Neutrino oscillation

As neutrino oscillation is in the physics of Bruno Pontecorvo in 1957 theoretically predicted conversion between different elementary particles, the electron, muon and tau neutrinos, referred due to quantum mechanical processes. That is, a neutrino was originally created with a specific of these three flavors, then a subsequent quantum measurement a different flavor arise ( conservation of Leptonenfamilienzahlen injured). Since the probabilities for each flavor change periodically with the propagation of neutrinos, one speaks of neutrino oscillations.

For these theoretical oscillation process would have a neutrino (albeit relatively small ) have mass, which would have far- reaching consequences for the Standard Model of elementary particle physics.

Solar neutrino deficit

For the first time discussed about possible neutrino oscillations in the discovery of the solar neutrino deficit. Neutrinos are produced in large numbers in nuclear fusion processes inside the sun.

In the 1960s, Raymond Davis Jr. began with the investigation of the solar neutrino stream with an electron-neutrino detector in the Homestake mine (chlorine detector ). The measured neutrino flux corresponded but only less than half of the expected result of the luminosity of the sun flow.

The luminosity of the sun can be theoretically calculated from the measured properties of atoms and atomic nuclei of complex so-called solar models. Some of these models are referred to as standard solar models ( SSM), because the scientific community has agreed as a reference model, after a long discussion on it. One then says that these models are " well understood " are. Under the assumption that these SSMs describe the sun correctly, and that neutrinos do not undergo significant interaction with matter, the result of the Homestake experiment may be interpreted as a " disappearance" of the neutrinos. The current view in the scientific community involved assumes that the SSMs are substantially correct and that the neutrinos do not undergo significant interaction with matter inside the Sun and in the Earth's atmosphere. The calculated under these conditions disappearance of neutrinos is explained by neutrino oscillation, in which the electron neutrinos are oscillating into muon neutrinos.

Raymond Davis Jr. won for the Homestake experiment for the detection of cosmic neutrinos (ie neutrinos that come from outer space ) the 2002 Nobel Prize in Physics. Important early observations also provided Donald H. Perkins.

Theoretical basis

It requires two assumptions. Firstly, neutrinos must have different masses, on the other hand are the mass eigenstates of the neutrinos with respect to the interaction states ( Pontecorvo - Maki - Nakagawa- Sakata - mixture (sometimes just MNS mix ) analogous to the CKM mixing in the quark sector) be mixed. This will be illustrated for the case of 2 -flavor oscillation of highly relativistic neutrinos, the interaction states are (at 3 - flavor). The mixture is then passed through a parameter, the mixing angle characterizes:

Where and are the mass eigenstates are, but can not be observed, since neutrinos participate only in weak interactions and thus are only in the interaction states and observed. If we consider the neutrino mass eigenstates is considered as a plane wave:

For hochrelativistische neutrinos with the approximation applies: whereby the pulse by

Can be approximated. The time can be expressed by the flight path. Thus, the plane wave is described wiefolgt:

For the time evolution of the interaction states, and thus results from the superposition of two slightly different plane waves:

If the two mass eigenstates are no longer in phase after a finite flight distance, so it is possible to find other posts of this condition in an originally generated interaction state. Then for the oscillation probability:

Here is the difference of mass squares of the flavors.

In neutrino oscillations in matter of so-called MSW effect (only when the density change ) occurs (named after Stanislaw Mikheyev, Alexei Smirnov, and Lincoln Wolfenstein Jurjewitsch ). This caused for certain electron densities and neutrino mass differences in matter a resonant enhancement of the oscillation.

Neutrino oscillations provide a first insight into the physics beyond the Standard Model. In the Standard Model neutrinos are massless and only act as the left-handed particles. With the observation of neutrino oscillations, these assumptions are no longer tenable. The necessary modifications to the standard model for the realization of massive neutrinos include, for example, the incidence of right-handed neutrinos or of Majorana neutrinos. Right-handed neutrinos but are not subject to the electroweak or strong interactions, ie they are sterile. Majorana neutrinos are their own antiparticles, so that the lepton number conservation is no longer guaranteed.

MNS matrix

(also Maki - Nakagawa- Sakata matrix)

The solar and atmospheric neutrino experiments have shown that neutrino oscillations result from a difference between the flavor and mass eigenstates of neutrinos. The relationship between these eigenstates is given by

In which

A neutrino with a specific flavor called α. α = e ( electron), μ ( muon ) or τ ( tauon ).
Is a neutrino with a given mass, indexed by = 1, 2, 3
Means the complex conjugation ( for antineutrinos must be those omitted from the second equation and it added to the first equation ).

Is the symbol for the Maki - Nakagawa- Sakata matrix ( also MNS matrix, neutrino mixing matrix, or sometimes called PMNS matrix to include Pontecorvo ). It is the analogue of the CKM matrix for quarks and parameterized by the Weinberg angle mixing matrix of the electroweak interaction. If this matrix is the identity matrix, then the flavor eigenstates would be the same as the mass eigenstates. However, show the above-mentioned experiments have shown that this is not the case.

If the standard three - neutrino theory is consistent, then it must be of a 3 × 3 matrix with only two different neutrinos (two flavors ) it would be a 2 × 2 matrix, with four neutrinos a 4 × 4 matrix. In the case of three flavors is given by:

Where cij = sij = cosθij and sinθij. The phase factors α1 and α2 are only different from zero if the neutrinos are Majorana particles ( this question is still undecided ) - but this is relatively unimportant for the neutrino oscillation. In the case of neutrinoless double beta decay of these factors only affect the rate. Δ the phase factor is different from zero only if the neutrino injured CP symmetry. Is indeed expected, but was not previously observed experimentally. Or other new physics beyond the Standard Model requires (same goes for the CKM matrix ): If the experiment was to show that this 3 × 3 matrix should not be unitary, then would sterile neutrinos (sterile neutrino English).

Current values are: The mass differences in the neutrino mass spectrum are given by

Where NH describes the normal hierarchy with IH and the inverse hierarchy. The angles are as follows:

In addition are the. This implies the following MNS matrices:

Experiments

Types

Radiochemical experiments as mentioned Homestake experiment to measure the electron - neutrino flux over a longer period. It makes use of in these experiments that the beta -decay by neutrino capture can be reversed. For example, 71Ga converts by capture of an electron neutrinos in 71Ge with the emission of an electron around. These individual atoms can then be detected by the return decomposition as in GALLEX experiment at Gran Sasso, chemically separated from the detector and.
Real-time experiments do not capture the neutrinos themselves, but its recoil partner. Its pulse is often evaluated via the Cherenkov radiation, but also other methods of detecting high-energy physics are used. At this Cherenkov type belongs to the Japanese Super - Kamiokande detector, a 50,000 t light -water target with more than 10,000 photomultipliers and the Canadian SNO detector. Another approach to detect the particles in ( almost ) real time, of the Laboratori Nazionali del located in the Italian Gran Sasso OPERA detector tracked ( direct detection of tau neutrino appearance).

Both types of experiments confirm the neutrino oscillations.

Astronomical observations

Solar neutrino oscillations were observed and Others with the Super Kamiokande and SNO mentioned above.

Reactor and accelerator experiments

These include LSND, KARMEN, K2K, T2K, Mini Boone, CNGS, Double Chooz and Daya Bay.

In the K2K experiment, were detected in the produced neutrinos from KEK to Super - Kamiokande detector, a neutrino deficit could also be measured. After generating some of the electron neutrinos were detected in the near-end detector of the KEK and predicted it how many neutrinos with or without oscillation in the Kamioka 250 km away (today Hida ) should be measured. There arrived only 70 % of the electron-neutrino events that were predicted without oscillation. In addition, a shift in the energy spectrum of the detected neutrinos was found, which is characteristic of neutrino oscillations.