Neutron electric dipole moment

SEMINAR Neutron electric dipole moment Author: Samo Štajner Mentor: doc. dr. Simon Širca 22. 2. 2011 Abstract In this paper we review the current experimental state of neutron electric dipole moment determination. First a theoretical overview of discrete symmetries is made and the importance of the CPT theorem highlighted. Next we introduce different experimental setups for the neutron electric dipole moment determination and compare them among themselves. Due to the extremely low upper limit on the value of the neutron electric dipole moment, account of the systematic errors of the recently employed setups is made. In the end we discuss potential development on this field of the experimental physics and mention experiments currently under construction.

Contents 1 Introduction 1 2 CPT symmetries 1 2.1 P - parity.................................... 2 2.2 T - time reversal................................ 3 2.3 C - charge conjugation............................. 5 2.4 The CPT theorem............................... 6 3 Experimental determination 7 3.1 Detection by NMR............................... 8 3.2 Ultra-cold neutrons............................... 8 3.3 Experiment with UCN............................. 10 3.4 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 of their properties remains inferior to other elementary particles. The obvious reason is that protons and electrons are charged and can be detected via electromagnetic interaction. Neutrons as neutral particles, on the other hand, can be observed only indirectly through their interaction with matter or by their decay. Nonetheless physicists are putting a lot of effort in measuring the Electric Dipole Moment (EDM) of neutrons. The reason for such laborious and determined search surpasses basic interest in neutron s properties. Existence of EDM in neutrons is a more fundamental topic, which addresses many unanswered questions in modern physics concerning the asymmetry of matter and antimatter. In this paper we deal with theoretical implications of existence of EDM in neutrons and current experimental state of affairs. In order to fully understand why the search for neutron EDM is such a prosperous experimental and theoretical conduct of research, we have to first examine the basic concepts of discrete symmetries in physics. It is believed that all physical processes in nature are CPT invariant. Therefore a process under simultaneous time reversal, charge conjugation and parity transformation, should be the same. In terms of quantum mechanics we can mathematically formulate this as (CP T ) 1 ψ CP T = 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 both were produced in the same amounts in the Big Bang. Violation of discrete symmetries could provide an answer and today there are many competing theories beyond Standard Model, which predict possible neutron EDM. By lowering the upper limit of the value of the neutron EDM, these can be disproven. If, on the other hand, a non-zero neutron EDM would be measured, this would be a direct proof of the most fundamental symmetry violation and could lead to entirely new physics. The search for the neutron EDM seems to be fully justified, as both outcomes give us new insight into the fundamentals of physics. At the same time we have to be aware that the expected asymmetry is very low, which also implies that the actual EDM will be very hard to detect. Currently the lowest limit is d = 3 10 26 e 0 cm [2-4]. If two elementary charges were separated by a width of a nucleus, corresponding dipole value would still be 10 orders smaller than the current lowest limit of neutron EDM. To be able to attain such a precise measurement, new technologies are being developed alongside, and many new phenomena 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 various properties of wave functions describing the observed system. In what follows we will individually introduce parity (P), time reversal (T) and charge conjugation (C) respectively. After introducing individual transformations we will take a look at the compound symmetries 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 : r P = r. (2) We use this definition to examine the Hamiltonain function in quantum mechanics. If we take a Hamiltonian for a central potential H = 2 2m 2 + V (r), (3) our eigenfunction can be separated in spherical coordinates as ψ nlm (r) = R nl (r) Y lm (θ, ϕ), (4) which leaves us with eigenvalues of the Parity operator η = ( 1) l. If the wave function is even it retains its sign under the P transformation, while an odd wave function changes its 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 U p is unitary. Table 1 gives an overview of how some relevant physical quantities change under the parity transformation U p ÂUp 1 = ηâ [1]. Table 1: Physical quantities under the parity transformation. The angular momentum is a cross product r p and is therefore invariant to P. Similar is true with analogy for spin and total angular momentum [1]. Â r p L S J U p ÂUp 1 r p L S J We are also interested in how the electric dipole operator transforms under space inversion. The electric dipole operator is defined as [1] ˆd = i eˆr i, (5) from where it follows b ˆd a = η b η a b ˆd a η b η a = 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 of angular momentum [1]. In our case we are interested in the EDM of neutrons ψ ˆd ψ = η 2 ψ ˆd ψ ψ ˆd ψ = 0, (7) as we have already determined that η = ±1. This is true for non-degenerate elementary particles 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 function with opposite parity. In combination with the prevailing component of the regular parity wave function, this would give a non-vanishing EDM expectation value. The magnitude of such Parity violation can be described by the coefficient F [1] The search for such Parity violation has been conducted by studying transition spectra in nuclear physics and none had been found to date [1]. But already in 1957 a case of broken space inversion symmetry in elementary particle physics had been found, with two groups of scientists separately observing such processes. Figure 1 shows the process of pion scattering on protons, where an asymmetry between up and down decaying secondary pions was observed [1]. Later in the same year Parity violation had been proven in beta decay [1]. 2.2 T - time reversal Ψ = ψ η + F ψ η Ψ a ˆd Ψ b = 0. (8) Figure 1: Λ 0 production-decay sequance. a) and b) show upward and downward oriented decays, respectively. Anizotropicaly oriented decay had been observed indicating Parity violation [1]. Time reversal symmetry is a bit unfortunate name, as what we observe is better described as motion reversal. We say that a process that obeys laws of physics under reversed motion is T invariant. The definition of motion reversal is given by [1] T : r T (t) = r( t). (9) Figure 2 shows how we can imagine time reversal. Instead of time propagation to the right, we propagate to the left. The immediate consequence of this definition is that odd 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 depend on the position of a particle and not on its velocity: m d2 r(t) = F(r(t)), (10) dt2 Under motion reversal equation stays the same [1]. If we would also have drag force or 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 the untransformed one, while the product of the mass and the acceleration would not. By using this definition we can see how different physical quantities transform. The results are displayed in Table 2. Next we want to study non-relativistic quantum mechanics. The Hamiltonian is constructed from quantities that are conserved under motion reversal: 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 the Lorentz force under time reversal [1]. Â r(t) p(t) L(t) E(t) B(t) ( m d2 dt r = e E + dr ) 2 dt B Â T r( t) p( t) L( t) E( t) B( t) invariant The time evolution of the wave function is given by the first time derivative and therefore changes the sign under the transformation [1], i t ψ(r, t) = Hψ(r, t) i ψ(r, t) = Hψ(r, t). (12) t We hence conclude that in order to appropriately describe the time reversal operator it must produce a complex conjugate of the wave function as well as change the sign of the time coordinate [1]: i t ψ (r, t) = H ψ (r, t) i t ψ (r, t) = Hψ (r, t), (13) when the Hamiltonian is Time reversal invariant. The wave function is then transformed as ψ T (r, t) = ψ (r, t). (14) We can further check how the expectation values of Hermitian operators change under T 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 opposite and other invariant, respectively [1]. Neutrons have half integer spin and it turns out that time reversal distinguishes between systems with half-integer and integer spins. In classical mechanics we anticipated that two consecutive T transformations should return the system to its original state. In half-spin systems a T transformation performed twice returns 1 instead of unity. This conclusion can be generalized as Ô(T ) 2 = ( 1) 2s, (15) where Ô(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 conclusion that the expectation value of neutron EDM has to be zero Φ m ˆd Φ m = Φ m ˆd Φ m = 0, (16) or time reversal Symmetry would be broken. In the last expression Φ m represents rest wave function of neutrons and ˆd is the dipole moment operator [1]. 2.3 C - charge conjugation Initially the Charge conjugation operation was intended to replace charge with an opposite charge of the same magnitude and swap the positions of electrons and positrons. With development of quantum mechanics Charge conjugation has been generalized to change all particles to their respective antiparticles and thus also change all of original particles internal quantum numbers like the baryon number B, the lepton number L, the hypercharge etc. Û c Φ Q 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 twice charge conjugation being unity that the eigenvalue corresponds to η c ± 1 [1]. Charge conjugation is usually used to analyze many-particle systems before and after the interaction. Therefore we need to know that charge conjugation is a multiplicative quantity, Ĉ = Π α Ĉ α, (18) which is also true for other discrete symmetries T and P already examined. The Hamiltonian stays invariant under charge conjugation as well [6]. For example, let us consider photons. Because the electric and the magnetic fields as well as the current all change sign under C, the eigenvalue of charge conjugation acting on a wave function describing photons is η c (photon) = 1 [1]. From the pion decay to two photons we can immediately determine the eigenvalues of C acting on wave functions describing pions to be η c (pion) = +1 [1]. That charge conjugation in fact is a symmetry is best illustrated from the neutral pion decaying to three photons being forbidden, which has really never been observed, although it is electromagnetically allowed. The test of C invariance in strong interactions has been carefully studied in positronium annihilation process in the years after the discovery of Parity violation in 1957. No conclusive 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 fifties also indicated C violation. Curiously enough, the combined CP symmetry invariance has been observed for the weak interaction processes observed at that time and it was believed that CP invariance was a property of nature [1]. This invariance held only until 1964 when CP violation was found in neutral Kaon decay [1]. Today CP violation is being carefully studied in the decay of various neutral bosons [1]. We will not go into the details of experimental study of these processes. We will rather examine another combined symmetry, namely CPT, but before we do so it is worth mentioning that after CP violation discovery many new theories were developed to accommodate these new observations. One of these theories is also Superweak interaction that predicts a non-zero neutron EDM and will be soon put to the test by the ever lowering upper 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 a higher combined symmetry and introduced the CP invariance. Now that we have found CP violation it is only natural to go another step higher and investigate CPT symmetry for 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 pointing magnetic field. In the center is located a particle with spin +1/2. After Time reversal is applied, the motion of electric current changes direction thus flipping magnetic field. Subsequent Parity transformation inverts 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 preserved while direction of spin is flipped. From this analysis it follows, that antiparticle should have opposite spin to 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 a very 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 also invariant under CPT transformation, whether or not it is invariant under C, P and T separately [1]. One example of CPT invariance is shown in Figure 3. In the picture we can see 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 the opposite spin. Invariance implies that both systems have the same energy. From here it follows that the magnetic moment of an anti-particle has to be opposite in sign and equal in 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 of processes where they were observed [1]. C P T example Yes Yes Yes strong, electromagnetic Yes No No none No No Yes β decay No Yes No none No No No neutral Kaon decay A proof of the CPT theorem is beyond our current interest, but we can happily use it to discuss our current topic of the neutron EDM. Obviously if a system is CP violating, it has 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 time reversal in a system which would be CP invariant even in the presence of EDM. 3 Experimental determination of the neutron EDM The first experimental test of the neutron EDM was conducted in 1950 in the Oak Ridge National Laboratory by a group of scientists led by Ramsey [4]. They used a neutron beam on which they performed measurements of Larmor frequency using NMR techniques. Although NMR is used for measurements of the magnetic moment it can be used to prepare neutron beam for subsequent measurement of EDM as will be discussed later. No EDM was measured at that point and interest in experimental search of it has died out for nearly a decade [4]. After the discovery of various symmetry violations the interest in the neutron EDM has been revived. There are mainly two techniques for EDM determination. One utilizes NMR, while the other is the scattering of a neutron beam on a stationary target[4,8]. Latter tries to utilize electric fields on an atomic scale, which are about factor 5 higher than any other achievable electric field in Figure 4: If the neutron would be of the size of the Earth, the current measurements would limit the displacement of opposite charges in its centre to less than a few microns [7]. the laboratory. Unfortunately, using a neutron beam has its disadvantages and preference has 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 d n = 3 10 26 e cm by an experiment conducted at Institute Laue-Langevin (ILL) in Grenoble [3]. This is an extremely small value and, just for illustration, the magnitude of the effective charge position displacement on a scale where the neutron s size would correspond to the size of the 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 constant magnetic field the neutron s spin direction will be precessing around the magnetic field direction unless they are collinear. The precession will occur with the Larmor frequency as is well known. If a neutron also possesses an electric dipole moment, then a shift in the Larmor frequency should be observed for parallel and anti-parallel electric and magnetic fields, given by [4,8] ω ± = γb 0 ± 2ed n E/. (19) Figure 5 schematically shows how this change occurs after the electric field is reversed while the magnetic field is held constant. This method is usually referred to as the NMR measurement 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 to the magnetic field so we can observe precession. Because the EDM of a neutron is always collinear with its magnetic moment we can observe changes in precession rate by inverting the electric field as indicated in Figure 5 [4]. The scattering experiments with a neutron beam try to make use of the atomic scale electric fields. The Hamiltonian for a neutron interacting with the electric and magnetic fields is given by [4,8] H = (µ B ) + d ne s s, (20) where the shifts in the energy of the beam in the electric and magnetic field are being searched for. The main experimental difficulty limiting the precision of the neutron beam experimental setup comes from the motional magnetic field [4,8] B m = E v c, (21) which for cold neutron beams corresponds to a field of about 1 mg [4]. A change in the Larmor frequency in a typical experimental setup would translate into a change of the magnetic field on a level of pg at the current limit. Therefore the systematic errors would be greater than expected neutron EDM and neutron beams are no longer in use in combination with NMR measurements [4]. Obviously we want the speed of hte neutrons to be minimal and neutrons can actually be prepared in a manner that they can be stored in a special bottle for measurements while moving at very low velocities. In what follows, we will concentrate on experimental methods with ultra-cold neutrons (UCN), as they provide the currently best experimental upper 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 been developed. 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 diminish preccesion rate [9]. by moderation in light atom liquid at low temperatures. Neutrons with kinetic energy of about 25 K can be obtained this way. It is hard to obtain lower temperatures of neutrons but fortunately, cold neutrons are almost Maxwell distributed and hence we can collect quite some neutrons of even lower energies. The neutrons with kinetic energies in the range of about 5 mk are usually referred to as being ultra cold. This energy corresponds to velocities of about 7 ms 1 [4]. In order to understand the generation of UCN we need to study how neutrons interact with matter. Classically we would expect neutrons to pass freely through matter unless scattered or absorbed by nuclei because they are neutral. Thus we would be unable to localize neutrons after their production and they would simply diffuse. Quantum mechanics luckily has a solution to this problem. Neutrons feel a small repulsive force in transition from the vacuum to a material although being neutral in charge. This effect occurs because of the boundary conditions on the wave function representing the neutron. Therefore also a repulsive potential U F will appear in the Hamiltonian function of a neutron s motion, given by [4] U F = 2π 2 ρa, (22) m where m is the mass of a neutron, ρ the number density of a nuclei of a given material and a the scattering length. For most nuclei a is a positive number and the potential will be repulsive [4]. It follows that a neutron with the kinetic energy component perpendicular to the wall of material smaller than U F will be reflected. Figure 6: Special containment bottle for the Ultra-cold neutrons. In the middle one can see 3 solid state detectors specially adopted for use within liquid Helium [10]. The potential U F is in the range of 100 300 nev, which gives a reflection angle of about 1 degree for cold (20 K) neutrons [4]. In this way cold and ultra cold neutrons can be guided away from the moderation chamber along a slightly bent guide to the experimental apparatus while faster neutrons will enter the material and be absorbed. If a neutron has a kinetic energy below the potential depth U F for the nuclei of a given 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(figure 6)). 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 from the 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 precision. Collisions of the neutron with the container wall are sufficiently short that not many UCN are being lost during a single run. The neutron lifetime of 886 s [2] (although being disputed [11,12]) also accounts for UCN losses and puts an upper limit on a complete duration time of a cycle [3,4]. 3.3 The EDM experiment with ultra-cold neutrons Figure 7: Apparatus used at the UCN EDM experiment conducted at ILL. Allong guides and polarization foils we can also see NMR radio frequency coils and comagnetometer setup for Hg atoms. [4] The containment of UCN is not enough to successfully measure the EDM. Polarized neutrons of only one spin are required so that the EDM does not average out. Neutron polarization now takes place at special ferromagnetic films on highly absorbing surfaces [4]. Due to the generalized Zeeman interaction given by the equation 20 the neutrons with the appropriate spin state will have a greater reflection angle θ c and will be reflected, while others will be lost in the absorbing material after penetrating ferromagnetic film. Today even optically pumped 3 He is used because of its increased absorbtion cross-section for one spin projection [4,8]. In order to maintain the neutron s spin state it is being guided to the containment bottle in moderate magnetic fields. This can be easily done if the neutron motion is so slow that we can approximately say that its magnetic moment always points along the guiding magnetic film, which can be assumed for UCN. The apparatus used at Institue Laue-Langevin can be seen in Figure 7 [4]. After polarizing the neutrons we still need to perform the NMR, therefore a RF coil is positioned right after the polarization foil in order to flip the spins. In the apparatus we need to monitor the background magnetic field very precisely in order to eliminate possible false EDM signals due to the inhomogeneous magnetic field [4]. The accuracy of the experimental setup is nowadays limited by the magnetic field monitoring. If we use SQUIDs or other external magnetometers outside of the containment bottle, we may not be measuring the actual field experienced by the UCN. Therefore an in situ magnetometer has been employed. Such magnetometers are called comagnetometers and it has been suggested that liquid helium could be used as comagnetometer. In practice it proved difficult to employ one, so 199 Hg atom gas was used instead. The 199 Hg comagnetometer is simply a gaseous 199 Hg mixed with the UCN and is not a true apparatus in itself. We call it a comagnetometer because we can reconstruct the actual magnetic field from parallel measurements of the Hg atom precession to the UCN precession [4]. 10

3.4 Systematics 3 EXPERIMENTAL DETERMINATION The idea is that Hg atoms do not have an EDM on their own [4], while having a magnetic dipole moment about three times smaller than neutrons. Therefore we can compare the precessions of UCN and Hg atoms to reconstruct whether frequency changes occur due to the neutron EDM or due to the fluctuating magnetic field. It is also important to mention that in the case that neutrons do have a non-zero EDM, that would also influence the Hg comagnetometer, but the EDM of Hg would be significantly shielded by its electrons, so the effect of the neutron EDM on 199 Hg comagnetometer can at present accuracy be neglected. In the setup we can see the Hg UV lamps which are used to optically pump the Hg atoms into the desired spin state [4]. Figure 8 is an example of neutron EDM data Figure 8: Blue circles represent the raw data frequency. After applying corrections due to the magnetic field variation red circles are obtained indicating no correlation of Larmor frequency with the electric field. The jump in the frequency seen in the raw data is due to changes in the magnetic field between two runs [13]. and results from the Institue Laue-Langevin experiment. The jump in the raw data was due to the uncorrected magnetic field changes between two runs. The red dots represent corrected data. No correlation with changes in electric field can be seen, thus no neutron EDM has been measured beyond experimental noise [3,12]. 3.4 Systematics For precision neutron EDM measurements with UCN we need a very precise knowledge of the background magnetic fields. Therefore it is important to identify the effects that can mimic the electric dipole moment and take them into account. One such effect from the motional magnetic field has already been mentioned. There are others, but we will not go into detailed analysis of them but rather briefly explain what else has been observed so far. Let us also note, that Van der Waals like induced electric dipole moment from neutron s vicinity should not be observed, as Electro-magnetic force is much weaker than strong interaction between quarks in the nuclei. Electric-field correlated magnetic effects appear because of the high electric potential applied to the systems. Because of this high electric fields leakage current can flow. If we imagine that such current flows along the containment bottle it will produce a magnetic dipole moment at its center. Because we will reverse the electric field in order to track any changes in the Larmor frequency, the direction of the leakage current might change accordingly, resulting in the reversed magnetic dipole moment. Such effects can mimic the true neutron EDM and in 1980 s two groups working independently reported neutron EDM readings due to systematics of this nature. After a short burst of excitement this systematic error has been found and the stir slowly faded [4]. Neutron EDM measurements are even so precise, that the gravitational field causes UCN and comagnetometer center of masses to separate by a tiny fraction. This separation in the orders of millimeters causes differences in frequencies of magnetometer and UCN. This rather masive displacement comes about because of very low kinetic energies and can provide unwanted experimental noise and in some configurations false EDM readings as well [4]. 11

REFERENCES The last systematic effect we will mention is the Geometric phase effect, which was discovered only recently after 60 years of experimental work. This effect can mimic the EDM signature when motional magnetic field is combined with the magnetic field gradient. The gradient in the magnetic field is crucial for an EDM signature as only motional magnetic field would average out in a UCN storage experiment. If we consider circular motion of the neutron due to small angle reflections with containment bottle a situation similar to leakage currents can occur. It can be shown that in combination with an inhomogenous magnetic field a false EDM signature can be produced [4]. 4 Conclusion Theoretical implications of finding a neutron EDM have revived experimental interest on this topic. The present experimental limit is only a factor 10 to 100 away from being able to test many theories beyond the Standard model and it is expected that within two to three years we could reach such a level of precision. There are several experimental setups in construction that will try to improve the ILL s limit. One of them is the CryoEDM experiment which is an upgrade of the ILL experiment where a liquid Helium bath will be introduced. It is expected that this will be the first experiment to improve the EDM limit, though potential for significant improvement is currently also attributed to the Spallation Neutron Source experiment currently under construction at Oak Ridge in USA. It will introduce a superfluid helium bath and combine it with increased UCN densities in containment bottles, thus further improving the sensitivity of the experimental setup [4]. The neutron EDM experiments have so far contradicted more theories than any other experiment. Figure 9 shows the historical progress of the neutron EDM search and which theories 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, expoeriments with beams have been terminated in 1980 and UCN experiments utilized henceforth. Since then many theories have been already been tested as seen on the right hand side. Presently constructed experiments will further improve the limit and put to the test new set of theories, while the Standard model for now remains out of reach [4]. 13