Electric dipole moment of the neutron

The electric dipole moment of the neutron (English Neutron electric dipole moment nEDM ) is a measure of the distribution of positive and negative charges within the neutron . A dipole moment other than zero can only exist if the centers of the positive and negative charge distributions within the particle do not coincide. The standard model or its extensions can be checked using the measured value . So far the nEDM could not be proven. The upper limit is currently d _n <1.3 · 10 ⁻²⁶ e · cm.

theory

A permanent electric dipole moment of an elementary particle violates the invariance of parity (P) and time reversal (T). This can be made clear as follows: Since the only specific direction for elementary particles is that of spin , the electric dipole moment must also point in the direction of spin. So it applies . The energy that an electric dipole generates due to this dipole moment is then . If you now carry out a P-transformation, the sign of this energy changes (whereby P is violated), since the spin as an axial vector remains unchanged, but the electric field changes its sign. In the case of a T-transformation, on the other hand, the electric field remains unchanged, but the spin changes its sign, which again changes the sign of the energy, which also violates T. According to the CPT theorem , this also means a CP violation . ${\displaystyle {\vec {d}}_{n}=|d_{n}|\cdot {\frac {\vec {s}}{|{\vec {s}}|}}}$ ${\displaystyle \Delta E=|d_{n}|\cdot {\frac {\vec {s}}{|{\vec {s}}|}}\cdot {\vec {E}}}$

Standard model

As shown before, one needs processes that violate the CP symmetry in order to generate a finite nEDM. CP-injury were in processes of weak interaction observed and are on the CP-violating phase of the CKM matrix in the standard model built. However, the severity of the CP violation is very small and the contribution to the nEDM is therefore only of the order of 10 ⁻³² e · cm.

Matter-antimatter asymmetry

→ Main article : Baryogenesis

A clear violation of CP invariance can be deduced from the asymmetry between matter and antimatter in the universe . Evidence of an nEDM that has a higher value than predicted by the Standard Model would confirm this suspicion and contribute to an understanding of the CP-violating processes.

Strong CP problem

Because the neutron is made up of quarks , it is prone to CP violations of the strong interaction . The Quantum - the theoretical description of the strong interaction - already contains by nature a term which breaks the CP-symmetry. The size of this term is characterized by the angle θ . The current limit for the nEDM limits this angle to less than 10 ⁻¹⁰ rad . The fact that this angle is not of the order of 1, as actually expected, is known as the strong CP problem .

SUSY CP problem

Supersymmetrical extensions of the standard model, such as B. the MSSM ( Minimum Supersymmetric Standard Model ), usually result in a high CP violation. Typical predictions for the electric dipole moment of the neutron are between 10 ⁻²⁵ e · cm and 10 ⁻²⁸ e · cm. As with the strong interaction, the CP-violating phase is restricted by the upper limit of the nEDM in supersymmetric theories, but not to the same extent so far.

Experimental approach

To determine the electric dipole moment of the neutron, one measures the Larmor precession of the neutron spin in the presence of parallel and antiparallel magnetic and electric fields. The precession frequency for both cases is given by

${\displaystyle h\nu =2\mu _{n}B\pm 2d_{n}E}$.

The term is made up of the contribution of the precession, due to the magnetic moment, in the magnetic field and the contribution of the precession, due to the electric dipole moment, in the electric field. The nEDM can now be determined from the difference between the two frequencies:

${\displaystyle d_{n}={\frac {h\,\Delta \nu }{4E}}}$

The biggest challenge of the experiment (and the biggest source of systematic error) is to make sure that the magnetic field does not change during the two measurements.

history

Measurement results for the upper limit of the nEDM. The areas in which the nEDM should be located according to the standard model and supersymmetric theories are also shown.

The first experiments looking for the nEDM used beams of thermal (and later cold) neutrons to make the measurements. It started with the experiment by Smith, Purcell and Ramsay in 1951 (published in 1957), which resulted in an upper limit of d _n = 5 · 10 ⁻²⁰ e · cm.

Neutron beams were still used for nEDM experiments until 1977, but then the systematic errors resulting from the high speeds of the neutrons became too large. The final limit reached with a neutron beam is d _n = 3 · 10 ⁻²⁴ e · cm.

After that, experiments with ultra-cold neutrons were continued. The first experiment of this kind was carried out in 1980 at the Leningrad Nuclear Physics Institute and resulted in an upper limit of d _n = 1.6 · 10 ⁻²⁴ e · cm This experiment and the one started in 1984 at the Laue-Langevin Institute improved the limit again by two orders of magnitude and achieved the above-mentioned, so far best upper limit for the nEDM in 2006.

In the 50 years in which such experiments have already been carried out, the value for the upper limit has already been improved by six orders of magnitude, whereby theoretical models are severely restricted.

Current experiments

There are currently several experiments around the world attempting to improve the upper limit for the nEDM to 10 ⁻²⁸ e · cm over the next 10 years (or to actually measure it for the first time). This will cover the entire area in which the electric dipole moment of neutrons could lie according to supersymmetric theories.

• nEDM experiment under construction at TRIUMF
• nEDM experiment under construction at the Laue-Langevin Institute
• nEDM experiment under construction at the new UCN source at the Paul Scherrer Institute
• JEDI (Jülich Electric Dipole Moment Investigations) experiment at Forschungszentrum Jülich

Individual evidence

1. ↑ C. Abel, et al .: Measurement of the permanent electric dipole moment of the neutron . In: Physical Review Letters . 124, No. 8, 2020, p. 081803. arxiv : 2001.11966 . doi : 10.1103 / PhysRevLett.124.081803 .
2. ^ Donald H. Perkins : Introduction to High Energy Physics . 4th edition. Cambridge University Press, Cambridge 2000, ISBN 978-0-521-62196-0 , pp. 82 .
3. ↑ Shahida Dar: The Neutron EDM in the SM: A Review . August 27, 2000, arxiv : hep-ph / 0008248 .
4. ^ S. Abel, S. Khalil, O. Lebedev: EDM constraints in supersymmetric theories . In: Nuclear Physics B . 606, 2001, pp. 151-182. arxiv : hep-ph / 0103320 . bibcode : 2001NuPhB.606..151A . doi : 10.1016 / S0550-3213 (01) 00233-4 .
5. ↑ M. Pospelov, A. Ritz: Electric dipole moments as probes of new physics . In: Annals of Physics . 318, 2005, pp. 119-169. arxiv : hep-ph / 0504231 . bibcode : 2005AnPhy.318..119P . doi : 10.1016 / j.aop.2005.04.002 .
6. ^ JH Smith, EM Purcell, NF Ramsey: Experimental Limit to the Electric Dipole Moment of the Neutron . In: Physical Review . 108, 1957, pp. 120-122. bibcode : 1957PhRv..108..120S . doi : 10.1103 / PhysRev.108.120 .
7. ^ WB Dress, et al .: Search for an electric dipole moment of the neutron . In: Physical Review D . 15, 1977, pp. 9-21. bibcode : 1977PhRvD..15 .... 9D . doi : 10.1103 / PhysRevD.15.9 .
8. ↑ IS Altarev, et al .: A search for the electric dipole moment of the neutron using ultracold neutrons . In: Nuclear Physics A . 341, No. 2, 1980, pp. 269-283. bibcode : 1980NuPhA.341..269A . doi : 10.1016 / 0375-9474 (80) 90313-9 .
9. ^ NF Ramsey: Electric-Dipole Moments of Particles . In: Ann. Rev. Nucl. Part. Sci. . 32, 1982, pp. 211-233. bibcode : 1982ARNPS..32..211R . doi : 10.1146 / annurev.ns.32.120182.001235 .
10. ↑ TRIUMF Ultracold Neutron Source
11. ↑ hepwww.rl.ac.uk CryoEDM experiment
12. ↑ psi.ch/nedm
13. ↑ http://www.fz-juelich.de/ikp/ikp-2/DE/Forschung/JEDI/_node.html