In this paper analytical expressions are derived to describe the spin motion of a particle in magnetic and electric fields in the presence of an axion field causing an oscillating electric dipole moment (EDM). These equations are used to estimate statistical sensitivities for axion searches at storage rings. The estimates obtained from the analytic expressions are compared to numerical estimates from simulations in S.P. Chang et al (Phys.Rev. D99 (2019) no.8, 083002). A good agreement is found.
A hypothetical pseudo-scalar particle axion, which is an immediate result of the Peccei-Quinn solution to the strong CP problem, may couple to gluons and lead to an oscillating electric dipole moment (EDM) of fundamental particles. This paper proposes a novel method of probing the axion-induced oscillating EDM in storage rings, using a radiofrequency (RF) Wien Filter. The Wien Filter at the frequency of the sidebands of the axion and $g-2$ frequency, $f_\text{axion} \pm f_{g-2}$, generates a spin resonance in the presence of an oscillating EDM, as confirmed both by an analytical estimation of …
We respond to a paper of Flambaum, et.al. [Phys. Rev. D95, no. 5, 058701 (2017)], claiming there is no effective induced oscillating electric dipole moment, e.g., for the electron, arising from interaction with an oscillating cosmic axion background via the anomaly. The relevant Feynman amplitude, Fig.(1), as computed by Flambaum et.al., becomes a total divergence, and vanishes. Contrary to this result, we obtained a nonvanishing amplitude, that yields physical electric dipole radiation for an electron (or any magnetic dipole moment) immersed in a cosmic axion field. We argue that the Flambaum…
We report on a search for ultra-low-mass axion-like dark matter by analysing the ratio of the spin-precession frequencies of stored ultracold neutrons and $^{199}$Hg atoms for an axion-induced oscillating electric dipole moment of the neutron and an axion-wind spin-precession effect. No signal consistent with dark matter is observed for the axion mass range $10^{-24}~\textrm{eV} \le m_a \le 10^{-17}~\textrm{eV}$. Our null result sets the first laboratory constraints on the coupling of axion dark matter to gluons, which improve on astrophysical limits by up to 3 orders of magnitude, and also im…
The axion electromagnetic anomaly induces an oscillating electric dipole for {\em any} static magnetic dipole. Static electric dipoles do not produce oscillating magnetic moments. This is a low energy theorem which is a consequence of the space-time dependent cosmic background field of the axion in the limit that it is only locally time dependent $(\overrightarrowβ=0)$. The electron will acquire an oscillating electric dipole of frequency $m_a$ and strength $\sim 10^{-32}$ e-cm, three orders of magnitude above the nucleon, and within four orders of magnitude of the present standard model DC li…
A cosmic axion, via the electromagnetic anomaly, induces an oscillating electric dipole for the electron of frequency $m_a$ and strength $\sim$(few)$\times 10^{-32}$ e-cm, two orders of magnitude above the nucleon, and within a few orders of magnitude of the present standard model constant limit. We give a detailed study of this phenomenon via the interaction of the cosmic axion, through the electromagnetic anomaly, with particular emphasis on the decoupling limit of the axion, $\partial_t a(t)\propto m_a \rightarrow 0$. The analysis is subtle, and we find the general form of the action involv…
We calculate the corrections for constant radial magnetic field in muon g--2 and electric-dipole-moment experiments in storage rings. While the correction is negligible for the current generation of g--2 experiments, it affects the upcoming muon electric-dipole-moment experiment at Fermilab.
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.
Permanent Electric Dipole Moments (EDMs) of elementary particles violate two fundamental symmetries: time reversal invariance (T) and parity (P). Assuming the CPT theorem this implies CP-violation. The CP-violation of the Standard Model is orders of magnitude too small to be observed experimentally in EDMs in the foreseeable future. It is also way too small to explain the asymmetry in abundance of matter and anti-matter in our universe. Hence, other mechanisms of CP violation outside the realm of the Standard Model are searched for and could result in measurable EDMs. Up to now most of the EDM…
A resonance method of measuring the electric dipole moment (EDM) of nuclei in storage rings is described, based on two new ideas: (1) Oscillating particles' velocities in resonance with spin precession, and (2) alternately producing two sub-beams with different betatron tunes--one sub-beam to amplify and thus make it easier to correct ring imperfections that produce false signals imitating EDM signals, and the other to make the EDM measurement.
Analysis of spin dynamics in storage ring electric-dipole-moment (EDM) experiments ascertains that the use of initial vertical beam polarization allows to cancel spin-dependent systematical errors imitating the EDM effect. While the use of this polarization meets certain difficulties, it should be considered as an alternative or supplementary possibility of fulfilling the EDM experiment.
Permanent electric dipole moments (EDMs) violate parity and time reversal symmetry. Within the Standard Model (SM) they are many orders of magnitude below present experimental sensitivity. Many extensions of the SM predict much larger EDMs, which are therefore an excellent probe for the existence of "new physics". Until recently it was believed that only electrically neutral systems could be used for sensitive searches of EDMs. With the introduction of a novel experimental method, high precision for charged systems will be within reach as well. The features of this method and its possibilities…
We present the concept of a compact storage ring of less than 0.5 m orbit radius to search for the electric dipole moment of the muon ($d_μ$) by adapting the "frozen spin" method. At existing muon facilities a statistics limited sensitivity of $d_μ\sim 5 \times 10^{-23} \ecm$ can be achieved within one year of data taking. Reaching this precision would demonstrate the viability of this novel technique to directly search for charged particle EDMs and already test a number of Standard Model extensions. At a future, high-power muon facility a statistical reach of $d_μ\sim 5 \times 10^{-25} \ecm$ …
Electric Dipole Moments (EDMs) of subatomic particles, are considered as one of the most powerful tools to study CP-violation beyond the Standard Model. Such CP-violating mechanisms are searched for to explain the dominance of matter over anti-matter in our universe. This paper discusses EDM searches of charged hadrons in storage rings. The document focuses on activities at the existing storage ring COSY at Forschungszentrum Jülich, Germany and the design of a 100\,m circumference prototype ring able to demonstrate key technologies and components. These include simultaneous clockwise and count…
If the technology for muon storage rings one day permits sensitivity to precession at the order of $10^{-8}$ Hz, the local gravitational field of Earth can be a dominant contribution to the precession of the muon, which, if ignored, can fake the signal for a nonzero muon electric dipole moment (EDM). Specifically, the effects of Earth's gravity on the motion of a muon's spin is indistinguishable from it having a nonzero EDM of magnitude $d_μ\sim 10^{-29}$ e cm in a storage ring with vertical magnetic field of $\sim$ 1 T, which is significantly larger than the expected upper limit in the Standa…
The presence of a permanent electric dipole moment in an elementary particle implies Charge-Parity symmetry violation and thus could help explain the matter-antimatter asymmetry observed in our universe. Within the context of the Standard Model, the electric dipole moment of elementary particles is extremely small. However, many Standard Model extensions such as supersymmetry predict large electric dipole moments. Recently, the muon electric dipole moment has become a topic of particular interest due to the tensions in the magnetic anomaly of the muon and the electron, and hints of lepton-flav…
The Storage Ring EDM Collaboration is completing a comprehensive proposal to DOE for a sensitive proton EDM experiment at the 10-29e\cdot cm level. This involves building an electric ring of radius R~40 m, with bending provided by stainless steel plates separated by 3 cm gap, providing an electric field of 10 MV/m. This ring can store protons of 0.7 GeV/c momentum, also known as "magic" due to the unique property that the spin and momentum vectors precess at the same rate in any electric field. If the spin is kept longitudinal for most of the duration of the storage time, the radial E-field ac…
We show that proton storage ring experiments designed to search for proton electric dipole moments can also be used to look for the nearly dc spin precession induced by dark energy and ultra-light dark matter. These experiments are sensitive to both axion-like and vector fields. Current technology permits probes of these phenomena up to three orders of magnitude beyond astrophysical limits. The relativistic boost of the protons in these rings allows this scheme to have sensitivities comparable to atomic co-magnetometer experiments that can also probe similar phenomena. These complementary appr…
We give the geralized expression of spin precession of extended bunch particles having both anomalous magnetic and electric dipole moments in storage ring in higher order than the previous work and in the presence of ${\bf E}$ field as well as ${\bf B}$ field. These addenda are essential since some experiments consider the focusing field in the second order of the beam extent and in the presence of both ${\bf B}$ and ${\bf E}$ fields . It is shown that some focusing fields with constant magnitude of the velocity considered in many literatures lead to the violation of self consistency.
We give the geralized expression of spin precession of extended bunch particles having both anomalous magnetic and electric dipole moments in storage ring. The transversal betatron oscillation formula of the bunch is also given. The latter is the generalization of the Farley's pitch correction \cite{Farley}, including radial oscillation as well as vertical one. Some useful formulae for muon storage ring are discussed in appendix.
Systematic effects caused by the Berry (geometric) phases in an electric-dipole-moment experiment in an all-electric storage ring are considered. We analyze the experimental setup when the spin is frozen and local longitudinal and vertical electric fields alternate. Due to the Berry phases, the spin rotates about the radial axis. The corresponding systematic error is rather important while it can be canceled with clockwise and counterclockwise beams. The Berry phases also lead to the spin rotation about the radial axis. This effect can be canceled with clockwise and counterclockwise beams as w…
It is shown that the Lorentz transformation cannot in general be formally applied to potentials and fields of particles locked in a certain region. In particular, this property relates to nucleons in nuclei and to particles and nuclei in storage rings. Even if they move with high velocities, their electric fields are defined by the Coulomb law. The result obtained is rather important for the planned deuteron electric-dipole-moment experiment in storage rings.
A new experiment is described to detect a permanent electric dipole moment of the proton with a sensitivity of $10^{-29}e\cdot$cm by using polarized "magic" momentum $0.7$~GeV/c protons in an all-electric storage ring. Systematic errors relevant to the experiment are discussed and techniques to address them are presented. The measurement is sensitive to new physics beyond the Standard Model at the scale of 3000~TeV.
Many experiments are underway in the world to search for a non-zero electric dipole moment (EDM) of a particle with spin 1/2 such as the neutron or the electron. Finding an EDM would reveal new sources of CP violation. EDM measurements are motivated by the high sensitivity to new physics beyond the Standard Model. They are relevant to find the explanation for the matter-antimatter asymmetry of the Universe. A variety of programs with different systems are being pursued, with free neutrons, diamagnetic atoms, paramagnetic systems, and charged particles in storage rings. This article presents a …
Time-reversal breaking and parity-conserving millistrong interactions, suggested in 1965, still remain a viable mechanism of CP-violation beyond the Standard Model. One of its possible manifestations is the T-odd asymmetry in the transmission of tensor-polarized deuterons through a vector-polarized hydrogen gas target. Upon the rotation of the deuteron polarization from the vertical direction into the ring plane, the T-odd asymmetries, odd against the reversal of the proton polarization in the target, will continuously oscillate with first or second harmonics of the spin precession frequency. …
We show that the proposed measurements of the electric dipole moments of light nuclei in storage rings would put strong constraints on models of flavor-diagonal CP violation. Our analysis is exemplified by a comparison of the Standard Model including the QCD theta term, the minimal left-right symmetric model, a specific version of the so-called aligned two-Higgs doublet model, and briefly the minimal supersymmetric extension of the Standard Model. By using effective field theory techniques we demonstrate to what extend measurements of the electric dipole moments of the nucleons, the deuteron, …
Searches of the electric dipole moment (EDM) at a pure magnetic ring, like COSY, encounter strong background coming from magnetic dipole moment (MDM). The most troubling issue is the MDM spin rotation in the so-called imperfection, radial and longitudinal, B-fields. To study the systematic effects of the imperfection fields at COSY we proposed the original method which makes use of the two static solenoids acting as artificial imperfections. Perturbation of the spin tune caused by the spin kicks in the solenoids probes the systematic effect of cumulative spin rotation in the imperfection field…
The proposed method exploits charged particles confined as a storage ring beam (proton, deuteron, possibly $^3$He) to search for an intrinsic electric dipole moment (EDM) aligned along the particle spin axis. Statistical sensitivities could approach 10$^{-29}$ e$\cdot$cm. The challenge will be to reduce systematic errors to similar levels. The ring will be adjusted to preserve the spin polarisation, initially parallel to the particle velocity, for times in excess of 15 minutes. Large radial electric fields, acting through the EDM, will rotate the polarisation from the longitudinal to the verti…
Misplacement of electrostatic elements can pose false EDM signal in a storage ring EDM experiment because of coupling between vertical electric field and magnetic dipole moment. A vertically misplaced quadrupole introduces electric field proportional to its misplacement, changing periodically in the particle's rest frame during the storage. This leads to accumulation of vertical spin component at every revolution. We investigated this effect by simulating a proton in an all-electric ring with several quadrupole scenarios. It turns out that the misplacement of quadrupoles is a critical item to …
Trapped ultracold neutrons (UCN) have for many years been the mainstay of experiments to search for the electric dipole moment (EDM) of the neutron, a critical parameter in constraining scenarios of new physics beyond the Standard Model. Because their energies are so low, UCN preferentially populate the lower region of their physical enclosure, and do not sample uniformly the ambient magnetic field throughout the storage volume. This leads to a substantial increase in the rate of depolarization, as well as to shifts in the measured frequency of the stored neutrons. Consequences for EDM measure…
