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arXiv:hep-ex/0401016v1 13 Jan 2004 et ic h neato aitna nthat in Hamiltonian interaction the since ments symmetries. reversal time and parity both violate h neato aitna hne inmean- if sign that changes ing Hamiltonian interaction the hnesg whereas sign change ieoeao sapid ..tevector the i.e. applied, is operator time ..Bx50,Utn Y19350,USA 11973-5000, NY Upton, 5000, Box P.O. a Semertzidis K. Particles Yannis Fundamental of Moments Dipole Electric whereas H interaction The by given rotation. is spin Hamiltonian particle’s due zero the to in defining out to average other component would direction no any other any is Phenomenologically there along since be vector. to vector have spin would sym- vector the (P) EDM parity an and (T) metries: time both violate would beyond models model. of standard space the parameter con- and the limits strained strict put Non-the-less have experiments far. fundamen- so EDM observed a been un- of has particle EDM an tal no reached level has small sensitivities precedented neutron the im- a been and have for proved techniques the search though Even Ramsey’s EDM. with approximately years started fifty particles fundamental of Motivation Theoretical 1. se by improve to promise searches generation levels. next sensitivity The model. rcfil etrrsetvl.Tesymbol The respectively. vector field tric where aiyteailvector axial Under the strength. parity moment dipole electric the notes rohvnNtoa aoaoy hsc Department, Physics Laboratory, National Brookhaven E hsi o h aefrtemgei ioemo- dipole magnetic the for case the not is This lcrcdpl oet(D)eprmnsaea h fore-fr the at are experiments (EDM) moment dipole Electric h emnn D ffnaetlparticles fundamental of EDM permanent The (EDM) moments dipole electric for search The = − S, ~ d E ~ E E ~ d S os h poiehpeswe the when happens opposite The does. ~ E eoetesi etradteelec- the and vector spin the denote · sntzr h aitna would Hamiltonian the zero not is E ~ E ~ a osnt nbt cases both In not. does S ~ osntcag sign change not does S ~ d E does de- (1) 1 hudb ntbe h eodwsta there that was second The unstable. be should universe. the our explain of to asymmetry is needed antimatter CP-violation in CERN matter requirements that [3] three the out Sakharov of pointed in one 1999. paper Ellis of CP- 1967 October his J. of in by importance [2] written Courier the is of CP-violation. violation overview means general also A T-violation theorem, [1]. Penny by described treatment sym- mechanical quantum above their po- the with respect metries the electric also as “permanent” they moments far exhibit dipole As that and molecules parity respected. lar symmetries, are both reversal, and time E-field square the the of to proportional becomes Hamiltonian α spootoa oteeeti edvector field electric cases those the in to vector proportional EDM is the moments dipole since electric allowed induced are the of etc? cases molecules, The polar induced of EDMs be permanent can EDMs, there then how considerations try the by respected and moments. parity are dipole the magnetic symmetries and change reversal sign time a Hamiltonian they suffer interaction reversal not the does time Therefore under do. both whereas sign change H is case ne aiybt xa vectors axial both parity Under E ~ M h rtrqieetwsta h proton the that was requirement first The conservation CPT fundamental the Through fEM r o loe yteaoesymme- above the by allowed not are EDMs If n o h pnvco.Teinteraction The vector. spin the not and = n fsac o hsc eodtestandard the beyond physics for search of ont ea reso antd h urn EDM current the magnitude of orders veral − d M S ~ · B ~ S ~ and B ~ onot do d ~ E (2) = 2 would be interactions violating C and CP and the third condition was that the universe would undergo a phase of extremely rapid expansion.

1.1. EDMs are Excellent Probes of Physics Beyond the SM In the standard model (SM) there is only one CP-violating phase (KM) which results to an EDM only after third order loops with virtual W ±s and quarks are considered. This results to a natural suppression of the SM EDMs by several orders of magnitude. In contrary, physics models beyond the SM allow for much higher values of EDM, see Figure 1 (from ref. [4]), many times in the experimentally accessible region. For example super-symmetry (SUSY) has more than 40 CP-violating phases and the first order EDM Figure 1. In many models, like SUSY, EDMs are calculation does not cancel as it does in the non-zero at the one loop level but the SM EDMs SM. Other models with similar EDM predictions are zero at that level. This is so because there include models with left-right symmetry, multi is only one CP-violating phase in the SM, and Higgs scenarios, etc. the W boson only couples to left handed particles. In contrast SUSY has more than 40 CP- violating phases, plus sfermions couple to both 2. Experimental Approach left and right-handed particles making unnatural The spin of a particle with an electric dipole the first order cancellation of EDMs. The figure moment d precesses in the presence of an electric is copied from reference [4]. field. Since the d value is presumably very small (non observed so far) the spin precession signal would be of very small frequency. A magnetic field is used to serve as a carrier signal by pressing 2.1. Schiff theorem the spin due to its magnetic dipole moment. The The experimental approach was influenced spin precession rate is given by by the Ramsey-Purcell-Schiff theorem [5] which states that for point like, charged particles in equilibrium the net electric field they feel aver- dS~ = ~µ B~ + d~ E~ (3) ages to zero. In an external electric field the elec- dt × × tronic and nuclear charge of an atom would be re-arranged so that the net (average) electric field dS~ 1 For a spin 1/2 particle dt = 2 ¯hω, where ω on all charged particles would be zero, known as is called the Larmor frequency. In case of an “Schiff’s theorem”. Otherwise they would be con- atomic or molecular electron the magnetic field tinuously accelerated. However as was pointed causes a spectral split in the line and the transi- out by Schiff himself and others [6] not all the tional frequency is called Zeeman splitting. One forces need to be electrical. The electric field can then compares the Larmor/Zeeman frequencies thus be compensated by magnetic, nuclear, etc. with the E-field vector flipped back and forth: forces and even though the total force is zero there ¯h(ω1 ω2)=4dE. In order to reduce the effects of is a net electrical force. This results to a non- a drifting− magnetic field another particle with an zero EDM value for the atom or molecule, called expected small EDM sensitivity value is used as “Schiff’s moment”. Sandars further pointed out a B-field sensor, also known as co-magnetometer. that in paramagnetic atoms, there is even an en- 3 hancement of the average electric field the un- and S~ the mercury spin, precessing in the hori- paired electron feels in the presence of an exter- zontal plane at the Larmor frequency, Figure 2. nal electric field when relativistic effects are taken The statistical accuracy of the method is given by into account. The reason for the enhancement is ¯h due to the very strong electric fields present near δd = (4) the nucleus. The enhancement factor calculated 2E√NτT 3 2 by Sandars [7] is given by R = da/de 10Z α ≈ with N the number of observed photons, E the which for large size atoms can be quite a big fac- electric field strength, τ the spin coherence time tor. da, is the atomic electric dipole moment and and T the total running time of the experiment. de that of the electron, Z is the atomic number The result is d(199Hg) < 2.1 10−27e cm, (90% and α the fine structure constant. As an example C.L.) [10,4]. | | × · R = 115 for the Cs atom and R = 585 for the Tl atom. Sandars work is the basis− so far of all the searches for the electron EDM with atoms or molecules.

2.2. Electron EDM The current experimental electron EDM limit comes from the Berkeley atomic thallium experiment [8]. It is a small scale, “table top”, experiment where Tl atomic beams are led to go through high electric field regions where there is also a magnetic field present. The Larmor frequency is probed with the standard technique of Ramsey separated fields. Motional magnetic fields of the form ~u B~ , with ~u the atomic Figure 2. The experimental principle of the × beam velocity can be a problem in the pres- 199Hg experiment; from reference [4]. ence of small misalignments between the E~ and B~ fields. Another potential systematic error is Berry’s phase and some 8 atomic beams with fluxes over 1018 atoms/sec are used to study 2.4. Neutron EDM the systematic effects using many different cor- The neutron EDM experiments have first relations. The final result of this experiment is started 50 years ago and have come along way −27 de < 1.6 10 e cm (90% C.L.) [8]. since. Currently ultra cold neutrons (UCN) from | | × · a nuclear reactor are brought to a region where 2.3. 199Hg EDM a large electric field is present along with a small The mercury EDM experiment is a “table top” magnetic field. The neutron EDM principle also effort at Washington state. [10] They look for uses the technique of Ramsey separated fields a shift in the Zeeman frequency in 199Hg va- to probe the Larmor precession. A potential por when the E-field is flipped. The mercury EDM signal is any phase shift correlated with vapor is contained in two adjacent vapor cells the reversal of the electric field vector. In order where the B and E-fields are parallel. The mer- to minimize systematic errors due to the mag- cury atoms are polarized by circularly polarized netic field drifts atomic 199Hg is used as a co- laser light of 254 nm modulated (chopped) at the magnetometer. The combined results give a limit −26 Larmor frequency. A plane (linearly) polarized of dn < 6.3 10 e cm (90% C.L.) [11]. An laser goes through the cell with the mercury vapor upgrade| | of the× Grenoble· experiment where more where its plane of polarization rotates according neutrons are to be collected and has as a goal −26 to α ~k S~, with ~k the laser propagation vector dn < 1.5 10 e cm [12]. ≈ · | | × · 4

2.5. Prospects < 102 b when their spins are parallel and 104 b The next generation experiments, are very when the spins are opposite. Since the gyromag-≈ promising. On the electron a Yale group un- netic ratio of 3He is within 10% the same as the der D. DeMille made great progress towards us- neutron’s the beat signal frequency is 10 times ing the metastable molecule of PbO∗ [9]. The smaller making it 10 times less sensitive to the group promises an order of magnitude improve- magnetic field fluctuations. One of the challenges ment over the current electron limits within a year of the experiment is to avoid even a single spark and another two orders within the next couple of of the 50 kV/cm electric field since that would years. S. Lamoreaux has described [13] a solid surely destroy the SQUID system that is needed state technique where the alignment of the atoms to monitor the magnetic field. in an electric field would align the spins of the atoms and hence it will lead to the magnetization of the sample. This work is well underway at Los Alamos and it promises to reach 10−31e cm or so within a year or two. ·

Figure 4. A schematic diagram of the new neutron EDM experiment experiment of Los Alamos. Figure 3. A schematic diagram of the new neu- From reference [13]. tron EDM experiment experiment of Los Alamos. From reference [13].

Clearly the competition between the diﬀerent

199 EDM experiments is intense (it’s a horse race!) On the Hg EDM experiment the Washing- and their prospects of finding a non-zero EDM ton group has upgraded the experiment, using value are very good. four cells, the middle two with opposite electric field and the outer two without any electric field 3. EDM in Storage Rings present, in order to monitor the magnetic field fluctuations. An improvement of the order of a Other than using either atoms, molecules or factor of four is expected by the group when the neutrons in the search of EDM it is possible experiment is done [4]. to look for EDM of charged particles in storage The Los Alamos neutron EDM effort uses a rings. The Schiff theorem does not hold here since very high flux of UCN in superfluid 4He. Po- the particles are in an accelerated frame. One, in larized 3He is used to probe the neutron spin principle, does not need an electric field present precession and as a co-magnetometer. The neu- in the lab frame to probe the EDM of the particle. tron spin precession is probed by the reaction Even in a purely magnetic field storage ring there 3He~ + ~n t + p the cross section of which is is an electric field in the particle’s rest frame due → 5 to Lorentz transformation: E~ = γ(~u B~ ), with ~u × ~ the particle’s velocity. Since the average B vec- e tor is vertical the induced electric field is radial aµ = D (5) 2mµ ℜ and the spin, due to an EDM, will precess in the dµ = D, (6) vertical direction. ℑ Compared to the traditional methods of search- where D and D are correspondingly the real ing for EDM one notices that the electric and and imaginaryℜ ℑ parts of D. Writing DNP = magnetic fields that the particle feels in its own DNP eiφCP as the contribution of “New Physics” rest frame are strongly coupled and one cannot to| D |provides a measure of the relative prob- significantly change their values independently. ing power of a and d experiments. If “New Furthermore there is no way of flipping the sign of µ µ Physics” gives rise to a discrepancy between the electric field while keeping the magnetic field experiment and Standard Model expectations, sign the same. More over, since the electric and aNP = aexp aSM, then one expects that same magnetic fields in the particle’s rest frame are not µ µ µ “New Physics”− to induce a muon EDM given by parallel but orthogonal to each other, the EDM effect on the particle is to precess its spin in a NP −22 aµ plane orthogonal to the g-2 precession plane.[14] dµ 3 10 tan φCP e cm . (7) ≃ × 3 10−9 · As a result the EDM effect is a small disturbance × ! on the regular g-2 precession. NP Non-the-less this method of searching for EDM Of course, the values of aµ and tan φCP are was used by the CERN as well as the BNL g-2 model dependent. + − experiments.[14,15] A new, dedicated method of For the current situation (assuming the e e searching for “EDM in Storage Rings” has been data for the hadronic contribution) [21–23] developed [16,17] in which the g-2 precession vec- aexp aSM 3(1) 10−9 (8) tor is cancelled by a radial electric field. A major µ − µ ≃ × development in this method was the realization that the EDM signal sign changes between clock- one expects wise (CW) and counter-clockwise (CCW) stor- −22 dµ 3 10 tan φCP e cm . (9) age.[16] This method has regained the advan- ≃ × · tages of a traditional EDM search and works best − So, exploring down to d 10 24 e cm would for charged particles with small anomalous mag- µ probe ∼ · netic moment values like the muon and deuteron promising several orders of magnitude sensitivity −3 tan φCP 3(1) 10 . (10) improvement over current methods. ≥ × Within specific models, predictions for the 3.1. Muon EDM muon EDM vary widely [24–28]. In particular, It also happens that the same particles provide the left-right supersymmetric model with the see- new opportunities: The muon is the only second saw mechanism of reference [29] predicts dµ as generation particle that can be probed at a very large as 5 10−23 e cm, 50 times larger than sensitive level. Furthermore it is the only system the sensitivity× of the· proposed experiment. The that can be probed in its elementary form and prediction for the EDM of the electron is of order not as part of another system. Therefore its in- 10−28 e cm, 10 times smaller than the present terpretation would be more straightforward than experimental· limit [8]. any other system. The muon anomalous magnetic moment, aµ, 3.2. Muon EDM Experimental Approach and electric dipole moment, dµ, can be related to In the presence of both electric and magnetic each other [18–20] as the real and imaginary parts fields, oriented orthogonally to the muon velocity of a more general dipole moment, D. and to each other, the angular frequency of muon 6 spin precession relative to the momentum is given Upper Detector by ~ ~ ~ v e ~ 1 β E η E ~ ~ ~ω = aB + 2 a × + + β B ,(11) m ( γ 1 − c 2 c × !) − + θ where a = (g 2)/2 and η is the EDM in units of E µ eh¯ − 4mc . B + The magnetic and electric dipole moments are e g eh¯ η eh¯ given by µ = and d = , respectively. 2 2m 2 2mc η plays a role for the EDM corresponding to the g factor for the magnetic dipole moment. The Lower Detector muon EDM couples to the external fields through Figure 5. Due to the spatial anisotropy in the de- the η(E~ +cβ~ B~ ) term. The external B-field cou- + + × cay µ e +νe +νµ detectors above and below ples to the EDM because it produces an E-field the storage→ region are expected to observe a time in the rest frame of the muon. In fact, for the pa- dependent change in the ratio of positron count- rameters envisioned in the present proposal, the ing signals. The positron angular distribution is ~ ~ motional E-field from the β B term is far larger indicated by the density of arrows. than that due to the applied× E-field. The EDM value is given in terms of the dimensionless parameter η by which we will assume here equal to about η e¯h −14 dµ = η 4.7 10 e cm. (12) 2 MV/m. Using Eqs. (11, 14) the spin preces- 2 2mµc ≃ × × · sion angular frequency is given by: for the muon. e η E~ Assuming that the EDM is 0, from Eq. (11), it ~ω = + β~ B~ , (15) is clear that at the “magic” γ, (γ = 29.3) −m 2 c × ! 1 a =0, (13) i.e. the g-2 precession is canceled and only the γ2 1 − − EDM is left to act on the spin. The torque in the and the muon spin precession depends only on center of mass is given by g-2 and the average B-field. The anomalous pre- ′ ′ cession frequency, due to the magnetic moment, dS/dt~ = d~ E~ . (16) × is measured by observing the time spectrum of muon decay electrons. In the muon rest frame, which in terms of laboratory quantities is the highest energy electrons are emitted prefer- dS/dt~ = d~ (E~ + cβ~ B~ ). (17) entially along the muon spin vector. As the spin × × vector precesses relative to the momentum vector, the number of high energy electrons observed in As previously mentioned, for realizable values for the lab frame is modulated at the precession fre- the applied E-field, the “motional” E-field from the β~ B~ term is much larger than that from the quency. ~ × For the dedicated EDM experiment proposed E term. in this document we will follow a new approach: Thus the muon spin direction will be “frozen” Use muons with much lower energies, and em- relative to the muon momentum if the EDM is ploy a radial electric field which cancels the g-2 zero. In the presence of a non-zero EDM, the ra- precession. The electric field in the lab required dial E-field in the muon’s rest frame will cause to cancel the g-2 precession is rotation of the spin in a vertical plane about an axis parallel to the radial direction. As the spin E aBcβγ2, (14) acquires a vertical component, the decay positron ≃ 7 momenta also acquire a vertical component, re- tric field direction needs to be radially outward, sulting in an up-down asymmetry in the number, in opposite direction than the muon case. − R = Nup Ndown of electrons which grows lin- The statistical accuracy of the deuteron exper- N Nup+Ndown early with time, see Figs. (5,6). Together with iment is estimated to be other improvements, which will significantly re- ¯haγ2 duce many systematic errors, this new experi- σd 6.5 2 (18) ≈ √τpER(1 + aγ )AP √NcfTT ot mental approach will improve our sensitivity to a muon EDM by five orders of magnitude. where τp 10s is the spin coherence time of the stored beam,≈ A 0.3 is the left/right asymmetry observed by≈ the polarimeter [30] when the deuteron beam is completely vertically polarized, P 0.55 the polarization of the beam, Nc 1011≈d/cycle the total number of stored particles≈ per cycle, f 0.01 the useful event rate fraction, ≈ 7 and TT ot 10 s the total running time of the ≈ experiment, and ER 3.5 MV/m the radial elec- ≈ −28 tric field strength. Then σd 5 10 e cm but it is estimated [31] that due≈ to× the presence· of the tensor polarization there will be a total loss in running time due to the need to run for systematic error determinations of about a factor of 16, or a factor of 4 in statistical error, i.e. −27 σd 2 10 e cm. The≈ current× status· of the deuteron EDM effort is that the collaboration is considering writing a proposal to do this experiment with the above sensitivity. There are three candidate places to host it: Brookhaven National Lab, Groningen University-KVI in The Netherlands, and Indiana Figure 6. MC simulation of the muon EDM sig- Nup−Ndown University Cyclotron Facility. nal, R = , versus time. −27 Nup+Ndown A deuteron EDM at the 10 e cm level con- stitutes an improvement in the sensitivity· of the T-odd nuclear forces by a factor of 100 over the 199Hg EDM experiment, a factor of 100,000 im- 3.3. 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