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Hep-Ex/0401016V1 13 Jan 2004 Et Ic H Neato Aitna Nthat in Hamiltonian Interaction the Since Ments Symmetries

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Hep-Ex/0401016V1 13 Jan 2004 Et Ic H Neato Aitna Nthat in Hamiltonian Interaction the Since Ments Symmetries Electric Dipole Moments of Fundamental Particles Yannis K. Semertzidisa aBrookhaven National Laboratory, Physics Department, P.O. Box 5000, Upton, NY 11973-5000, USA Electric dipole moment (EDM) experiments are at the fore-front of search for physics beyond the standard model. The next generation searches promise to improve by several orders of magnitude the current EDM sensitivity levels. 1. Theoretical Motivation case is The search for electric dipole moments (EDM) HM = dM S~ B~ (2) of fundamental particles started approximately − · fifty years with Ramsey’s search for a neutron Under parity both axial vectors S~ and B~ do not EDM. Even though the techniques have been im- change sign whereas under time reversal they proved and the sensitivities has reached an un- both do. Therefore the interaction Hamiltonian precedented small level no EDM of a fundamen- does not suffer a sign change and the parity and tal particle has been observed so far. Non-the-less time reversal symmetries are respected by the EDM experiments have put strict limits and con- magnetic dipole moments. strained the parameter space of models beyond If EDMs are not allowed by the above symme- the standard model. try considerations how then there can be induced The permanent EDM of fundamental particles EDMs, permanent EDMs of polar molecules, etc? would violate both time (T) and parity (P) sym- The cases of the induced electric dipole moments arXiv:hep-ex/0401016v1 13 Jan 2004 metries: an EDM vector would have to be along are allowed since the EDM vector in those cases the spin vector since there is no other defining is proportional to the electric field vector d~ = vector. Phenomenologically any component in E αE~ and not the spin vector. The interaction any other direction would average out to zero due Hamiltonian becomes proportional to the square to the particle’s spin rotation. The interaction of the E-field and both symmetries, parity and Hamiltonian is given by time reversal, are respected. As far as the po- HE = dES~ E~ (1) lar molecules that exhibit “permanent” electric − · dipole moments they also respect the above sym- where S,~ E~ denote the spin vector and the elec- metries with their quantum mechanical treatment tric field vector respectively. The symbol dE de- described by Penny [1]. notes the electric dipole moment strength. Under Through the fundamental CPT conservation parity the axial vector S~ does not change sign theorem, T-violation also means CP-violation. whereas E~ does. The opposite happens when the A general overview of the importance of CP- time operator is applied, i.e. the vector S~ does violation is written by J. Ellis in the CERN change sign whereas E~ does not. In both cases Courier [2] in October of 1999. Sakharov [3] in the interaction Hamiltonian changes sign mean- his 1967 paper pointed out that CP-violation is ing that if dE is not zero the Hamiltonian would one of three requirements needed to explain the violate both parity and time reversal symmetries. matter antimatter asymmetry of our universe. This is not the case for the magnetic dipole mo- The first requirement was that the proton ments since the interaction Hamiltonian in that should be unstable. The second was that there 1 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 mod- els beyond the SM allow for much higher val- ues 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 parti- cles. 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 exper- iment [8]. It is a small scale, “table top”, ex- periment where Tl atomic beams are led to go through high electric field regions where there is also a magnetic field present. The Larmor fre- quency 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.
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