We present the final report from a series of precision measurements of the muon anomalous magnetic moment, a µ = (g − 2)/2. The details of the experimental method, apparatus, data taking, and analysis are summarized. Data obtained at Brookhaven National Laboratory, using nearly equal samples of positive and negative muons, were used to deduce a µ (Expt) = 11 659 208.0(5.4)(3.3) × 10 −10 , where the statistical and systematic uncertainties are given, respectively. The combined uncertainty of 0.54 ppm represents a 14-fold improvement compared to previous measurements at CERN. The standard model value for a µ includes contributions from virtual QED, weak, and hadronic processes. While the QED processes account for most of the anomaly, the largest theoretical uncertainty, ≈ 0.55 ppm, is associated with first-order hadronic vacuum polarization. Present standard model evaluations, based on e + e − hadronic cross sections, lie 2.2 -2.7 standard deviations below the experimental result.

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High precision measurements of the ground state hyperfine structure interval of muonium and of the muon magnetic moment

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.