The Neutron Electric Dipole Moment - Essay Example

The Neutron Electric Dipole Moment (Neutron EDM) Abstract The search for the probable existence of a non-zero electric dipole moment (EDM) of the neutron has been a constant interest in the field of Physics. Understanding the nature of neutron EDM has a profound impact on our comprehending of the nature of the electro-weak and strong forces.1 Throughout the years, neutron EDM experiments and studies have had immense bearing in “shaping and constraining numerous models of CP violations.”2 It is possible that through these experiments new sources of CP-T violations maybe uncovered. The objective of this dissertation is to present the techniques used in the calculation of neutron EDM given a variety of hypothetical and conjectural set-ups. A concise introduction and explanation of the different experimental techniques used in the study of neutron EDM is provided in this research work. These techniques include the room-temperature experiment, Ramsey’s technique and the mercury magnetometer. A brief discussion of the prevailing systematic uncertainties such as the geometric phase effect is also included. A recent neutron EDM experiment, which is more sensitive and still in progress is also incorporated and detailed in this study. Acknowledgment The researcher wishes to extend her heartfelt gratitude and deep appreciation to the following for their help in making this dissertation possible: To her family, for all the support, understanding and encouragement, To her mentor, for giving advice and constructive criticisms, To her friends who consecutively helped in doing this study, To her colleagues for valuable discussions and suggestions. Table of Contents Tile Page Abstract Acknowledgment Table of Contents List of Figures CHAPTER I Introduction CHAPTER II Background CP and T Violation The Neutron EDM Ultra-Cold Neutrons Modelling of Neutron Spin Summary CHAPTER III Experimental Techniques Room Temperature Experiment: Apparatus Ramsey’s Technique of Separated Oscillatory Fields Mercury Magnetometer Sensitivity Summary CHAPTER IV Systematic Uncertainties Systematic Uncertainties Overview Geometric Phase Effect Magnetic Dipoles Summary CHAPTER V Modelling of Systematic Effects Modelling of Magnetic Dipoles Depolarization Studies Effects of Gravity Summary CHAPTER VI Conclusions BIBLIOGRAPHY List of Figures Figure 1 Sensitivity of neutron EDM experiments over time. On the left of the graph are some theoretical predictions of the magnitude of the neutron EDM. Figure 2 The direction of the emitted electron (arrow) reverses on mirror reflection, but the direction of rotation (angular momentum) is not changed. Figure 3 Parity (P) and Time Reversal (T) Violation Due to an Electric Dipole Moment Figure 4 Ramsey’s Hunting Table Figure 5 Measured Upper Limits of the Neutron EDM; also provided are the predictions resulting from SUSY and Standard Model Figure 6 Ultra-cold Neutron Energy Properties Figure 7 Ultra-cold Neutron Temperature Properties Figure 8 Ramsey’s Neutron EDM Measurement Principle CHAPTER I Introduction For over 50 years, the quest for an electric dipole moment (EDM) of a neutron has been a great endeavour in the field of physics.3 4 5 Ramsay’s search for a permanent EDM in the 1950’s leads the way to what seems to be an endless pursuit. Experimental sensitivity has increased significantly; in fact it improved by more than 106 factor.6 An impressive breakthrough in improving the experimental sensitivity, accountable for every eight years or so, is shown in Figure 1.7 Despite such remarkable accomplishment, there was no EDM ever observed. Why do some scientists still spend so much time and effort looking for an EDM, something that is almost deemed a lost cause? Lamareoux and Golub8 explained: The reason for this apparently obsessive behavior by a small group of dedicated physicists is that the observation of a nonzero neutron EDM would be evidence of time reversal violation and for physics beyond the so-called standard model of electroweak interactions. An essential point is that the standard model predictions of the magnitude of time reversal violation is inconsistent with our ideas of the formation of the universe; namely, the production of the presently observed matter-antimatter asymmetry requires time reversal violation many orders of magnitude greater than that predicted by the standard model. Figure 2 Sensitivity of neutron EDM experiments over time. On the left of the graph are some theoretical predictions of the magnitude of the neutron EDM. According to Steven Weinberg, the electric dipole moments may offer one of the most thrilling prospects for progress in particle physics; a bright future awaits prospective experiments because calculating electric dipole moments has been progressive recently.9 Golub and Huffman10 summarized the expectations of scientists and physicists in finding neutron electric dipole moments by saying, “the search for a neutron EDM represents the best existing hope for finding physics beyond the Standard Model as the detection of any non-zero neutron EDM would be unambiguous proof of the breakdown of the Standard Model.” CHAPTER II Background CP and T Violation Parity P, time reversal invariance T, and charge conjugation C are significant symmetry principles in nuclear science. In particle physics, these symmetries play a crucial point in understanding weak interactions or weak forces. It is also the key point in understanding “whether a nucleus behaves in a different way if its spatial configuration is reversed (P), if the direction of time is made to run backwards instead of forward (T), or if the matter particles of the nucleus are changed to antimatter (C).”11 In CP symmetry, charge conjugation transforms a particle into its antiparticle while parity creates the mirror image of an object. It has always been believed that physical laws are invariant or unchangeable even going through parity transformation. Nuclear properties such as space, time or charge are said to be reflected or reversed in mirror-like changes in symmetry properties. It is expected in our natural universe to have inverse, or mirror symmetries. Because parity symmetry has been validated for all reactions involving electromagnetism and strong forces, parity conservation was included among the fundamental conservational laws such as conservation of energy and conservation of momentum. In 1956, however, Physicist Tsung-Dao Lee and Chen Ning Yang contradicted these long held beliefs when they revealed that parity conservation is not verified in reactions concerning weak forces. To prove this further, Chien-Shiung Wu and her colleagues experimented on the beta decay of Cobalt-60 nuclei. They found out that when the nucleus was placed in a magnetic field, electrons from the beta decay were preferentially emitted in the direction opposite that of the aligned angular momentum of the nucleus.12 13 They concluded that the weak forces violate the P symmetry since some of the actual reactions did not proceed as supposed to their mirror images. When parity (P) reversal takes place, the charge distribution would be switched but the spin direction remains unchanged; time (T) reversal on the other hand, would change the spin direction but leave the spatial distribution of charge unaffected.14 Matis15 exemplified this situation in the image shown in Figure 2; an additional visual presentation of P and T violation is illustrated in Figure 3. Figure 2 The direction of the emitted electron (arrow) reverses on mirror reflection, but the direction of rotation (angular momentum) is not changed.16 Figure 3 Parity (P) and Time Reversal (T) Violation Due to an Electric Dipole Moment17 The actual directional preference is represented by the nucleus in front of the mirror while its reflection corresponds to a directional preference which does not exist in nature.18 If the mirror in Figure 2 both reversed spatial direction and changed matter into its antimatter, then the nucleus experiment in front would be the same as its reflection.19 We can therefore deduce that changing both C and P results in CP symmetry. On the other hand, a separate violation of C and T symmetries respectively fails to preserve CP symmetry.20 No asymmetry will arise if and only if all the symmetry elements charge, space and time are altered simultaneously. CP symmetry implies T symmetry and CP violation entails time-reversal invariance (T) violation as well.21 22 The Neutron EDM By definition, neutron electric dipole moment or nEDM is “a measure for the distribution of positive and negative charge inside the neutron.”23 A permanent electric dipole moment can only exist ‘with positive and negative charge centres of the neutron slightly off’.24 In such case Harris25 explains: A parity reversal would swap the charge distribution while leaving the spin direction unchanged, whereas T would reverse the direction of the spin but leave the spatial distribution of charge unaltered. In either case, the resulting particle would be distinct from the initial neutron. In some other systems, this is perfectly acceptable; the ammonia molecule, for instance, exists in two degenerate mirror-image forms, and an EDM is therefore possible without parity violation. In nuclear physics, however, Pauli’s exclusion principle is applied: no two identical neutrons may occupy the same quantum state simultaneously. Thus the existence of a finite EDM would be a direct result of CP and T violation.26 More than half a century has gone by since Ramsey ignited the quest for an electric dipole moment but not a single one has been found until now. Nuclear physicists and scientists, however, have not yet given up because the present neutron EDM limit has reached an unprecedented scale currently at .27 Theoretically, we can represent electric dipole moment, EDM, as the product of charge c, a given length l and a T-violation factor f.28 29 Thus, . As shown in Figure 1, neutron EDM experiments’ sensitivity has increased a hundred fold. Ramsey’s hunting table shown in Figure 430 provides some additional insights on neutron EDM limit. Figure 4 Ramsey’s Hunting Table As discussed earlier, CP violation has been observed in weak forces and is incorporated in the Standard Model (SM) of particle physics. The Standard Model, however, gives a very scanty amount of CP violation consequently contributing less to neutron EDM, .31 Extension to the Standard Model such as the Supersymmetry (SUSY) “postulates the existence of a fermionic (bosonic) ‘superpartner’ for every boson (fermion)”; which lead to a great CP violation.32 A strong CP violation, however, presents a challenge in putting constraints on CP violating phases. With this, the neutron EDM predictions only range from  and 33, as shown in the figure below. Figure 5 Measured Upper Limits of the Neutron EDM; also provided are the predictions resulting from SUSY and Standard Model.34 Ultra Cold Neutrons Initial experiments in search of neutron EDM made use of beams of thermal neutrons to carry out measurements. Smith, Purcell and Ramsey started their experiment in 1951 (results were published in 1957) wherein they acquired a limit of.35 It was only until 1977 that neutron beams were used for neutron EDM experiments; impossible high velocities of neutron in the beam made measurements incoherent. The ultimate neutron EDM limit achieved with a neutron beam was.36 Afterwards, ultra-cold neutrons or UCNs took over the succeeding experiments. UCNs are neutrons “which are reflected at any angle of incidence.”37 Several information pertaining to ultra-cold neutron properties are displayed in Figure 6 and 7.38 Figure 6 Ultra-cold Neutron Energy Properties Figure 7 Ultra-cold Neutron Temperature Properties Leningrad Nuclear Physics Institute (LNPI) was the first to use Ultra-cold neutrons in their neutron EDM studies; the produced nEDM upper limit was.39 The current and best upper limit of nEDM mentioned earlier was measured in 2006 at Institut Laue-Langevin (ILL) during an experiment which began in 1984.   Modelling of Neutron Spin Neutron EDM measurement attempts were based primarily upon the application of Ramsey’s technique of separated oscillatory fields to free neutrons.40 41 This technique involves the magnetic moment or ‘spin’ of neutrons. The simplified illustration and basic explanation of Ramsey’s measurement principle is shown in Figure 8. A more detailed discussion of Ramsey’s technique of separated oscillatory fields will be presented in Chapter III. Summary This Chapter presented the background of the study. It considered the crucial role of CP and T symmetry and violation in understanding weak interactions and its impact and contribution in measuring neutron electric dipole moments. It was emphasized that in order for a neutron EDM to exist, there should be a violation in CP and T symmetry. Although the experiments and studies conducted in search for neutron EDM has considerable success, an actual electric dipole moment is yet to be found. Experiments conducted today, including this study, endeavours to increase measurement sensitivity in order to get closer in finding neutron EDM. Figure 8 Ramsey’s Neutron EDM Measurement Principle.42 43 The following chapter will provide an in-depth review of the different experimental techniques employed in the study of neutron electric dipole moment. It will also include data and analysis of the present progress and development in the discovery of neutron EDM. BIBLIOGRAPHY 1. N. F. Ramsey, Molecular Beams (Oxford University Press, 1956). 2. J. H. Smith, E. M. Purcell, and N.F. Ramsey, Phys. Rev. 108, 120 (1957). 3. W. B. Dress, et al., Search for an Electric Dipole Moment of Neutron, Physical Review D 15: 9 (1977). 4. I. S. Altarev, et al., A Search for the Electric Dipole Moment of the Neutron Using Ultracold Neutrons, Nuclear Physics A 341, 269 (1980). 5. Philip Harris, The Neutron EDM Experiment, Department of Physics and Astronomy, University of Sussex, Falmer, Brighton BN1 9QH, UK. 6. D. Perkins, Introduction to High Energy Physics, 3rd Edition (Addison-Wesley, 1987). 7. E. A. Hinds and J. M. Pendlebury, Nucl. Instrum. Methods, Phys. Res. A 440, 471 (2000). 8. S. Dar, The Neutron EDM in SM: A Review, arXiv:hep-ph/0008248[hep-eh] (2000). 9. S. Abel, S. Khalil, and O. Lebedev, EDM Constraints in Supersymmetry Theories, Nuclear Physics B 606, 151 (2001). 10. J. M. Pendlebury, W. Heil, Yu Sobolev, P. G. Harris, J. D. Richardson, R. J. Baskin, D. D. Doyle, P. Geltenbort, K. Green, M. G. D. van der Grinten, P. S. Iaydjiev, S. N. Ivanov, D. J. R May, and K. F. Smith, Geometric-phase-induced False EDM Signals for Particles in Traps, Phys. Rev. A 70, 032102 (2001). 11. S. K. Lamoreaux and R. Golub, Detailed Discussion of a Linear Electric Field Frequency Shift Induced in Confined Gases by a Magnetic Field Gradient: Implications for Neutron EDM Experiments, Phys. Rev. A 71, 032104 (2005). 12. R. Golub and P.R. Huffman, Search for a Neutron Electric Dipole Moment, Journal of Research of the National Institute of Standards and Technology, Vol. 110, No. 3 (2005), 169-172. 13. M. Pospelov and A. Ritz, Electric Dipole Moments as Probes of New Physics, Annals of Physics 318, 119 (2005). 14. C. A. Baker, D. D. Doyle, P. Geltenbort, K. Green, M. G. D. van der Grinten, P. G. Harris, P. S. Iaydjiev, S. N. Ivanov, D. J. R May, J. M. Pendlebury, J. D. Richardson, D. Shiers, and K. F. Smith, Improved Experimental Limit on the Electric Dipole Moment of the Neutron, Physical Review Letters 97, 131801 (2006). 15. Oscar Naviliat – Cuncic, The Neutron Electric Dipole Moment, International Workshop on Fundamental Symmetries: from nuclei and neutrinos to the Universe ECT Trento (June 25-29 2007). 16. M. S. Sozzi, Discrete Symmetries and CP Violation (Oxford University Press, 2008) ISBN 978 – 0 – 19 – 929666 – 8. 17. Neutron Electric Dipole Moment (27 June 2010) at http://en.wikipedia.org/wiki/Neutron_electric_dipole_moment (July 19 2010). Read More