Towards an Independent Determination of Muon <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mi>g</mml:mi><mml:mo>−</mml:mo><mml:mn>2</mml:mn></mml:mrow></mml:math> from Muonium Spectroscopy

Abstract

We show that muonium spectroscopy in the coming years can reach a precision high enough to determine the anomalous magnetic moment of the muon below one part per million (ppm). Such an independent determination of muon $g\ensuremath{-}2$ would certainly shed light on the $\ensuremath{\sim}2\text{ }\text{ }\mathrm{ppm}$ difference currently observed between spin-precession measurements and ($R$-ratio based) standard model predictions. The magnetic dipole interaction between electrons and (anti)muons bound in muonium gives rise to a hyperfine splitting (HFS) of the ground state which is sensitive to the muon anomalous magnetic moment. A direct comparison of the muonium frequency measurements of the HFS at J-PARC and the 1S-2S transition at PSI with theory predictions will allow us to extract muon $g\ensuremath{-}2$ with high precision. Improving the accuracy of QED calculations of these transitions by about 1 order of magnitude is also required. Moreover, the good agreement between theory and experiment for the electron $g\ensuremath{-}2$ indicates that new physics interactions are unlikely to affect muonium spectroscopy down to the envisaged precision.

Topics & Concepts