A review of the experimental and theoretical determinations of the anomalous magnetic moment of the muon is given. The anomaly is defined by a = (g −2)/2, where the Landé g-factor is the proportionality constant that relates the spin to the magnetic moment. For the muon, as well as for the electron and tauon, the anomaly a differs slightly from zero (of order 10 −3 ) because of radiative corrections. In the Standard Model, contributions to the anomaly come from virtual 'loops' containing photons and the known massive particles. The relative contribution from heavy particles scales as the square of the lepton mass over the heavy mass, leading to small differences in the anomaly for e, µ, and τ . If there are heavy new particles outside the Standard Model which couple to photons and/or leptons, the relative effect on the muon anomaly will be ∼ (m µ /m e ) 2 ≈ 43 × 10 3 larger compared with the electron anomaly. Because both the theoretical and experimental values of the muon anomaly are determined to high precision, it is an excellent place to search for the effects of new physics, or to constrain speculative extensions to the Standard Model. Details of the current theoretical evaluation, and of the series of experiments that culminates with E821 at the Brookhaven National Laboratory are given. At present the theoretical and the experimental values are known with a similar relative precision of 0.5 ppm. There is, however, a 3.4 standard deviation difference between the two, strongly suggesting the need for continued experimental and theoretical study.

The anomalous magnetic moment of the negative muon has been measured to a precision of 0.7 ppm (ppm) at the Brookhaven Alternating Gradient Synchrotron. This result is based on data collected in 2001, and is over an order of magnitude more precise than the previous measurement for the negative muon. The result a(mu(-))=11 659 214(8)(3) x 10(-10) (0.7 ppm), where the first uncertainty is statistical and the second is systematic, is consistent with previous measurements of the anomaly for the positive and the negative muon. The average of the measurements of the muon anomaly is a(mu)(exp)=11 659 208(6) x 10(-10) (0.5 ppm).

A new highly sensitive method of looking for electric dipole moments of charged particles in storage rings is described. The major systematic errors inherent in the method are addressed and ways to minimize them are suggested. It seems possible to measure the muon EDM to levels that test speculative theories beyond the standard model. PACS numbers: 13.40. Em, 12.60.Jv, 14.60.Ef, 29.20.Dh The existence of a permanent electric dipole moment (EDM) for an elementary particle would violate parity (P) and time reversal symmetry (T) [1]. Therefore under the assumption of CPT invariance, a non-zero EDM would signal CP violation. In the standard model, the electron EDM is < 10 −38 e · cm [2] with the muon EDM scaled up by the mass ratio m µ /m e , a factor of 207, but some new theories predict much larger values [3,4]. For example, ref.[4] predicts the muon EDM could be as large as 5 × 10 −23 e · cm, while the electron EDM is predicted to be ∼ 10 −28 e · cm, an order of magnitude below the present limit [5]. The current 95% confidence limit for the muon EDM is 10 −18 e·cm [6]. This paper discusses a new way of using a magnetic storage ring to measure the EDM of the muon, which also can be applied to other charged particles.To measure the EDM experimentally, the particle should be in an electric field which exerts a torque on the dipole and induces an observable precession of its spin. If the particle is charged this electric field inevitably accelerates the particle; it will move to a region where the field is zero or leave the scene. An example is the nucleus at the center of an atom in equilibrium; the net force and therefore the net electric field at the nucleus must average to zero according to Schiff's theorem [7]. Any applied external electric field will be shielded from the nucleus by the electrons in the atom. The overall effect is to suppress the EDM signal, making it more difficult to measure. The suppression would be total but for the many known exceptions to Schiff's theorem when weak and strong forces, weak electron-nucleon forces, finite particle sizes, and relativistic effects are included. Suppression of the EDM signal by Schiff's theorem is completely avoided in a magnetic storage ring [8,9] such as proposed here, because the particle is not in equilibrium; there is a net centripetal force, and this force is entirely supplied by a net electric field as seen in the muon rest frame.In particular, when a muon of velocity β = v/c and relativistic mass factor γ = (1 − β 2 ) − 1 2 is circulating in a horizontal plane due to a vertical magnetic field B, it will according to a Lorentz transformation experience both an electric and a magnetic field, E * and B * , in its own rest frame. The so-called motional electric field, E * = γc β × B, can be much larger than any practical applied electric field. Its action on the particle supplies the radial centripetal force, Thomas spin precession, and spin precession due to any non-vanishing EDM. B * produces precession due to the muon magnetic moment. The combined spi...

Three independent searches for an electric dipole moment (EDM) of the positive and negative muons have been performed, using spin precession data from the muon g À 2 storage ring at Brookhaven National Laboratory. Details on the experimental apparatus and the three analyses are presented. Since the individual results on the positive and negative muons, as well as the combined result, d ¼ ð0:0 AE 0:9Þ Â 10 À19 e cm, are all consistent with zero, we set a new muon EDM limit, jd j < 1:8 Â 10 À19 e cm (95% C.L.). This represents a factor of 5 improvement over the previous best limit on the muon EDM.

We review the status of the theoretical and experimental determinations of the muon magnetic moment anomaly, a μ = ( g μ − 2)/2. We discuss future experimental efforts, as well as implications for physics beyond the Standard Model that come from past and future experiments.