Sixth-Order Vacuum-Polarization Contribution to the Lamb Shift of the Muonic Hydrogen

Abstract

The sixth-order electron-loop vacuum-polarization contribution to the $2P_{1/2}-2S_{1/2}$ Lamb shift of the muonic hydrogen (${\mu }^{-}{p}^{+}$ bound state) has been evaluated numerically. Our result is 0.007608(1) meV. This eliminates the largest uncertainty in the theoretical calculation. Combined with the proposed precision measurement of the Lamb shift it will lead to a very precise determination of the proton charge radius.

arXiv comment4 pages, 5 figures the totoal LS number is changed

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• Chiral Corrections to Lattice Calculations of Charge Radii
• Massive Quark Production in Electron Positron Annihilation to Order ${\alpha }_s^2$

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• Proton Polarization Shifts in Electronic and Muonic Hydrogen
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• Relativistic and Recoil Corrections to Light-Fermion Vacuum Polarization for Bound Systems of Spin-0, Spin-1/2, and Spin-1 Particles
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