New Method of Measuring Electric Dipole Moments in Storage Rings

Abstract

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...

Nuclear electric dipole moment of three-body systems

“…The study of the EDM is particularly important for the simplest few-nucleon systems, the result of which may lead to a better understanding of TRIV effects in heavier nuclei. Moreover, few-nucleon systems meet requirements for a number of proposals to measure EDMs of light nuclei in storage rings [4][5][6][7].…”

Screening of nucleon electric dipole moments in nuclei

“…(12) has to be calculated numerically for each particular nucleus. In this paper we consider the deuteron, which is the simplest system proposed for nuclear EDM measurements in storage rings [12][13][14][15]. In future work, we plan to further investigate the screening of EDMs in heavier nuclei, which would be required for precision calculations of nuclear EDMs.…”

“…Though the measurement of the nuclear EDM without electrons would have less uncertainty from a theoretical point of view, the acceleration of the charged nucleus in an electric field made this approach impractical and most EDM searches have focused on neutral systems. However, with the recent advance in using the fine-tuned momentum technique in storage rings, direct measurements of nuclear EDMs will be feasible in the near future [12][13][14][15].…”

Atomic electric dipole moment induced by the nuclear electric dipole moment: The magnetic moment effect

“…Further motivation for this work comes from the growing interest in measuring nuclear EDMs in ion storage rings [12][13][14][15]. In ions the nuclear EDM is not screened and can be measured directly.…”