Muonic vacuum polarization correction to the bound-electron $g$-factor

Abstract

The muonic vacuum polarization contribution to the g-factor of the electron bound in a nuclear potential is investigated theoretically. The electric as well as the magnetic loop contributions are evaluated. We found these muonic effects to be observable in planned trapped-ion experiments with light and medium-heavy highly charged ions. The enhancement due to the strong Coulomb field boosts these contributions much above the corresponding terms in the free-electron g-factor. Due to their magnitude, muonic vacuum polarization terms are also significant in planned determinations of the fine-structure constant from the bound-electron g-factor.

Light-by-light scattering in the Lamb shift and the bound electron g factor

“…Numerically, (14) gives g ML (muon) = 5.5 • 10 −22 for hydrogen, Z = 1, and 4.3 • 10 −18 for Z = 6, the much studied carbon ion. Both numbers are about two orders of magnitude smaller than the values given in [25]. Thus, contrary to the conclusion [25], we believe that the effect of the magnetic muon loop is too small to discern because of nuclear uncertainties.…”

“…Both numbers are about two orders of magnitude smaller than the values given in [25]. Thus, contrary to the conclusion [25], we believe that the effect of the magnetic muon loop is too small to discern because of nuclear uncertainties.…”

“…Here we reevaluate the magnetic loop, Fig. 5, that on the basis of the results in [25] seems easiest to confirm experimentally among the LBL effects induced by virtual muons. We find its contribution to be…”

“…This results in an effect O α(Zα) 5 , already evaluated in [23,24]. Recently [25] the contribution of virtual muon loops to the bound electron g-factor has been computed. Here we reevaluate the magnetic loop, Fig.…”