Precision Measurement of the Electron/Muon Gyromagnetic Factors

TL;DR

This paper emphasizes the importance of highly precise measurements of the electron and muon orbital g-factors, reviewing theoretical corrections and analyzing experimental data to suggest small deviations from classical values, with implications for fundamental physics.

Contribution

It introduces a modified Dirac theory predicting linear dependence of g-factors on a parameter and estimates the correction magnitude from experimental data, highlighting the need for ultra-precise measurements.

Findings

Evidence suggests gS may not be exactly 2, indicating quantum effects modify classical values.

Proposed linear correction model for g-factors with an estimated correction DELTA of about 1.0×10^-3.

High-precision measurements are essential to determine true gL values to parts in a trillion.

Abstract

Clear, persuasive arguments are brought forward to motivate the need for highly precise measurements of the electron/muon orbital g, i.e. gL. First, we briefly review results obtained using an extended Dirac equation, which conclusively showed that, as a consequence of quantum relativistic corrections arising from the time-dependence of the rest-energy, the electron gyromagnetic factors are corrected. It is next demonstrated, using the data of Kusch & Foley on the measurement of deltaS minus 2 deltaL together with the modern precise measurements of the electron deltaS where deltaS identically equal to gS minus 2, that deltaL may be a small, non-zero quantity, where we have assumed Russel-Saunders LS coupling and proposed, along with Kusch and Foley, that gS = 2 plus deltaS and gS = 1 plus deltaL. Therefore, there is probable evidence from experimental data that gS is not exactly equal to 1; the expectation that quantum effects will significantly modify the classical value of the orbital g is therefore reasonable. Finally, we show that if, as suggested by the results obtained from the modified Dirac theory, deltaS and deltaL depend linearly on a dimensionless parameter DELTA such that the gyromagnetic factors are considered corrected as follows; gS = 2 plus 2 DELTA and gL = 1 minus DELTA, then the Kusch-Foley data implies that the correction DELTA approximately equals 1.0 times 10-3 . Modern, high precision measurements of the electron and muon orbital gL are therefore required, in order to properly determine by experiments the true value of gL minus 1, perhaps to about one part in a trillion as was recently done for gS minus 2.