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Register a new userElementary quantum mechanics of the neutron with an electric dipole moment
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The neutron, in addition to possibly having a permanent electric dipole moment as a consequence of violation of time-reversal invariance, develops an induced electric dipole moment in the presence of an external electric field. We present here a unified non-relativistic description of these two phenomena, in which the dipole moment operator, $vec{cal D}$, is not constrained to lie along the spin operator. Although the expectation value of $vec{cal D}$ in the neutron is less than $10^{-13}$ of the neutron radius, $r_n$, the expectation value of $vec {cal D},^2$ is of order $r_n^2$. We determine the spin motion in external electric and magnetic fields, as employed in past and future searches for a permanent dipole moment, and show that the neutron electric polarizability, although entering the neutron energy in an external electric field, does not affect the spin motion. In a simple non-relativistic model we show that the expectation value of the permanent dipole is, to lowest order, proportional to the product of the time reversal-violating coupling strength and the electric polarizability of the neutron.
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Until now no electric dipole moment of the neutron (nEDM) has been observed. Why it is so vanishingly small, escaping detection for the last 65 years, is not easy to explain. In general it is considered as one of the most sensitive probes for the violation of the combined symmetry of charge and parity (CP). A discovery could shed light on the poorly understood matter/antimatter asymmetry of the Universe. The neutron EDM might one day help to distinguish different sources of CP-violation in combination with measurements of paramagnetic molecules, diamagnetic atoms and other nuclei. This review presents an overview of the most important concepts in searches for an nEDM as well as a brief overview of the worldwide efforts.
We present the result of an experiment to measure the electric dipole moment (EDM) of the neutron at the Paul Scherrer Institute using Ramseys method of separated oscillating magnetic fields with ultracold neutrons (UCN). Our measurement stands in the long history of EDM experiments probing physics violating time reversal invariance. The salient features of this experiment were the use of a Hg-199 co-magnetometer and an array of optically pumped cesium vapor magnetometers to cancel and correct for magnetic field changes. The statistical analysis was performed on blinded datasets by two separate groups while the estimation of systematic effects profited from an unprecedented knowledge of the magnetic field. The measured value of the neutron EDM is $d_{rm n} = (0.0pm1.1_{rm stat}pm0.2_{rm sys})times10^{-26}e,{rm cm}$.
The connection between a regularization-independent symmetric momentum substraction (RI-$tilde{rm S}$MOM) and the $overline{rm MS}$ scheme for the quark chromo EDM operators is discussed. A method for evaluating the neutron EDM from quark chromoEDM is described. A preliminary study of the signal in the matrix element using clover quarks on a highly improved staggered quark (HISQ) ensemble is shown.
A new measurement of the neutron EDM, using Ramseys method of separated oscillatory fields, is in preparation at the new high intensity source of ultra-cold neutrons (UCN) at the Paul Scherrer Institute, Villigen, Switzerland (PSI). The existence of a non-zero nEDM would violate both parity and time reversal symmetry and, given the CPT theorem, might lead to a discovery of new CP violating mechanisms. Already the current upper limit for the nEDM (|d_n|<2.9E-26 e.cm) constrains some extensions of the Standard Model. The new experiment aims at a two orders of magnitude reduction of the experimental uncertainty, to be achieved mainly by (1) the higher UCN flux provided by the new PSI source, (2) better magnetic field control with improved magnetometry and (3) a double chamber configuration with opposite electric field directions. The first stage of the experiment will use an upgrade of the RAL/Sussex/ILL groups apparatus (which has produced the current best result) moved from Institut Laue-Langevin to PSI. The final accuracy will be achieved in a further step with a new spectrometer, presently in the design phase.
Considering the CP violating phases, we analyze the neutron electric dipole moment (EDM) in a CP violating supersymmetric extension of the standard model where baryon and lepton numbers are local gauge symmetries(BLMSSM). The contributions from the one loop diagrams and the Weinberg operators are taken into account. Adopting some assumptions on the relevant parameter space, we give the numerical results analysis. The numerical results for neutron EDM can reach $1.05times 10^{-25}(e.cm)$, which is about the experimental upper limit.
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