SEMINAR

Neutron electric dipole moment

Author: Samo Stajner

Mentor: doc. dr. Simon Sirca22. 2. 2011

Abstract

In this paper we review the current experimental state of neutron electric dipolemoment determination. First a theoretical overview of discrete symmetries is madeand the importance of the CPT theorem highlighted. Next we introduce differentexperimental setups for the neutron electric dipole moment determination and com-pare them among themselves. Due to the extremely low upper limit on the value ofthe neutron electric dipole moment, account of the systematic errors of the recentlyemployed setups is made. In the end we discuss potential development on this fieldof the experimental physics and mention experiments currently under construction.

Contents

1 Introduction 1

2 CPT symmetries 12.1 P - parity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22.2 T - time reversal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32.3 C - charge conjugation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52.4 The CPT theorem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

3 Experimental determination 73.1 Detection by NMR . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83.2 Ultra-cold neutrons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83.3 Experiment with UCN . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103.4 Systematics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

4 Conclusion 12

2 CPT SYMMETRIES

1 Introduction

Half the mass of all visible matter in the universe is made of neutrons, yet our knowledge oftheir properties remains inferior to other elementary particles. The obvious reason is thatprotons and electrons are charged and can be detected via electromagnetic interaction.Neutrons as neutral particles, on the other hand, can be observed only indirectly throughtheir interaction with matter or by their decay. Nonetheless physicists are putting a lotof effort in measuring the Electric Dipole Moment (EDM) of neutrons.

The reason for such laborious and determined search surpasses basic interest in neu-tron’s properties. Existence of EDM in neutrons is a more fundamental topic, whichaddresses many unanswered questions in modern physics concerning the asymmetry ofmatter and antimatter.

In this paper we deal with theoretical implications of existence of EDM in neutronsand current experimental state of affairs. In order to fully understand why the search forneutron EDM is such a prosperous experimental and theoretical conduct of research, wehave to first examine the basic concepts of discrete symmetries in physics. It is believedthat all physical processes in nature are CPT invariant. Therefore a process under simul-taneous time reversal, charge conjugation and parity transformation, should be the same.In terms of quantum mechanics we can mathematically formulate this as

(CPT )−1 ψ CPT = ηψ, (1)

where in the case of CPT invariance the eigenvalue η will be equal to unity [1].In nature we fortunately observe a slight asymmetry between matter and anti-matter,

which indicates that physical laws should slightly differ for matter and antimatter, if bothwere produced in the same amounts in the Big Bang. Violation of discrete symmetriescould provide an answer and today there are many competing theories beyond StandardModel, which predict possible neutron EDM. By lowering the upper limit of the valueof the neutron EDM, these can be disproven. If, on the other hand, a non-zero neutronEDM would be measured, this would be a direct proof of the most fundamental symmetryviolation and could lead to entirely new physics.

The search for the neutron EDM seems to be fully justified, as both outcomes give usnew insight into the fundamentals of physics. At the same time we have to be aware thatthe expected asymmetry is very low, which also implies that the actual EDM will be veryhard to detect. Currently the lowest limit is d = 3× 10−26 e0 cm [2-4]. If two elementarycharges were separated by a width of a nucleus, corresponding dipole value would still be10 orders smaller than the current lowest limit of neutron EDM. To be able to attain sucha precise measurement, new technologies are being developed alongside, and many newphenomena that produce false EDM measurements are being examined and discovered.

2 CPT symmetries

Symmetries play an important role in physics. When dealing with Classical mechanics,the translational symmetry of the Lagrange function implies momentum conservation [5].In similar fashion discrete symmetries in elementary particle physics account for variousproperties of wave functions describing the observed system. In what follows we will indi-vidually introduce parity (P), time reversal (T) and charge conjugation (C) respectively.After introducing individual transformations we will take a look at the compound sym-metries and show how the neutron EDM measurement would violate the CPT symmetry.

1

2.1 P - parity 2 CPT SYMMETRIES

2.1 P - parity

Parity or space inversion is defined as

P : rP = −r. (2)

We use this definition to examine the Hamiltonain function in quantum mechanics. If wetake a Hamiltonian for a central potential

H = − ~2

2m∇2 + V (r), (3)

our eigenfunction can be separated in spherical coordinates as

ψnlm(r) = Rnl(r) Ylm(θ, ϕ), (4)

which leaves us with eigenvalues of the Parity operator η = (−1)l. If the wave function iseven it retains its sign under the P transformation, while an odd wave function changesits sign. It follows that η can take values ±1 [1].

Formally we can derive further properties of space inversion from the condition that P 2

should return our initial state and that the parity operator Up is unitary. Table 1 gives anoverview of how some relevant physical quantities change under the parity transformationUpAU

−1p = ηA [1].

Table 1: Physical quantities under the parity transformation. The angular momentum is a crossproduct ~r × ~p and is therefore invariant to P. Similar is true with analogy for spin and totalangular momentum [1].

A UpAU−1p

r −rp −pL LS SJ J

We are also interested in how the electric dipole operator transforms under spaceinversion. The electric dipole operator is defined as [1]

d =∑i

eri, (5)

from where it follows

〈b|d|a〉 = −ηbηa〈b|d|a〉 ⇒ ηbηa = −1, (6)

where |a〉 and |b〉 are two arbitrary states.This means that states occuring in the Hamiltonian have opposite parities for electric

dipole radiation, where electric dipole radiation by definition carries away one unit ofangular momentum [1]. In our case we are interested in the EDM of neutrons

〈ψ|d|ψ〉 = −η2〈ψ|d|ψ〉 ⇒ 〈ψ|d|ψ〉 = 0, (7)

as we have already determined that η = ±1. This is true for non-degenerate elementaryparticles in ground states [1]. Let us assume that we do observe a non-zero EDM in an

2

2.2 T - time reversal 2 CPT SYMMETRIES

elementary particle. This implies that its ground state has an admixture of a wave functionwith opposite parity. In combination with the prevailing component of the regular paritywave function, this would give a non-vanishing EDM expectation value. The magnitudeof such Parity violation can be described by the coefficient F [1]

Ψ = ψη + Fψ−η ⇒ 〈Ψa|d|Ψb〉 6= 0. (8)

Figure 1: Λ0 production-decay sequance. a) and b) show up-ward and downward oriented decays, respectively. Anizotropi-caly oriented decay had been observed indicating Parity viola-tion [1].

The search for such Parity vi-olation has been conducted bystudying transition spectra in nu-clear physics and none had beenfound to date [1]. But already in1957 a case of broken space inver-sion symmetry in elementary par-ticle physics had been found, withtwo groups of scientists separatelyobserving such processes. Figure 1shows the process of pion scatter-ing on protons, where an asymme-try between up and down decay-ing secondary pions was observed[1]. Later in the same year Parityviolation had been proven in betadecay [1].

2.2 T - time reversal

Time reversal symmetry is a bit unfortunate name, as what we observe is better describedas motion reversal. We say that a process that obeys laws of physics under reversed motionis T invariant. The definition of motion reversal is given by [1]

T : rT (t) = r(−t). (9)

Figure 2 shows how we can imagine time reversal. Instead of time propagation tothe right, we propagate to the left. The immediate consequence of this definition is thatodd time derivatives of position will change sign in comparison to the original system.Classically we would have T invariance if the force in equation of motions will only dependon the position of a particle and not on its velocity:

md2

dt2r(t) = F(r(t)), (10)

Under motion reversal equation stays the same [1]. If we would also have drag forceor friction, then one component of the force would depend on the particle’s velocity,time invariance would be broken. The force in reversed motion would differ from theuntransformed one, while the product of the mass and the acceleration would not.

By using this definition we can see how different physical quantities transform. Theresults are displayed in Table 2. Next we want to study non-relativistic quantum me-chanics. The Hamiltonian is constructed from quantities that are conserved under motionreversal:

H = − ~2

2m∇2 + V (r), (11)

3

2.2 T - time reversal 2 CPT SYMMETRIES

(a) (b)

Figure 2: Under time reversal body in b) follows the same path as in a) while flipping time coordinate.Thus motion appears reversed [1].

and therefore the Hamiltonian itself is invariant on the transformation [1].

Table 2: Physical quantities under time reversal. The last line shows the equivalence of theLorentz force under time reversal [1].

A AT

r(t) r(−t)p(t) −p(−t)L(t) −L(−t)E(t) E(−t)B(t) −B(−t)

md2

dt2r = e

(E+

dr

dt×B

)invariant

The time evolution of the wave function is given by the first time derivative andtherefore changes the sign under the transformation [1],

i~∂

∂tψ(r, t) = Hψ(r, t) ⇒ −i~ ∂

∂tψ(r,−t) = Hψ(r,−t). (12)

We hence conclude that in order to appropriately describe the time reversal operator itmust produce a complex conjugate of the wave function as well as change the sign of thetime coordinate [1]:

i~∂

∂tψ∗(r,−t) = H∗ψ∗(r,−t) ⇒ i~

∂

∂tψ∗(r,−t) = Hψ∗(r,−t), (13)

when the Hamiltonian is Time reversal invariant. The wave function is then transformedas

ψT (r, t) = ψ∗(r,−t). (14)

We can further check how the expectation values of Hermitian operators change underT quantum mechanically and it turns out that they transform in accordance with their

4

2.3 C - charge conjugation 2 CPT SYMMETRIES

classical analogs. We can further add the values of spin and helicity, where one is oppositeand other invariant, respectively [1].

Neutrons have half integer spin and it turns out that time reversal distinguishes be-tween systems with half-integer and integer spins. In classical mechanics we anticipatedthat two consecutive T transformations should return the system to its original state. Inhalf-spin systems a T transformation performed twice returns −1 instead of unity. Thisconclusion can be generalized as

O(T )2 = (−1)2s, (15)

where O(T ) is the operator of time reversal and s the spin of the observed system [1].The expectation value of the EDM for neutrons can be again calculated before and

after the transformation. From comparison of both results we arrive at the conclusionthat the expectation value of neutron EDM has to be zero

〈Φm|d|Φm〉 = −〈Φm|d|Φm〉 = 0, (16)

or time reversal Symmetry would be broken. In the last expression Φm represents restwave function of neutrons and d is the dipole moment operator [1].

2.3 C - charge conjugation

Initially the Charge conjugation operation was intended to replace charge with an op-posite charge of the same magnitude and swap the positions of electrons and positrons.With development of quantum mechanics Charge conjugation has been generalized tochange all particles to their respective antiparticles and thus also change all of originalparticles’ internal quantum numbers like the baryon number B, the lepton number L, thehypercharge etc.

Uc ΦQ~pλ = Φ−Q~pλ, (17)

where Q and λ denote all internal quantum numbers and the spin, respectively [1].Because of its definition the eigenfunctions of charge conjugation can only be wave

functions describing neutral mesons with zero strangeness. Again it follows from twicecharge conjugation being unity that the eigenvalue corresponds to ηc ± 1 [1].

Charge conjugation is usually used to analyze many-particle systems before and afterthe interaction. Therefore we need to know that charge conjugation is a multiplicativequantity,

C = ΠαCα, (18)

which is also true for other discrete symmetries T and P already examined. The Hamil-tonian stays invariant under charge conjugation as well [6].

For example, let us consider photons. Because the electric and the magnetic fields aswell as the current all change sign under C, the eigenvalue of charge conjugation actingon a wave function describing photons is ηc(photon) = −1 [1]. From the pion decay totwo photons we can immediately determine the eigenvalues of C acting on wave functionsdescribing pions to be ηc(pion) = +1 [1]. That charge conjugation in fact is a symmetryis best illustrated from the neutral pion decaying to three photons being forbidden, whichhas really never been observed, although it is electromagnetically allowed.

The test of C invariance in strong interactions has been carefully studied in positron-ium annihilation process in the years after the discovery of Parity violation in 1957. Noconclusive evidence of violation had been found. Similar was the outcome of C symmetry

5

2.4 The CPT theorem 2 CPT SYMMETRIES

studies in hadronic electro-magnetic interactions where C violation again remained elusive[1].

On the other hand, Parity violation in weak interaction discovered in the late fiftiesalso indicated C violation. Curiously enough, the combined CP symmetry invariance hasbeen observed for the weak interaction processes observed at that time and it was believedthat CP invariance was a property of nature [1].

This invariance held only until 1964 when CP violation was found in neutral Kaondecay [1]. Today CP violation is being carefully studied in the decay of various neutralbosons [1]. We will not go into the details of experimental study of these processes. Wewill rather examine another combined symmetry, namely CPT, but before we do so it isworth mentioning that after CP violation discovery many new theories were developed toaccommodate these new observations. One of these theories is also Superweak interactionthat predicts a non-zero neutron EDM and will be soon put to the test by the ever loweringupper limit on neutron EDM [4].

2.4 The CPT theorem

In the previous section we pointed out that C and P violation can be overcome by ahigher combined symmetry and introduced the CP invariance. Now that we have foundCP violation it is only natural to go another step higher and investigate CPT symmetryfor previously violating processes. It turns out that these are CPT invariant [1].

Figure 3: First picture indicates counter-clockwise current in a coil, that produces an upward pointingmagnetic field. In the center is located a particle with spin +1/2. After Time reversal is applied, themotion of electric current changes direction thus flipping magnetic field. Subsequent Parity transformationinverts the position of the coil but retains clockwise electric current, as well as direction of particles’ spin.Charge conjugation finally transforms electrons and particle in the middle into positrons and antiparticle,respectively. Resulting situation is depicted on the right hand side where the initial current is preservedwhile direction of spin is flipped. From this analysis it follows, that antiparticle should have opposite spinto its respective particle as energies of both systems need be the same according to the CPT theorem [1].

CPT invariance is believed to be a fundamental symmetry property of nature for avery long time now. Already in 1955 the CPT theorem had been formulated stating that

6

3 EXPERIMENTAL DETERMINATION

in quantum field theory every Hamiltonian under proper Lorentz transformation is alsoinvariant under CPT transformation, whether or not it is invariant under C, P and Tseparately [1]. One example of CPT invariance is shown in Figure 3. In the picture we cansee that CPT retains the current in the coil and hence the electric and the magnetic field.Conjugation also changes a particle with spin λ to a corresponding anti-particle with theopposite spin. Invariance implies that both systems have the same energy. From here itfollows that the magnetic moment of an anti-particle has to be opposite in sign and equalin magnitude with respect to the particle. Such a condition seems to be obeyed in nature.Some possible symmetry violation combinations are examined in Table 3 [1].

Table 3: Posible combinations of symmetry invariance under CPT theorem with examples ofprocesses where they were observed [1].

C P T exampleYes Yes Yes strong, electromagneticYes No No noneNo No Yes β decayNo Yes No noneNo No No neutral Kaon decay

A proof of the CPT theorem is beyond our current interest, but we can happily use itto discuss our current topic of the neutron EDM. Obviously if a system is CP violating, ithas to be T violating as well [1]. So if we find a CP invariant system and find T violation,we would disprove the CPT theorem. This is what search for neutron EDM is all about.In comparison with mezon factories, we want to find a symmetry violation due to timereversal in a system which would be CP invariant even in the presence of EDM.

3 Experimental determination of the neutron EDM

Figure 4: If the neutron would beof the size of the Earth, the currentmeasurements would limit the dis-placement of opposite charges in itscentre to less than a few microns [7].

The first experimental test of the neutron EDM was con-ducted in 1950 in the Oak Ridge National Laboratoryby a group of scientists led by Ramsey [4]. They used aneutron beam on which they performed measurementsof Larmor frequency using NMR techniques. AlthoughNMR is used for measurements of the magnetic momentit can be used to prepare neutron beam for subsequentmeasurement of EDM as will be discussed later. No EDMwas measured at that point and interest in experimentalsearch of it has died out for nearly a decade [4].

After the discovery of various symmetry violationsthe interest in the neutron EDM has been revived. Thereare mainly two techniques for EDM determination. Oneutilizes NMR, while the other is the scattering of a neu-tron beam on a stationary target[4,8]. Latter tries toutilize electric fields on an atomic scale, which are aboutfactor 5 higher than any other achievable electric field inthe laboratory. Unfortunately, using a neutron beam has its disadvantages and preferencehas recently been given to the NMR methods [4,8].

7

3.1 Detection by NMR 3 EXPERIMENTAL DETERMINATION

The present upper limit on the neutron EDM has been set at dn = 3 × 10−26 e cmby an experiment conducted at Institute Laue-Langevin (ILL) in Grenoble [3]. This isan extremely small value and, just for illustration, the magnitude of the effective chargeposition displacement on a scale where the neutron’s size would correspond to the size ofthe Earth, is shown in Figure 4 [7].

3.1 Detection of neutron EDM by NMR techniques

Because the neutron is a spin 1/2 system it interacts with the magnetic field. In a constantmagnetic field the neutron’s spin direction will be precessing around the magnetic fielddirection unless they are collinear. The precession will occur with the Larmor frequencyas is well known. If a neutron also possesses an electric dipole moment, then a shift in theLarmor frequency should be observed for parallel and anti-parallel electric and magneticfields, given by [4,8]

ω± = γB0 ± 2ednE/~. (19)

Figure 5 schematically shows how this change occurs after the electric field is reversedwhile the magnetic field is held constant. This method is usually referred to as the NMRmeasurement of the neutron EDM but we have to be aware of what is meant by this.We only use NMR to flip the magnetic moment of a neutron to a plane perpendicular tothe magnetic field so we can observe precession. Because the EDM of a neutron is alwayscollinear with its magnetic moment we can observe changes in precession rate by invertingthe electric field as indicated in Figure 5 [4].

The scattering experiments with a neutron beam try to make use of the atomic scaleelectric fields. The Hamiltonian for a neutron interacting with the electric and magneticfields is given by [4,8]

~H = −(µ~B + dn ~E

)· ~s|s|, (20)

where the shifts in the energy of the beam in the electric and magnetic field are beingsearched for. The main experimental difficulty limiting the precision of the neutron beamexperimental setup comes from the motional magnetic field [4,8]

~Bm = ~E × ~v

c, (21)

which for cold neutron beams corresponds to a field of about 1 mG [4]. A change inthe Larmor frequency in a typical experimental setup would translate into a change ofthe magnetic field on a level of pG at the current limit. Therefore the systematic errorswould be greater than expected neutron EDM and neutron beams are no longer in use incombination with NMR measurements [4].

Obviously we want the speed of hte neutrons to be minimal and neutrons can actuallybe prepared in a manner that they can be stored in a special bottle for measurementswhile moving at very low velocities. In what follows, we will concentrate on experimentalmethods with ultra-cold neutrons (UCN), as they provide the currently best experimentalupper limit on the neutron EDM [3,4,8]

3.2 Ultra-cold neutrons

In order to eliminate the motional magnetic field UCN production technology has beendeveloped. Cold neutrons are those with velocities below 1000 ms−1. They can be obtained

8

3.2 Ultra-cold neutrons 3 EXPERIMENTAL DETERMINATION

Figure 5: Parallel or anti-parallel orientation of Electric and magnetic fields either enhance or diminishpreccesion rate [9].

by moderation in light atom liquid at low temperatures. Neutrons with kinetic energy ofabout 25 K can be obtained this way. It is hard to obtain lower temperatures of neutronsbut fortunately, cold neutrons are almost Maxwell distributed and hence we can collectquite some neutrons of even lower energies. The neutrons with kinetic energies in therange of about 5 mK are usually referred to as being ultra cold. This energy correspondsto velocities of about 7 ms−1 [4].

In order to understand the generation of UCN we need to study how neutrons interactwith matter. Classically we would expect neutrons to pass freely through matter unlessscattered or absorbed by nuclei because they are neutral. Thus we would be unable tolocalize neutrons after their production and they would simply diffuse.

Figure 6: Special containment bottle forthe Ultra-cold neutrons. In the middle onecan see 3 solid state detectors speciallyadopted for use within liquid Helium [10].

Quantummechanics luckily has a solution to thisproblem. Neutrons feel a small repulsive force intransition from the vacuum to a material althoughbeing neutral in charge. This effect occurs becauseof the boundary conditions on the wave functionrepresenting the neutron. Therefore also a repulsivepotential UF will appear in the Hamiltonian func-tion of a neutron’s motion, given by [4]

UF =2π~2

mρa, (22)

where m is the mass of a neutron, ρ the numberdensity of a nuclei of a given material and a thescattering length. For most nuclei a is a positivenumber and the potential will be repulsive [4]. Itfollows that a neutron with the kinetic energy com-ponent perpendicular to the wall of material smallerthan UF will be reflected.

The potential UF is in the range of 100 − 300 neV, which gives a reflection angle ofabout 1 degree for cold (20 K) neutrons [4]. In this way cold and ultra cold neutrons can beguided away from the moderation chamber along a slightly bent guide to the experimentalapparatus while faster neutrons will enter the material and be absorbed.

If a neutron has a kinetic energy below the potential depth UF for the nuclei of agiven material it can be contained in a specially prepared bottle made of a high potential

9

3.3 Experiment with UCN 3 EXPERIMENTAL DETERMINATION

material (usually stainless steel with coating designed to increase it even further(Figure6)). This way we can harvest UCN and store them for experimental use [3,4].

There are some difficulties with this technique as well, as UCN will gain energy fromthe collisions with the container wall and because the neutrons have a finite lifetime.Therefore the neutrons will be lost during the experiment which limits our overall preci-sion. Collisions of the neutron with the container wall are sufficiently short that not manyUCN are being lost during a single run. The neutron lifetime of 886 s [2] (although beingdisputed [11,12]) also accounts for UCN losses and puts an upper limit on a completeduration time of a cycle [3,4].

3.3 The EDM experiment with ultra-cold neutrons

Figure 7: Apparatus used at the UCN EDMexperiment conducted at ILL. Allong guidesand polarization foils we can also see NMRradio frequency coils and comagnetometersetup for Hg atoms. [4]

The containment of UCN is not enough to suc-cessfully measure the EDM. Polarized neutrons ofonly one spin are required so that the EDM doesnot average out. Neutron polarization now takesplace at special ferromagnetic films on highly ab-sorbing surfaces [4]. Due to the generalized Zee-man interaction given by the equation 20 the neu-trons with the appropriate spin state will have agreater reflection angle θc and will be reflected,while others will be lost in the absorbing materialafter penetrating ferromagnetic film. Today evenoptically pumped 3He is used because of its in-creased absorbtion cross-section for one spin pro-jection [4,8].

In order to maintain the neutron’s spin stateit is being guided to the containment bottle inmoderate magnetic fields. This can be easily doneif the neutron motion is so slow that we can ap-proximately say that its magnetic moment alwayspoints along the guiding magnetic film, which canbe assumed for UCN. The apparatus used at In-stitue Laue-Langevin can be seen in Figure 7 [4].

After polarizing the neutrons we still need toperform the NMR, therefore a RF coil is posi-tioned right after the polarization foil in order to flip the spins. In the apparatus we needto monitor the background magnetic field very precisely in order to eliminate possiblefalse EDM signals due to the inhomogeneous magnetic field [4].

The accuracy of the experimental setup is nowadays limited by the magnetic field mon-itoring. If we use SQUIDs or other external magnetometers outside of the containmentbottle, we may not be measuring the actual field experienced by the UCN. Therefore anin situ magnetometer has been employed. Such magnetometers are called comagnetome-ters and it has been suggested that liquid helium could be used as comagnetometer. Inpractice it proved difficult to employ one, so 199Hg atom gas was used instead. The 199Hgcomagnetometer is simply a gaseous 199Hg mixed with the UCN and is not a true appara-tus in itself. We call it a comagnetometer because we can reconstruct the actual magneticfield from parallel measurements of the Hg atom precession to the UCN precession [4].

10

3.4 Systematics 3 EXPERIMENTAL DETERMINATION

Figure 8: Blue circles represent the raw datafrequency. After applying corrections due to themagnetic field variation red circles are obtainedindicating no correlation of Larmor frequencywith the electric field. The jump in the fre-quency seen in the raw data is due to changesin the magnetic field between two runs [13].

The idea is that Hg atoms do not have anEDM on their own [4], while having a magneticdipole moment about three times smaller thanneutrons. Therefore we can compare the pre-cessions of UCN and Hg atoms to reconstructwhether frequency changes occur due to theneutron EDM or due to the fluctuating mag-netic field. It is also important to mention thatin the case that neutrons do have a non-zeroEDM, that would also influence the Hg comag-netometer, but the EDM of Hg would be sig-nificantly shielded by its electrons, so the effectof the neutron EDM on 199Hg comagnetome-ter can at present accuracy be neglected. In thesetup we can see the Hg UV lamps which areused to optically pump the Hg atoms into thedesired spin state [4].

Figure 8 is an example of neutron EDM dataand results from the Institue Laue-Langevin experiment. The jump in the raw data wasdue to the uncorrected magnetic field changes between two runs. The red dots representcorrected data. No correlation with changes in electric field can be seen, thus no neutronEDM has been measured beyond experimental noise [3,12].

3.4 Systematics

For precision neutron EDM measurements with UCN we need a very precise knowledge ofthe background magnetic fields. Therefore it is important to identify the effects that canmimic the electric dipole moment and take them into account. One such effect from themotional magnetic field has already been mentioned. There are others, but we will notgo into detailed analysis of them but rather briefly explain what else has been observedso far. Let us also note, that Van der Waals like induced electric dipole moment fromneutron’s vicinity should not be observed, as Electro-magnetic force is much weaker thanstrong interaction between quarks in the nuclei.

Electric-field correlated magnetic effects appear because of the high electric potentialapplied to the systems. Because of this high electric fields leakage current can flow. If weimagine that such current flows along the containment bottle it will produce a magneticdipole moment at its center. Because we will reverse the electric field in order to trackany changes in the Larmor frequency, the direction of the leakage current might changeaccordingly, resulting in the reversed magnetic dipole moment. Such effects can mimicthe true neutron EDM and in 1980’s two groups working independently reported neutronEDM readings due to systematics of this nature. After a short burst of excitement thissystematic error has been found and the stir slowly faded [4].

Neutron EDM measurements are even so precise, that the gravitational field causesUCN and comagnetometer center of masses to separate by a tiny fraction. This separationin the orders of millimeters causes differences in frequencies of magnetometer and UCN.This rather masive displacement comes about because of very low kinetic energies andcan provide unwanted experimental noise and in some configurations false EDM readingsas well [4].

11

REFERENCES

The last systematic effect we will mention is the ’Geometric phase effect’, which wasdiscovered only recently after 60 years of experimental work. This effect can mimic theEDM signature when motional magnetic field is combined with the magnetic field gradi-ent. The gradient in the magnetic field is crucial for an EDM signature as only motionalmagnetic field would average out in a UCN storage experiment. If we consider circularmotion of the neutron due to small angle reflections with containment bottle a situa-tion similar to leakage currents can occur. It can be shown that in combination with aninhomogenous magnetic field a false EDM signature can be produced [4].

4 Conclusion

Theoretical implications of finding a neutron EDM have revived experimental interest onthis topic. The present experimental limit is only a factor 10 to 100 away from being ableto test many theories beyond the Standard model and it is expected that within two tothree years we could reach such a level of precision.

There are several experimental setups in construction that will try to improve theILL’s limit. One of them is the CryoEDM experiment which is an upgrade of the ILLexperiment where a liquid Helium bath will be introduced. It is expected that this will bethe first experiment to improve the EDM limit, though potential for significant improve-ment is currently also attributed to the Spallation Neutron Source experiment currentlyunder construction at Oak Ridge in USA. It will introduce a superfluid helium bath andcombine it with increased UCN densities in containment bottles, thus further improvingthe sensitivity of the experimental setup [4].

The neutron EDM experiments have so far contradicted more theories than any otherexperiment. Figure 9 shows the historical progress of the neutron EDM search and whichtheories have already been put to the test and which will follow shortly. Because of this,the neutron EDM will remain in the experimental focus for some time.

References

[1] W. M. Gibson and B. R. Pollard, Symmetry Principles in Elementary Particle Physics(Cambridge Univarsity Press, Cambridge, 1976).

[2] Particle Data Group, J. Phys. G: Nucl. Part. Phys., 37, No7A (2010)

[3] C. A. Baker, D. D. Doyle, P. Geltenbort, K. Green, M. G. D. van der Grinten, P. G. Harris,P. Iaydjiev, S. N. Ivanov, D. J. R. May, J. M. Pendlebury, J. D. Richardson, D. Shiers,and K. F. Smith, Phys. Rev. Lett., 97, 131801 (2006)

[4] S. K. Lamoreaux and R. Golub, J. Phys. G: Nucl. Part. Phys. 36, 104002 (2009)

[5] L. D. Landau in E. M. Lifshitz, Mechanics (Pergamon Press, Oxford, 1976).

[6] W. Greiner, Quantum Mechanics: Symmetries (Springer, Berlin, 1994).

[7] http://www.neutronedm.org/motivation6.htm

[8] R. Golub and S. K. Lamoreaux, Phys. Rep. 237, 1-62 (1994)

[9] http://www.neutronedm.org/method3.htm

[10] http://www.neutronedm.org/cryo/cryo2.htm

12

REFERENCES REFERENCES

[11] A. Serebrov, V. Varlamov, A. Kharitonov, A. Fomin, Yu. Pokotilovski, P. Geltenbort, J.Butterworth, I. Krasnoschekova, M. Lasakov, R. Taldaev, A. Vassiljev, O. Zherebtsov,Phys. Lett. B 605, 72 (2005)

[12] A. P. Serebrov and A. K. Fomin, Phys. Rev. C 82, 035501 (2010)

[13] http://www.neutronedm.org/method6.htm

Figure 9: Time evolution of the neutron EDM upper limit. Due to systematic errors, expoerimentswith beams have been terminated in 1980 and UCN experiments utilized henceforth. Since then manytheories have been already been tested as seen on the right hand side. Presently constructed experimentswill further improve the limit and put to the test new set of theories, while the Standard model for nowremains out of reach [4].

13