Precision Measurement of the Electron/Muon Gyromagnetic Factors

Clear, persuasive arguments are brought forward to motivate the need for highly precise measurements of the electron/muon orbital g, i.e. g$_{L}$, as a test of QED. It is demonstrated, using the data of Kusch {\&} Foley on the measurement of ($\delta _{S}$ - 2$\delta _{L})$ together with the modern precise measurements of the electron $\delta _{S}$ ($\delta _{S}$ $\equiv $ g$_{S}$ -- 2)), that $\delta _{L}$ may be a small (--0.6 x 10$^{-4})$, non-zero quantity, where we have assumed Russel-Saunders (LS) coupling and proposed, along with Kusch and Foley, that g$_{S}$ = 2 + $\delta _{S}$ and g$_{L}$ = 1 + $\delta _{L}$. Therefore, there is probable evidence from experimental data that g$_{L}$ is not equal to 1 exactly; the expectation that quantum effects will significantly modify the classical value of the orbital g is therefore reasonable. It is significant that available spectroscopic data indicate that g$_{S}$ and g$_{L}$ are probably modified such that g$_{S}$ is increased by $\delta _{S}$ while g$_{L}$ is decreased by $\delta _{L}$. Modern, high precision measurements of the electron and muon orbital g$_{L}$ are therefore required, in order to properly determine by experiments the true value of g$_{L}$ -- 1, perhaps to about one part in a trillion as was recently done for g$_{S}$ -- 2.