Lepton Dipole Moments

From the famous experiments of Stern and Gerlach to the present, measurements of magnetic dipole moments, and searches for electric dipole moments of “elementary” particles have played a major role in our understanding of sub-atomic physics. In this talk I discuss the progress on measurements and theory of the magnetic dipole moments of the electron and muon. I also discuss a new proposal to search for a permanent electric dipole moment (EDM) of the muon and put it into the more general context of other EDM searches. INTRODUCTION AND THEORY OF THE LEPTON ANOMALIES Over the past 82 years, the study of dipole moments of elementary particles has provided a wealth of information on subatomic physics. From the pioneering work of Stern[1] through the discovery of the large anomalous magnetic moments of the proton[2] and neutron[3], the ground work was laid for the discovery of spin, of radiative corrections and the renormalizable theory of QED, of the quark structure of baryons and the development of QCD. A charged particle with spin~s has a magnetic moment ~μs = gs( e 2m )~s; μ = (1+a) eh̄ 2m ; a ≡ (gs −2) 2 ; (1) where gs is called the gyromagnetic ratio. The expression in the middle is the quantity one finds listed in the Particle Data Tables.[4] The quantity a is the anomalous magnetic dipole moment (or simply the anomaly) which is related to the g-factor in the right-hand equation. The Dirac equation tells us that g ≡ 2 for spin angular momentum, and is unity for orbital angular momentum (the latter having been verified experimentally[6]). This can be seen from the non-relativistic reduction for an electron in a weak magnetic field: ih̄ ∂ψ ∂ t = [ p2 2m − e 2m (~L+2~S)·~B ]