Michejew-Smirnow-Wolfenstein effect

The Michejew-Smirnow-Wolfenstein effect ( MSW effect for short ) is a particle physical process that influences neutrino oscillations in matter . The work of the US physicist Lincoln Wolfenstein from 1978 and the work of the Soviet physicists Stanislaw Michejew and Alexei Smirnow from 1986 made it possible to understand the effect.

Explanation

Neutrinos can be represented both as a superposition (“mixed state”) of three propagation eigenstates (mass eigenstates) and as a superposition of the flavor eigenstates electron-neutrino, muon-neutrino and tau-neutrino. The presence of electrons in matter changes the energy levels and flavor composition of the mass eigenstates due to the coherent forward scattering of the electron component by charged currents of the weak interaction . This influences the frequency , amplitude and coherence length of the neutrino oscillation. The coherent forward scattering is comparable to the electromagnetic process, which leads to different refractive indices of light in the medium.

In a vacuum and with low electron densities, neutrinos are always created with substantial proportions of all three eigenstates of mass, the relative phases of which can change during propagation, especially in matter, which becomes evident as neutrino oscillation.

In the core of the sun , electron neutrinos are generated with a very high electron density. For these high-energy solar neutrinos, which are observed in neutrino observatories such as the Sudbury Neutrino Observatory  (SNO) or Super-Kamiokande , the eigenstate of mass (index m for "matter") is much higher than and is practically identical to that Electron flavor intrinsic state and is therefore generated almost purely (very small proportions and ). When escaping from the sun, the state continuously changes into the vacuum state , whose electron flavor proportion of only 0.31 explains the observed neutrino deficit. ${\displaystyle \nu _{\mathrm {2m} }}$ ${\displaystyle \nu _{\mathrm {1m} }}$ ${\displaystyle \nu _{\mathrm {3m} }}$ ${\displaystyle \nu _{\mathrm {1m} }}$ ${\displaystyle \nu _{\mathrm {3m} }}$ ${\displaystyle \nu _{\mathrm {2m} }}$ ${\displaystyle \nu _{2}}$

At a certain electron density and ( MSW resonance ) cross each other . A conversion would occur if the curve of the electron density were steep enough. In the sun, however, the adiabatic theorem applies . ${\displaystyle n}$ ${\displaystyle \nu _{\mathrm {2m} }(n)}$ ${\displaystyle \nu _{\mathrm {3m} }(n)}$ ${\displaystyle \nu _{\mathrm {2m} }\rightarrow \nu _{\mathrm {3m} }}$

Experimental evidence

The Michejew-Smirnow-Wolfenstein effect is important for high-energy solar neutrinos and leads to the prediction that the probability that an electron neutrino has not changed its flavor state after propagation is, where denotes the solar mixing angle . This has been confirmed experimentally by the Sudbury Neutrino Observatory (SNO): the scientists of the SNO determined the flux of solar electron neutrinos to be about 34% of the total neutrino flux. The flow of electron neutrinos was determined via interactions with charged currents, and the total flow via interactions with neutral currents . ${\displaystyle P_{\mathrm {ee} }=\sin ^{2}(\theta )}$ ${\displaystyle \theta =34^{\circ }}$

For solar neutrinos of low energy the effect of the matter is negligible and the approximation of the vacuum oscillations is therefore valid. The size of the source (the core of the sun) is significantly larger than the oscillation length. Averaging over the oscillating factor (see Theoretical Basics of Neutrino Oscillation ) is therefore obtained . For the same value of the mixing angle, this corresponds to a probability of around 60% that an electron neutrino does not change its flavor state. This coincides with measurements of solar neutrinos in the lower energy range in the Homestake experiment (the first experiment which discovered the solar neutrino deficit), GALLEX , GNO and SAGE ( radiochemical experiments that used gallium as a scattering body ) and in the Borexino experiment. The results are also supported by the KamLAND reactor experiment . ${\displaystyle P_{\mathrm {ee} }=1-{\frac {1}{2}}\sin ^{2}(2\theta )}$ ${\displaystyle \theta =34^{\circ }}$

The transition between the range of low energy with a negligible Michejew-Smirnow-Wolfenstein effect and the range of high energy, in which the oscillation probability is determined by matter, is around 2 MeV for neutrinos from the sun.

The Michejew-Smirnow-Wolfenstein effect can also influence neutrino oscillations in the Earth's interior ; future searches for new oscillation effects or leptonic CP violation could exploit this fact.

literature

• G. Brooijmans: Neutrino Oscillations in Matter: the MSW Effect . In: A New Limit on ν _μ → ν _τ Oscillations (PDF; 3.1 MB) . Université catholique de Louvain . July 28, 1998. Retrieved April 24, 2010.
• Alexei Jurjewitsch Smirnow : Solar neutrinos: Oscillations or No-oscillations? September 2016, arxiv : 1609.02386 .
• B. Schwarzschild: Antineutrinos From Distant Reactors Simulate the Disappearance of Solar Neutrinos . In: Physics Today . 56, 2003, p. 14. bibcode : 2003PhT .... 56c..14S . doi : 10.1063 / 1.1570758 .

Individual evidence

1. ↑ L. Wolfenstein : Neutrino oscillations in matter . In: Physical Review D . 17, No. 9, 1978, p. 2369. bibcode : 1978PhRvD..17.2369W . doi : 10.1103 / PhysRevD.17.2369 .
2. ↑ S. Michejew , A. Smirnow : Resonant amplification of ν oscillations in matter and solar-neutrino spectroscopy . In: Nuovo Cimento C . 9, No. 1, 1986, pp. 17-26. doi : 10.1007 / BF02508049 .