Storage Ring Electric Dipole Moment Experiments: The Case for a Deuteron EDM
By Yannis Semertzidis
Even though the possession of a non-zero value of a magnetic dipole moment (MDM) by a fundamental particle is common place there is not a single case observed so far for the possession of an electric dipole moment (EDM). Such an observation would have a profound implication about our understanding of the universe because it would point to a new, large source of CP-violation (the combined charge (C) and parity (mirror reflection, P) symmetries); much bigger than what is allowed by the standard model (SM). The observation in the near future of a non-zero EDM of a fundamental particle would point to new physics, beyond the SM, and at the same time could help solve the mystery of the baryon asymmetry of our universe (BAU).
The study of the bare nucleus of the deuteron and proton in a storage ring would be the first sensitive experiment of a charged particle directly using the strong electric field present in the particle’s rest frame. The deuteron EDM (dEDM) at the 10-29e∙cm level would be the best sensitivity hadronic EDM experiment. It will probe new physics at the 103 TeV mass scale and, if new physics is discovered at the LHC, it will probe the CP-violating phases at the 10-5 rad level, both of which are beyond the design sensitivity of LHC.
There are several neutron EDM (nEDM) experiments underway with the most ambitious one having a sensitivity goal of 10-28 e∙cm. Therefore the question why do the deuteron EDM rises naturally. The deuteron is the simplest nucleus, a weakly bound proton and neutron, predominantly in 3S1 state with a small contribution from the D-state. The deuteron is special compared to the nEDM because one has the possibility to study the T-odd and P-odd nucleon-nucleon interaction in a sensitive manner. It is estimated that the isovector part of this interaction contributes to the dEDM by more than an order of magnitude than the same interaction contributes to the nEDM. In contrast the classical θQCD term contribution to the dEDM is only about 1/3 of the same contribution to the nEDM. The dEDM is therefore better and complementary to the nEDM since it is sensitive to a different linear combination of CP-violating sources.
Quantum mechanics requires that in any particle with spin the EDM vector is proportional to the spin vector. The interaction energy of a particle with an EDM (d) in an electric field is given by the scalar product of the EDM and the electric field. Applying the T-symmetry we get:
indicating that a non-zero value of an EDM requires the violation of T-symmetry. Similarly the application of the parity symmetry (P) gives:
indicating again that a non-zero EDM value requires parity violation as well. Assuming the conservation of the combined CPT symmetry, T-violation also means CP-violation.
The study of EDMs started with the study of the neutron by Ramsey and Purcell in the 1950s, improving the EDM limits to ever smaller value since then. Even though no EDM has been found so far, every new theoretical model had to conform to those limits and the claim is that no other experimental method killed so many theoretical models as the strict experimental EDM limits did. The SM contribution to the CP-violation is several orders of magnitude below the current experimental limit whereas most of the physics beyond the SM predict values in the neighborhood of the current experimental limits. EDMs are therefore excellent probes of physics beyond the SM.
In addition, EDMs could also shed light into another mystery. The current ratio of the number of baryons to photons is inferred by observations to be approximately 10-10 whereas the SM predicts a value several orders of magnitude less. An EDM of a fundamental particle would point to a new CP-violating source that could help solve the BAU mystery.
Magnetic dipole moments couple to magnetic fields and electric dipole moments couple to electric fields. The spin precession in the presence of magnetic and electric fields is given by:
The usual experimental approach for searching for an EDM is to apply a strong electric field and look for a change in the spin precession rate when flipping the direction of the electric field. The advantage of using the rest frame electric field of a relativistically moving particle in a magnetic storage ring is that the strength of such a field can be much larger than is possible to have in the laboratory. For example the equivalent electric field present in the rest frame of a relativistic particle moving in a 2 T magnetic field is 600 MV/m; much bigger than what is possible in the lab. The statistical accuracy is given by:
with β the particle velocity, B the magnetic field, P the beam polarization and A the spin analyzing power, N the number of particles in the ring per injection cycle, τ the spin coherence time and T the lifetime of the experiment. It is therefore important to keep the velocity, the polarization, the analyzing power, the number of particles injected into the ring/cycle, the spin coherence time and the total running time of the experiment as large as possible. Satisfying all those (sometimes competing) requirements while at the same time minimizing the systematic errors is an exceptional task that requires extensive studies by the experts in the corresponding fields. Brookhaven National Laboratory is presently the most appropriate lab to host such an experiment since there is experience with high intensity polarized beams as the host of the only polarized proton collider in the world, a world class facility.
A proposal describing the latest version of the EDMs in storage rings is given in reference  referring to an idea by Yuri Orlov of Cornell University to use longitudinally polarized deuteron beams with a synchrotron tune in resonance with the spin tune. If there is an EDM the deuteron spin will accumulate with time in the vertical direction. The deuteron spin is monitored by a polarimeter placed in one straight section of Figure 1 showing a preliminary ring lattice. The solid line in the center of the lattice elements describe the path of the equilibrium particle and the dashed lines the path of the particles with higher momentum (P>) and lower momentum (P<).
The large, rest frame, electric field being proportional to the vector product of the velocity and the vertical magnetic field vectors, is pointing along the radial direction. That means when the deuteron spin is longitudinal the spin will precess vertically (let's say up) when the spin is directed along the momentum and in the other direction (down) when the spin is opposite to the momentum direction. Without the velocity modulation the vertical spin component would cancel within a g-2 precession period. However, with the velocity modulation at the g-2 frequency the vertical spin gain is larger in the first half of the spin precession cycle than in the second half. The net effect is that the vertical spin component grows a little bit for every g-2 cycle, which when integrated over more than a billion cycles, can become substantial.
Those working with spin know that it is very treacherous to modulate the velocity of a stored particle at its spin tune. There are many systematic errors lurking, which, if are not taken care of, could dominate the vertical spin growth. BNL is the laboratory with the best accelerator expertise for the type described here. It’s the home with the highest intensity polarized sources in the world, with particle spin manipulation expertise, with intrinsic and external spin and beam dynamic resonances, as well as with classical accelerator techniques. Currently the storage ring EDM collaboration (SREC), which includes a large constituency of the very successful muon g-2 collaboration and a large number of the BNL accelerator experts, is currently working towards the dEDM proposal. Our presentation of the LOI to the BNL PAC was met with enthusiasm for its physics goals. The PAC suggested to the collaboration to study the polarimeter and spin related systematic errors before submitting a proposal, which we did in March 2007. The PAC has endorsed the collaboration R&D plan and suggested it be funded.
We are going to study the polarimeter issues as well as other, spin related, technical issues at KVI (The Netherlands) and COSY (Germany), where we have already been approved to use their polarized deuteron beams. At BNL we are focusing on studying the spin related systematic errors using particle spin tracking software, developed originally to study spin effects at AGS and RHIC, as well as analytical methods.
Other approaches of studying EDMs in storage rings are described in references ,  and  and more information can be found in .
1. Yuri F. Orlov, William M. Morse, Yannis K. Semertzidis, Phys. Rev. Lett.96: 214802, 2006, hep-ex/0605022
2. F.J.M. Farley, et al., Phys. Rev. Lett.93: 052001, 2004, e-Print: hep-ex/0307006
3. A New method for a sensitive deuteron EDM experiment by Y. Semertzidis et al., AIP Conf.Proc.698:200-204,2004, hep-ex/0308063
4. Sensitive search for a permanent muon electric dipole moment, by Y. Semertzidis et al., hep-ph/0012087
5. http://www.bnl.gov/edm/ the official Storage Ring EDM Collaboration web site.