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MPINP:
Research group Z. Harman – Division C. H. Keitel
Abstract:
In this thesis, the theory of the g-factor of bound electrons and muons is presented. For
light muonic ions, we include one-loop self-energy as well as one- and two-loop vacuum
polarization corrections with the interaction with the strong nuclear potential taken into
account to all orders. Furthermore, we include effects due to nuclear structure and mass.
We show that our theory for the bound-muon g-factor, combined with possible future
bound-muon experiments, can be used to improve the accuracy of the muon mass by one
order of magnitude. Alternatively, our approach constitutes an independent access to
the controversial anomalous magnetic moment of the free muon. Furthermore, two-loop
self-energy corrections to the bound-electron g-factor are investigated theoretically to
all orders in the nuclear coupling strength parameter Z alpha. Formulas are derived in the
framework of the two-time Green's function method, and the separation of divergences
is performed by dimensional regularization. Our numerical evaluation by treating the
nuclear Coulomb interaction in the intermediate-state propagators to zero and first order
show that such two-loop terms are mandatory to take into account in stringent tests of
quantum electrodynamics with the bound-electron g-factor, and in projected near-future
determinations of fundamental constants.
