Precise Matter and Antimatter Tests of the Standard Model with $${\mathrm{{e}}}^{-}, {\mathrm{{e}}}^{+}, {\mathrm{{p}}}, \,\overline{\mathrm{{p}}}$$ and $$\overline{\mathrm{{H}}}$$

Abstract

Extremely precise tests of the Standard Model of particle physics and its CPT theorem come from low energy measurements of the electron, positron, proton and antiproton magnetic moments and charge-to-mass ratios. Ground state antihydrogen atoms are now available for measurements that could eventually reach a higher precision, though no precise $$\mathrm{\overline{H}}$$ measurements have yet been carried out. After a brief summary of the results and status of such measurements, the focus is upon the most precisely measured and precisely calculated property of an elementary particle. The electron magnetic moment, measured to $$3$$ parts in $$10^{13}$$ , is a probe of the interaction of the electron with the fluctuating vacuum described by quantum electrodynamics (QED). It is also a probe for electron substructure not predicted by the Standard Model. The measured magnetic moment, together with fine structure constant determined by a different method, is the most stringent test of QED and the Standard Model of particle physics. The measured magnetic moment and QED theory together yield the most precise measured value of the fine structure constant. The summary includes the antiproton magnetic moment that was recently measured precisely for the first time. The $$4$$ parts in $$10^6$$ precision is much less than the electron precision or the $$9$$ parts in $$10^{11}$$ at which the antiproton and proton charge-to-mass ratios have been compared, but very large increases in precision seem possible as quantum methods are incorporated.