particles with spins j 6= 1=2.Modern methods of perturbative quantum electrodynamics will be used to perform all of the calculations.