On June 15, 2011, the international T2K (Tokai-to-Kamioka) experiment announced the detection of 6 events that are candidates for electron neutrinos. The data accumulated during the experiment with a beam of muon neutrinos from January 2010 to the earthquake in Japan on March 11, 2011 were analyzed. For the first time, direct experimental indication of the oscillations of muon neutrinos into electron neutrinos was obtained.

A little about the properties of neutrinos

There are three types of neutrinos in nature - electron (ν e), muon (ν μ) and tau neutrino (ν τ), which, being neutral leptons, are associated with the corresponding charged leptons electron, muon and tau lepton. Each neutrino has its own antiparticle - an antineutrino. Each type of neutrino has its own lepton number, the same as its partner - the charged lepton. The weak interaction, in which neutrinos participate, conserves lepton numbers. For example, when a muon decays, it must emit a muon neutrino. In the Standard Model, neutrinos are massless particles that, when propagating at the speed of light, cannot change their flavor (type), i.e., they do not mix, since the laws of conservation of the lepton number are postulated for each of the three families of leptons separately.

The reality turned out to be more complicated. There is an interesting quantum mechanical effect: particle oscillations. Particles can transform into each other on the fly, if this is not prohibited by conservation laws. In free flight, it is not a particle of a certain type that “lives”, but a “mass state” - a combination of two particles transforming into each other. Let’s say that at birth the mass state is represented by a particle of one type, then after some time it turns into another type, then back, etc. The period of transformations is inversely proportional to the difference in the squares of the particle masses (i.e., at least one of them must have non-zero mass). The transition may not be complete, i.e., only a quantum mechanical impurity of the second particle appears, and the magnitude of the impurity is determined by a parameter called the “mixing angle” of the particles. The hypothesis of neutrino oscillations was first put forward by B. M. Pontecorvo in 1957.

It turned out that neutrinos oscillate! This means they have a small non-zero mass, mix, and neutrino flavors (lepton numbers) are not conserved. Neutrinos participating in weak interactions are a linear combination of their own mass states ν 1, ν 2, ν 3, which correspond to masses m 1, m 2, m 3. The physics of neutrino oscillations is described by a unitary matrix, which is generally parameterized through three mixing angles θ 12, θ 23 and θ 13, one CP odd phase δ and two Majorana phases.

Neutrinos participate in weak interactions as ν e, ν μ, ν τ, i.e., having a certain flavor. And to see the effect of mixing, you need to work with mass states that can manifest themselves in the process of neutrino propagation as free particles through a vacuum. The neutrino, which was purely muonic at the moment of birth (t = 0), after a time interval (t > 0) is no longer such, acquiring a certain admixture of electron neutrinos.

Measuring oscillations can be done in two ways. One method is to measure the known initial neutrino flux and observe the decrease in this flux compared to the predicted value in the absence of oscillations.

This method is called an "extinction" experiment. Another method is to detect β flavor neutrinos in a neutrino beam that initially consists only of α flavor neutrinos. This method is called an "emergence" experiment.

Experiments with solar, atmospheric, reactor and accelerator neutrinos have clearly established that neutrinos mix. From solar and reactor experiments, the value θ 12 ~ 34° was obtained, and from experiments with atmospheric and accelerator neutrinos it follows that θ 23 ~ 45°. For the mixing angle θ 13 in the CHOOZ experiment, an upper limit of about 12° was obtained. Unlike quarks, neutrinos have large mixing angles, which was an unexpected result. To get a complete picture of neutrino oscillations, it is necessary to obtain three pieces of missing information: 1) measure the angle θ 13; 2) determine the CP odd phase δ; 3) find out which mass hierarchy (m 3 > m 2 or m 2 > m 3) is realized in nature. The search for oscillations ν μ → ν e and measurement of the angle θ 13 are currently one of the key problems of neutrino physics. This is connected both with understanding the nature of oscillations and with the search for CP violation in the lepton sector.

Experiment T2K

The main goal of the first stage of the T2K experiment is to search for oscillations ν μ → ν e and measure the angle θ 13. The next stage (in the case of a non-zero and not small value of θ 13) is a measurement with a beam of muon antineutrinos, a search for CP violation and a measurement of the phase δ. The T2K collaboration includes more than 500 scientists and engineers representing 59 institutes from 12 countries. INR RAS is participating on behalf of Russia in the experiment.

The main elements of the T2K installation are a neutrino channel, a complex of near neutrino detectors at a distance of 280 m from the target, and a far neutrino detector.

SuperKamiokande, located under Mount Ikenoyama. From the place of their birth to registration in SuperKamiokande, neutrinos travel a distance of 295 km through the Earth, as shown in Figure 1.

The experiment uses a pure (the admixture of electron neutrinos in the maximum of the spectrum is less than 0.5%) beam of muon neutrinos, the energy of which has a small spread and is tuned to the first oscillation maximum. Such a beam is obtained by using the kinematics of the decay of pions produced during the interaction of protons with a target into muons and muon neutrinos and choosing the direction of the neutrinos relative to the direction of the proton beam. An approximate expression for the transitions of muon neutrinos to electrons is as follows.

For an angle between the proton beam and the direction to the far detector of 2.5 degrees, the maximum intensity of the neutrino spectrum corresponds to an energy of 600 MeV, which allows you to tune in to the maximum sensitivity to neutrino oscillations, corresponding to the maximum probability in the above formula for the selected flight base of 295 km and parameters Dm 2 13 = 2.4·10 3 eV 2, sin 2 2q 23 ~ 1.0, obtained from “atmospheric” oscillations.

The near neutrino detector (ND280) is used to measure the initial (before oscillations) neutrino beam, to continuously monitor its parameters, and to measure neutrino cross sections in the energy region of about 1 GeV. The ND280 consists of two detectors. A single detector located on the beam axis controls the intensity, profile and direction of the beam with an accuracy of better than 1 mrad. The second detector (off-axis) is a complex installation consisting of several detectors (one of which, the muon range detector (SMRD), was developed and created at the INR RAS), which makes it possible to control the direction of the neutrino beam and measure the neutrino energy with an accuracy of about 15 MeV and measure cross sections for neutrino interaction through charged and neutral currents. The main elements of the off-axis detector, located at an angle of 2.5 degrees, are shown in Figure 2. To measure the momentum and charge of the particles, a magnetic field is used, created by a magnet that was previously used at CERN in the UA1 and NOMAD experiments.

The SuperKamiokande long-range detector is a giant tank with a diameter of 39 m and a height of 42 m, filled with clean water. Along the walls, bottom and roof of the detector, with a pitch of 70 cm, there are about 11,000 large photomultiplier tubes, which record Cherenkov radiation from charged particles resulting from the interaction of neutrinos with the detector matter. The detector registers neutrinos in the energy range from 4.5 MeV to 1 TeV. The size, direction, and shape of the Cherenkov cone are used to identify the event: a single-ring muon-like event, a single-ring electron-like event, or a multi-ring event. The muon-like ring from the Cherenkov radiation of the muon has a shape with sharp edges, and the ring from the electron has a blurry shape. Time synchronization with the proton beam is carried out through the GPS navigation system with an accuracy of about 50 nanoseconds. This accuracy makes it possible to observe the time structure of recorded neutrino events and its correspondence to the time structure of the proton beam, which makes it possible to suppress the background from atmospheric neutrinos to a negligible level. Neutrino events were recorded within an interval of ±500 μs relative to the expected time of appearance of neutrinos from J-PARC.

The creation of a neutrino channel and a nearby neutrino detector began in April 2004 and was completed in 2009. The collection of statistics began in January 2010. During this time, 88 neutrino events were recorded in the active volume of the detector of 22.5 kt, the energy of which was more than 30 MeV and was measured entirely in the detector. All these events were in the time interval from –2 to 10 μs with respect to the time trigger synchronized with the proton beam structure, while the background level from atmospheric neutrinos in this time interval was only 0.003 events. After additional analysis, 6 events were identified as electron-like events resulting from the interaction of electron neutrinos with energies from 100 to 1250 MeV in the detector through a charged current (i.e., with the birth of an electron and the disappearance of a neutrino). One such event is shown in Figure 3.

The expected number of such events, assuming the absence of oscillations ν μ → ν e (for θ 13 = 0), was 1.5±0.3. The main contribution to background events comes from electron neutrinos contained in the initial beam of muon neutrinos, as well as the contribution from neutral pions resulting from the interaction of muon neutrinos through neutral currents. The energy distribution of recorded electron-like events is shown in Figure 4.

The probability that 6 events appeared as a result of fluctuations in background events, and were not the result of oscillations, is 0.7%. Thus, with a probability of 99.3%, this result can be interpreted as an indication of oscillations ν μ → ν e. The central value for sin 2 2θ 13 is 0.11 for the normal neutrino mass hierarchy (m 3 > m 2) and 0.14 for the inverse hierarchy (m 3< m 2) в случае δ = 0.

T2K collected until March 11, 2011, when the earthquake and tsunami occurred in Japan, approximately 2% of the statistics that were planned to be collected for the entire duration of the experiment. Fortunately, the earthquake did not cause fatal damage to the J-PARC accelerator complex, the neutrino channel and the ND280 detector. Intensive restoration work is currently underway, and at the same time, some elements are being modernized to increase the intensity of the proton beam. We expect that the collection of statistics will resume at the end of 2011, and by the end of the first phase of the experiment, the number of neutrino events in Super Kamiokande will increase by approximately 50 times, which will significantly improve the accuracy of the already known oscillation parameters and measure the angle θ 13 with good accuracy. The MINOS neutrino experiment (Fermilab, USA) presented on June 24 a new result in the search for oscillations ν μ → ν e. 62 events were detected that were interpreted as electron neutrinos. Despite the larger number of events, the accuracy of the result is lower, since the expected background is 50 events. This result is in agreement with our result, although the sensitivity achieved in MINOS only allows us to conclude that the value θ 13 = 0 is excluded at the 89% CL level. In the near future, the first results of experiments by DoubLeChooz (France), Reno (Korea), Daya Bay (China), which measure the angle θ 13 using reactor antineutrinos, should also appear.

The second phase of the T2K experiment aims to search for CP violation in the lepton sector. For this purpose, experiments will be carried out with a beam of muon antineutrinos and measurements of oscillations of muon antineutrinos into electron antineutrinos will be performed. A comparison of the probabilities of such oscillations for neutrinos and antineutrinos will provide the first information about the violation of CP invariance in the lepton sector.

Conclusion

The result obtained in the T2K experiment is undoubtedly a significant event in neutrino physics. The further development of research with accelerator and reactor neutrinos largely depends on the results of T2K. Together with the results of other experiments, T2K significantly improves our understanding of the properties of neutrinos, and it is likely that we are on the threshold of a new and exciting new stage in neutrino physics. These studies can shed light on the problem of combining quarks and leptons, as well as on the role of neutrinos in the emergence of baryon asymmetry of the Universe, i.e., be the key to unraveling one of the mysteries of nature about the predominance of matter over antimatter in the Universe. As has already happened more than once in neutrino physics, the emergence of new and, very likely, completely unexpected results is possible.

Literature:
1) T2K CoLLaboration, arXiv: 1106.2822
2) T2K CoLLaboration, arXiv:

The theory of neutrino oscillations has emerged as a possible solution to the problem of solar neutrino deficiency. The crux of the problem was that in the sun, according to the standard model, neutrinos mainly arise as a result of the proton-proton cycle reaction:

p + p 2 H + e + + e + 0.42 MeV

(The relative probability of such a reaction is 99.75%)

The main source of high-energy neutrinos on the Sun are the decays of 8 B isotopes, which arise in the reaction 7 Be(p,) 8 B (a rare branch of the proton-proton cycle):

13 N 13 C + e + + e + 1.20 MeV

15 O 15 N + e + + e + 1.73 MeV

Currently, there are four series of experimental data on the registration of various groups of solar neutrinos. Radiochemical experiments based on the reaction 37 Cl + e 37 Ar + e - have been conducted for 30 years. According to the theory, the main contribution to this reaction should be made by neutrinos from the decay of 8 V. Research on the direct detection of neutrinos from the decay of 8 V with measurements of the energy and direction of neutrino motion has been carried out in the KAMIOKANDE experiment since 1987. Radiochemical experiments on the reaction 71 Ga + e 71 Ge + e - have been conducted for the last five years by two groups of scientists from a number of countries. An important feature of this reaction is its sensitivity mainly to the first reaction of the proton-proton cycle p + p 2 D + e + + e. The rate of this reaction determines the rate of energy release in the solar fusion furnace in real time. All experiments show a deficit in solar neutrino fluxes compared to the predictions of the Standard Solar Model.
A possible solution to the problem of solar neutrino deficiency is neutrino oscillations - the transformation of electron neutrinos into muon and tau neutrinos.
The first thing you need to pay attention to when starting to discuss the properties of neutrinos is the existence of their different varieties.
As you know, at present we can definitely talk about three such varieties:
ν e , ν μ , ν τ and, accordingly, their antineutrinos. When exchanged with a charged W boson, an electron neutrino turns into an electron, and a muonic neutrino turns into a muon (ν τ produces a tau lepton). This property made it possible at one time to establish the difference in the nature of electron and muon neutrinos. Namely, neutrino beams formed at accelerators consist mainly of decay products of charged π-mesons:

π + μ + + ν
π − μ − + ν

If neutrinos do not distinguish between types of leptons, then neutrinos produced in this way are equally likely to produce electrons and muons when interacting with the nuclei of matter. If each lepton corresponds to its own type of neutrino, then only muon types are generated in pion decays. Then the neutrino beam from the accelerator will in the overwhelming majority of cases produce muons, not electrons. This is precisely the phenomenon that was recorded experimentally.
After clarifying the fact of the difference between neutrino types, the question arose: how deep is this difference? If we turn to the analogy with quarks, we should pay attention to the fact that electroweak interactions do not preserve the type (flavor) of quarks. For example, the following chain of transitions is possible:

which leads to mixing of states that differ only in strangeness, for example, neutral K-mesons K 0 and K 0 . Can different types of neutrinos mix in a similar way? When answering this question, it is important to know what the masses of neutrinos are. From observations we know that neutrinos have very small masses, significantly less than the masses of the corresponding leptons. So, for the electron neutrino mass we have a limitation

m(e)< 5.1 эВ,

while the electron mass is 0.51099906 ± 0.00000015 MeV
In the vast majority of cases, we can assume the masses of all three neutrinos to be zero. If they are exactly equal to zero, it is impossible to notice the effects of possible mixing of different types of neutrinos. Only if neutrinos have non-zero masses does mixing acquire physical meaning. Note that we do not know any fundamental reasons leading to the strict equality of neutrino masses to zero. Thus, the question of whether there is mixing of different neutrinos is a problem that should be solved by physical methods, primarily experimental. For the first time, the possibility of mixing electron and muon types of neutrinos was pointed out by B.M. Pontecorvo.

Mixing of neutrino states

Let's consider the problem of two types of neutrinos: e, ν μ,. For mixing effects, consider how states evolve over time. Evolution in time is determined by the Schrödinger equation

From this point on we use the system of units h = c = 1, which is commonly used in particle physics. This system is convenient because it has only one dimensional quantity, for example energy. Now momentum and mass have the same dimensions as energy, and the coordinate x and time t have the dimension of inverse energy. Applying this relation to the case of neutrinos we are considering, when their masses are much less than the momentum, we obtain instead of (2):

Based on (5), we understand equation (4) as a system of equations for the functions (t), (t):

For brevity, such a system is usually written in the form (4), but then (t) is understood as a column of , , and in parentheses the first term is proportional to the identity matrix, while the value M 2 becomes some (2 x 2) matrix with matrix elements that are easy to obtain from system (6). The value is very important here, the difference from zero leads to mixing effects. If it is not there, the system breaks up into two independent equations and neutrinos, electron and muon, exist separately with their own masses.
So, H 0. Then we will look for solutions to system (6) in the form of combinations

1 (t) = cos e (t) + sin ν μ (t), 2 (t) = -sin e (t) + cos ν μ (t).

(7)

which have a certain frequency, that is, they have the form (3). For further purposes, it is important to note that at small 0 1 is almost pure electron neutrino, and at /2 it is almost completely muon. Adding the first of equations (6), multiplied by cos, with the second, multiplied by sin, we obtain the condition that the left side also contains only 1:

Happening m e > , that is =/4, corresponds to maximum mixing and is realized almost exactly for a system of neutral K-mesons. States (7) have certain masses, which we obtain from system (6):

(10)

The signs in (10) correspond to the case > m e. From (10) we see that with zero mixing = 0 we get m 1 = m e, m 2 = . In the presence of mixing, a mass shift occurs. If we consider it very small, then

Let's imagine that at the initial moment of time t = 0 an electron neutrino was born. Then from (7) and (12) we obtain the time dependence of the state under consideration (we omit the common factor e -ikt)

(13)

Let's introduce the notation m 2 = m 1 2 - m 2 2 . We see that, along with the electron neutrino that was initially present, the muon neutrino state also appears here. The probability of its occurrence, according to the rules of quantum mechanics, is the square of the amplitude modulus, that is, the coefficient at | ν μ >. It, as can be seen from (13), depends on time and amounts to

W(t) = sin 2 2 sin 2 ((E 1 -E 2)t/2) = sin 2 2 sin 2 (m 2 t/4k) = sin 2 2 sin 2 (1.27m 2 L/E),

(14)

where we measure the distance L in meters, the neutrino energy in megaelectronvolts and the difference in squared masses m2 in square electronvolts. Of course, we take into account the smallness of the neutrino masses, so L = ct. The muon component has a characteristic oscillating dependence; this phenomenon is called neutrino oscillations. What should be observed as an effect of neutrino oscillations? We know that electron neutrinos produce an electron as a result of a reaction with the exchange of W, and muon neutrinos produce a muon. Consequently, a beam initially consisting of electron neutrinos, when passing through recording equipment, produces not only electrons, but also muons with a probability depending on the distance to the starting point, described by formula (14). Simply put, we need to look for the birth of “alien” leptons.
Experiments to search for neutrino oscillations are being actively carried out and, as a rule, lead not to measuring the effect, but to restrictions on the parameters in (14) and m 2. It is clear that there is no effect at all if at least one of these parameters is equal to zero. Recently, there have been reports of serious indications of the existence of neutrino oscillations in experiments at the Japanese Super-Kamiokande facility. These experiments studied the neutrino flux from the decays of particles produced in the upper atmosphere by high-energy cosmic rays. Depending on the angles of inclination to the horizon at which the neutrinos being studied arrive at the instrument, they travel distances from several tens of kilometers (directly from above) to many thousands of kilometers (directly from below). The result of continuous one and a half year measurements turned out to be incompatible with calculations based on the theory without oscillations. At the same time, the introduction of oscillations leads to excellent agreement with experiment. In this case, transitions ν μ e are necessary:

sin 2 > 0.82,
510 -4 < m 2 < 610 -2

that is, their values ​​are explicitly required. So far, scientific public opinion has not yet inclined to definitively accept the discovery of neutrino oscillations and is awaiting confirmation of the result. Experiments continue, but meanwhile it turned out that even richer information can be provided by studying neutrino oscillations, taking into account their interaction with matter.

Neutrino oscillations in matter

The elucidation of the possibilities associated with the effects of neutrino propagation in matter is associated with the work of L. Wolfenstein and S.P. Mikheev and A.Yu. Smirnova.
Let us again consider the case of two neutrinos - electron and muon. Matter contains protons and neutrons in nuclei and electrons. The interaction of both types of neutrinos with protons and neutrons due to the exchange of W and Z occurs in the same way and therefore does not lead to new effects compared to propagation in a vacuum. The situation is completely different with the scattering of neutrinos by electrons. A muonic neutrino can interact with an electron only through the exchange of a neutral boson Z, while the exchange of a charged boson W contributes to the scattering of an electron neutrino (and antineutrino) on an electron. Indeed, for example, W - goes into a pair e, so the process scattering follows the pattern

When antineutrinos are scattered by an electron, they merge into W, and when neutrinos are scattered, W is exchanged, in which the initial neutrino gives an electron and W +, which is absorbed by the original electron, giving the final neutrino. For a muon neutrino such transitions are impossible.
So, the electron neutrino has an additional interaction with the electron, which is described by the additional term in the first line of (6):

Then the system of equations describing the dependence of the wave function on time changes:

where = 2kV W, and this quantity is associated with the scattering of electron neutrinos on electrons due to the exchange of W. The electroweak theory gives a simple expression

,

(17)

Where G F = (1.16637 + 0.00002) . 10 -5 GeV -2 is the known Fermi constant, characterizing weak interactions, and N e- electron density in the substance. This density is proportional to the atomic number Z of the element and the usual density of the substance p, which is reflected in the numerical form of relation (17). Then the value can be represented in the form (A is the atomic weight of the corresponding element)

Considering expression (16) for the masses of neutrino states and (19) for the mixing angle in matter, we obtain the most interesting phenomenon of resonant oscillation of neutrinos in matter. Let the mixing of neutrinos in vacuum be very small, that is, sin 2< 1. Представим себе, что нейтрино с некоторым импульсом k (первоначально электронное) проходит через вещество с переменной плотностью, меняющейся монотонно, например убывающей. Если при этом в каком-то слое плотность такова, что выполняется равенство

1.526. 10 -7 Zk/A = m 2 cos 2,

(20)

then resonance is realized. Indeed, for sin 2 m<< 1 и нейтрино остается электронным. Однако при выполнении равенства (20) sin 2 m = 1, при дальнейшем уменьшении плотности sin 2 m вновь становится малым, но это значит, что 2 m становится близким к , а m - к /2. Из (7) видно, что это соответствует уже почти полностью нейтрино мюонному. Таким образом, при прохождении резонанса происходит смена сорта нейтрино, причем тем полнее, чем меньше вакуумный угол смешивания. Поэтому такая резонансная осцилляция является фактически единственной возможностью проявления малого смешивания нейтрино.
The phenomenon of resonant oscillation is also clearly manifested in the dependence of neutrino masses in matter on density (16). Indeed, let's start with expression (16) with a minus sign, which, in accordance with equations (15), describes the initial electron neutrino (since it contains its characteristic interaction with electrons V W). Let the density change while passing through resonance. Then the square of the mass before resonance at a small angle is equal to m e 2 + V W , and after resonance -. When passing through resonance, the type of neutrino completely changes.
It should be noted that if instead of a neutrino we consider an antineutrino, then the main difference lies in the sign of the term describing the interaction with the exchange W. The signs of V W for neutrinos and antineutrinos are opposite. This means that the resonance condition is achieved depending on the sign of m 2 either only for neutrinos or only for antineutrinos. For example, if a muonic neutrino is heavier than an electron one, then resonance can be observed only for the initial state of the electron neutrino, but not for the antineutrino.
Thus, the propagation of neutrino (and antineutrino) beams in matter provides rich physical information. If the main parameters, that is, m 2 and , are known, then by shining a neutrino beam through a certain object, for example a planet, a star, etc., from the composition of the neutrino beam at the output, one can obtain a picture of the density distribution inside the illuminated object. You can pay attention to the close analogy with the transmission of small objects (including living ones) with X-rays.

Examples of possible manifestations and applications

The phenomenon of neutrino oscillations has not yet been experimentally registered, but there are indications of their existence, and they are associated precisely with possible resonance phenomena. The fact is that registration methods are sensitive mainly to electron neutrinos (antineutrinos), since muon and especially tau neutrinos with energies of several megaelectronvolts cannot give a reaction, for example

37 Cl + 37 Ar + e - .

which is used in the chlorine-argon method for detecting neutrinos. This is due to the fact that for the birth of a muon it is necessary to expend energy of more than 100 MeV (and even more for the birth of tau). At the same time, a similar reaction with an electron neutrino can occur. Nuclear reactions in the Sun are the source of electron (anti-)neutrinos, so the method used seemed quite adequate. However, if along the way from the point of birth to the device an oscillation occurs and the neutrino turns, for example, into a muon, then the reaction does not occur and the neutrino becomes “sterile”. This could serve as an explanation for the deficit of solar neutrinos.
At first they tried to use ordinary (first section) oscillations in the space between the Sun and the Earth to explain. The admixture of muon neutrinos is determined by the mixing angle. Referring to formula (14), we can conclude that the fraction of such sterile neutrinos on Earth

where we use angle brackets to denote the average value. Averaging is necessary since the distance L from the Earth to the Sun changes significantly during the measurement process due to its orbital movement. The average value of the function sin 2x over a large interval is 1/2, therefore, the fraction of sterile neutrinos is

Thus, it is generally possible to suppress the neutrino flux from the Sun by half, but this requires maximum mixing sin 2 = 1. Searches for oscillations show that for a wide range of neutrino masses such large mixing is excluded by experience. In addition, this explanation gives the same suppression of the neutrino flux for all neutrino energies, while experimental results indicate an energy dependence of the effect.
A more adequate explanation turns out to be using resonant oscillations in the matter of the Sun. In order for a resonant transition of neutrinos to a sterile state to occur, condition (20) must be satisfied on a certain layer of solar matter. Let the mixing angle be very small, so that cos is 21. Let us take the parameter values ​​as an example

Z/A = 1.05, = 10 g/cm2, E = 1 MeV,

where the first number reflects the fact that the Sun consists mainly of hydrogen with an admixture of helium and other elements. Then condition (20) gives for the difference in squared neutrino masses

It is precisely this order of neutrino masses that is needed to use the resonance mechanism of neutrino oscillations in matter to explain the deficit of solar neutrinos, including the energy dependence of this effect. The situation here is this: if the existing experimental data receive final confirmation, then no other explanation other than resonant oscillation can be offered. This will be the most important result, opening the way to further understanding of the structure of the physical world. In addition, we will get a new way of X-ray scanning of celestial bodies, including our Earth. Indeed, bearing in mind that the densities of earthly rocks are 3-6 g/cm 3 in the mantle and 9-12 g/cm 3 in the core, we are convinced that with the neutrino mass (22), resonance conditions are achieved for neutrinos with energies of the order of several megaelectronvolt. By forming such beams and conducting a program of transilluminating the Earth with recording the effect at a network of neutrino stations, it is possible to obtain tomograms of the Earth's thickness. In the future, this may lead both to the clarification of the details of the structure of the Earth and to practical results, for example, in application to the search for deep-lying minerals.

Almost all geeks have heard about neutrino oscillations. A lot of professional literature and a lot of popular articles have been written about this phenomenon, but only the authors of textbooks believe that the reader understands field theory, and even quantum theory, and the authors of popular articles usually limit themselves to phrases in the style of: “The particles fly and fly, and then BAM and turn into others,” and with a different mass (!!!). Let's try to figure out where this interesting effect comes from and how it is observed using huge installations. And at the same time we will learn how to find and extract several necessary atoms from 600 tons of matter.

Another neutrino

In a previous article, I talked about how the idea of ​​the existence of neutrinos appeared in 1932 and how this particle was discovered 25 years later. Let me remind you that Reines and Cowan registered the interaction of an antineutrino with a proton. But even then, many scientists believed that neutrinos could be of several types. A neutrino that actively interacts with an electron is called electron, and a neutrino that interacts with a muon is called muonic. The experimenters needed to figure out whether these two conditions were different or not. Lederman, Schwartz, and Steinberger conducted a remarkable experiment. They examined a beam of pi mesons from the accelerator. Such particles readily decay into muons and neutrinos.

If neutrinos really have different types, then a muon should be born. Then everything is simple - we place a target in the path of the born particles and study how they interact: with the birth of an electron or a muon. Experience has clearly shown that electrons are almost never created.

So now we have two types of neutrinos! We are ready to move on to the next step in discussing neutrino oscillations.

This is some kind of “wrong” Sun

The first neutrino experiments used an artificial source: a reactor or accelerator. This made it possible to create very powerful streams of particles, because interactions are extremely rare. But it was much more interesting to register natural neutrinos. Of particular interest is the study of the flow of particles from the Sun.

By the middle of the 20th century, it was already clear that there was no firewood burning in the Sun - they did the math and it turned out that there wouldn’t be enough firewood. Energy is released during nuclear reactions in the very center of the Sun. For example, the main process for our star is called the “proton-proton cycle,” when a helium atom is assembled from four protons.

It can be noted that at the first step the particles of interest to us should be born. And here neutrino physics can show all its power! Only the surface of the Sun (photosphere) is accessible for optical observation, and neutrinos pass unhindered through all layers of our star. As a result, the registered particles come from the very center where they are born. We can “observe” the core of the Sun directly. Naturally, such research could not help but attract physicists. In addition, the expected flux was almost 100 billion particles per square centimeter per second.

The first such experiment was carried out by Raymond Davis in the largest gold mine in America - the Homestake Mine. The installation had to be hidden deep underground to protect itself from a powerful flow of cosmic particles. A neutrino can pass through one and a half kilometers of rock without any problems, but other particles will be stopped. The detector was a huge barrel filled with 600 tons of tetrachlorethylene - a compound of 4 chlorine atoms. This substance is actively used in dry cleaning and is quite cheap.

This method of registration was proposed by Bruno Maksimovich Pontecorvo. When interacting with neutrinos, chlorine turns into an unstable isotope of argon,

which captures an electron from the lower orbital and decays back in an average of 50 days.

But! Only about 5 neutrino interactions are expected per day. In a couple of weeks, only 70 born argon atoms will accumulate, and they must be found! Find several dozen atoms in a 600 ton barrel. A truly fantastic task. Every two months, Davis purged the barrel with helium, blowing out the resulting argon. The repeatedly purified gas was placed in a small detector (Geiger counter), where the number of decays of the resulting argon was counted. This is how the number of neutrino interactions was measured.

Almost immediately it turned out that the neutrino flux from the Sun was almost three times lower than expected, which created a great sensation in physics. In 2002, Davis and Koshiba-san shared the Nobel Prize for their significant contributions to astrophysics, including the discovery of cosmic neutrinos.

A small note: Davis recorded neutrinos not from the proton-proton reaction, which I described above, but from slightly more complex and rare processes with beryllium and boron, but this does not change the essence.

Who is to blame and what to do?

So, the neutrino flux is three times less than expected. Why? The following options can be offered:

These fickle neutrinos

A year before the results of Davis's experiment were obtained, the already mentioned Bruno Pontecorvo developed a theory of how exactly neutrinos can change their type in a vacuum. One consequence is that different types of neutrinos should have different masses. And why on earth should particles just like this on the fly change their mass, which, generally speaking, should be conserved? Let's figure it out.

We cannot do without a little introduction to quantum theory, but I will try to make this explanation as transparent as possible. All you need is basic geometry. The state of the system is described by a “state vector”. Since there is a vector, then there must be a basis. Let's look at the color space analogy. Our “state” is the color green. In the RGB basis we will write this vector as (0, 1, 0). But in the CMYK basis, almost the same color will be written differently (0.63, 0, 1, 0). It is obvious that we do not and cannot have a “main” basis. For different needs: images on a monitor or printing, we must use our own coordinate system.

What basis will there be for neutrinos? It is quite logical to decompose the neutrino flux into different types: electron (), muon () and tau (). If we have a stream of exclusively electron neutrinos flying from the Sun, then this state is (1, 0, 0) in such a basis. But as we've already discussed, neutrinos can be massive. Moreover, they have different masses. This means that the neutrino flux can also be decomposed into mass states: with masses, respectively.

The whole point of oscillations is that these bases do not coincide! The blue ones in the picture show the types (sorts) of neutrinos, and the red ones show states with different masses.

That is, if an electron neutrino appeared in the decay of a neutron, then three mass states appeared at once (projected at ).

But if these states have slightly different masses, then the energies will be slightly different. And since the energies are different, then they will propagate in space differently. The picture shows exactly how these three states will evolve over time.

(c) www-hep.physics.wm.edu

In the picture the movement of the particle is shown in the form of a wave. This representation is called de Broglie wave, or the wave of probability of registering a particular particle.

Neutrinos interact depending on the type (). Therefore, when we want to calculate how a neutrino will manifest itself, we need to project our state vector onto (). And thus there will be a probability of registering one or another type of neutrino. These are the probability waves we will get for an electron neutrino depending on the distance traveled:

How much the type will change is determined by the relative angles of the described coordinate systems (shown in the previous figure) and the mass differences.

If the terminology of quantum mechanics does not scare you, and you have the patience to read up to this point, then a simple formal description can be found on Wikipedia.

What is it really like?

The theory is, of course, good. But we still cannot decide which of the two options is realized in nature: the Sun is “not like that” or neutrinos are “not like that.” New experiments are needed that will definitively show the nature of this interesting effect. I will literally describe in a nutshell the main settings that played a key role in the research.

Kamioka Observatory

The history of this observatory begins with the fact that they tried to find proton decay here. That is why the detector received the appropriate name - “Kamiokande” (Kamioka Nucleon Decay Experiment). But having discovered nothing, the Japanese quickly refocused on a promising direction: the study of atmospheric and solar neutrinos. We have already discussed where solar energy comes from. Atmospheric ones are born in the decays of muons and pi-mesons in the Earth's atmosphere. And while they reach the Earth they manage to oscillate.

The detector began collecting data in 1987. They were wildly lucky with the dates, but more on that in the next article :) The installation was a huge barrel filled with the purest water. The walls were paved with photomultiplier tubes. The main reaction by which neutrinos were caught was the knocking out of an electron from water molecules:

A fast-flying free electron glows dark blue in water. This radiation was recorded by photomultipliers on the walls. Subsequently, the installation was upgraded to Super-Kamiokande and continued its work.

The experiment confirmed the deficit of solar neutrinos and added to this the deficit of atmospheric neutrinos.

Gallium experiments

Almost immediately after the launch of Kakiokande in 1990, two gallium detectors began operation. One of them was located in Italy, under the Grand Sasso mountain in a laboratory of the same name. The second is in the Caucasus, in the Baksan Gorge, under Mount Andyrchi. The Neutrino village was built specifically for this laboratory in the gorge. The method itself was proposed by Vadim Kuzmin, inspired by the ideas of Pontecorvo, back in 1964.

When interacting with neutrinos, gallium turns into an unstable isotope of germanium, which decays back to gallium in an average of 16 days. Over the course of a month, several dozen germanium atoms are formed, which must be very carefully extracted from gallium, placed in a small detector, and the number of decays back into gallium counted. The advantage of gallium experiments is that they can catch very low-energy neutrinos that are inaccessible to other facilities.

All the experiments described above showed that we see fewer neutrinos than expected, but this does not prove the presence of oscillations. The problem may still be an incorrect model of the Sun. The SNO experiment put the last and final point in the problem of solar neutrinos.

Sudbury Observatory

Canadians built a huge “death star” in the Creighton mine.

At a depth of two kilometers, an acrylic sphere was placed, surrounded by photomultipliers and filled with 1000 tons of heavy water. This water differs from ordinary water in that ordinary hydrogen with one proton is replaced by deuterium - a compound of a proton and a neutron. It was deuterium that played a key role in solving the problems of solar neutrinos. Such an installation could register both the interactions of electron neutrinos and the interactions of all other types! Electron neutrinos will destroy deuterium with the birth of an electron, while all other types of electrons cannot give birth. But they can slightly “push” deuterium so that it falls apart into its component parts, and the neutrino flies onward.

A fast electron, as we have already discussed, glows when moving in a medium, and a neutron should quickly be captured by deuterium, emitting a photon. All this can be recorded using photomultiplier tubes. Physicists are finally able to measure the full flow of particles from the Sun. If it turns out that it coincides with expectations, then electron neutrinos are transferred to others, and if it is less than expected, then the wrong model of the Sun is to blame.

The experiment began work in 1999, and measurements confidently indicated that there was a deficiency of the electronic component

Let me remind you that almost exclusively electron neutrinos can be born in a star. This means that the rest were obtained in the process of oscillations! For these works, Arthur MacDonald (SNO) and Kajita-san (Kamiokande) received the 2015 Nobel Prize.

Almost immediately, at the beginning of the 2000s, other experiments began studying oscillations. This effect was also observed for man-made neutrinos. The Japanese experiment KamLAND, located in the same place, in Kamioka, already in 2002 observed oscillations of electron antineutrinos from the reactor. And the second, also Japanese, K2K experiment for the first time recorded a change in the type of neutrinos created using an accelerator. The well-known Super-Kamiokande was used as a long-range detector.

Now more and more installations are studying this effect. Detectors are being built on Lake Baikal, in the Mediterranean Sea, and at the South Pole. There were also installations near the North Pole. All of them catch neutrinos of cosmic origin. Accelerator and reactor experiments are running. The parameters of the oscillations themselves are being refined, and attempts are being made to find out something about the magnitude of the neutrino masses. There are indications that it is with the help of this effect that the predominance of matter over antimatter in our Universe can be explained!

Below the spoiler is a small remark for the most thoughtful.

The 2015 prize was issued with the wording “for the discovery of neutrino oscillations, showing the presence of mass in them.” This statement caused some confusion among physicists. When measuring solar neutrinos (SNO experiment), we are insensitive to mass differences. Generally speaking, the mass can be zero, but the oscillations will remain. This behavior is explained by the interaction of neutrinos with solar matter (the Mikheev-Smirnov-Wolfenstein effect). That is, there are oscillations of solar neutrinos, their discovery is a fundamental breakthrough, but this has never indicated the presence of mass. In fact, the Nobel committee awarded the prize with the wrong wording.
It is in vacuum that oscillations manifest themselves for atmospheric, reactor and accelerator experiments. Add tags

First, a small quote from Wikipedia: " Neutrino oscillations are the transformation of neutrinos (electron, muon or taon) into neutrinos of a different type (generation), or into antineutrinos. The theory predicts the existence of a law of periodic change in the probability of detecting a particle of a certain type, depending on the proper time elapsed since the creation of the particle. The idea of ​​neutrino oscillations was first put forward by the Soviet-Italian physicist B. M. Pontecorvo in 1957. The presence of neutrino oscillations is important for solving the solar neutrino problem."

Neutrino oscillations were invented because the number of solar electron neutrinos detected on Earth is two to three times less than predicted by solar models. To do this, they made up a fairy tale that the electron neutrino, muon neutrino and the so-called tau neutrino have almost the same rest mass. And this lie went unnoticed. No one has measured the rest mass of a muon neutrino. Even the rest mass of the electron neutrino, emitted in gigantic quantities by the sun and produced in nuclear reactors, cannot yet be measured, let alone the unstable muon neutrino, and even more so its even shorter-lived first excited state, called (historically) tau neutrino.

The rest mass of elementary particles is determined by their set of quantum numbers, as physics is not yet able to answer this question. But from experience we know that each elementary particle (with the exception of fictional ones) has its own value of rest mass. For example, an electron and a muon have different sets of quantum numbers and their rest masses are dramatically different. Then from what it follows that the electron and muon neutrino have the same value of rest mass - the answer does not follow from anything. These are different elementary particles and they will have different rest mass values. And so does the first excited state of the muon neutrino. Because in addition to the first excited state, there is also a second, third, fourth (about which the standard model knows nothing) and they all differ in their own value of internal energy, and therefore in rest mass. And as soon as we established that each type of neutrino has its own value of rest mass, we thereby learned that the law of conservation of energy prohibits their spontaneous mutual transformations. Only those reactions of elementary particles that proceed in accordance with the laws of nature remain allowed - for example, the decay of a muon neutrino. But the latter further increases the flux of solar electron neutrinos passing through the Earth.

3 Now let's look at neutrino transformations from the point of view of classical electrodynamics.

An elementary particle differs from its antiparticle in that its electric and magnetic field strengths have opposite signs. Those. in order to turn, for example, an electron into a positron, all its electromagnetic fields must be reversed. It is clear that such a miraculous transformation completely rejects the laws of classical electrodynamics. It is clear that such transformations with electrons cannot occur in nature and therefore they have never been observed. Then why can they occur with an electron neutrino or a muon neutrino. Do electrons have their own laws of nature, and electron neutrinos have their own? When some “theories” or “models” require each elementary particle to have its own laws of nature, this indicates that these theoretical constructions do not correspond to nature.

Now about the miraculous transformation of one type of neutrino into another. Each type of neutrino (both electron and muon) has its own set of quantum numbers and therefore their electromagnetic fields will be different. When one type of neutrino transforms into another, a spontaneous change in their electromagnetic fields will occur, which contradicts the laws of classical electrodynamics. Electromagnetic fields cannot arise from nothing and disappear into nowhere, which also applies to the electromagnetic fields of elementary particles. Electromagnetic fields can be transformed in accordance with the laws of classical electrodynamics.

The fact that the standard model does not notice either the structure of the neutrino or its electromagnetic fields does not indicate their absence, but rather the shortcomings of the standard model itself. If physics has established the presence of magnetic fields in neutral baryons, then it follows that neutral leptons should not have them - the laws of nature must be the same for all elementary particles .

As we see, classical electrodynamics also does not allow spontaneous transformations of neutrinos.

To summarize we can say the following: it was necessary to reduce the flow of solar neutrinos coming to the Earth by two or three times - so they came up with a fairy tale about neutrino oscillations.

Vladimir Gorunovich
25.01.2013

4 Nobel Prize in Physics 2015 (for neutrino oscillations) - another mistake of the Nobel Committee for Physics

I didn’t want to write this, but I can’t calmly remain silent when they are once again trying to fool us with a mathematical FAIRY TALE, passing it off as a discovery in physics allegedly made by experimenters. - It is impossible to open something that is not there, but you can pretend that you have opened it. Two years ago, the Nobel Prize was awarded for the fabulous “Higgs boson”, which has nothing to do with gravity, now a fairy tale about neutrino oscillations. If you look at the decisions of the Nobel Committee on Physics over the past 10 years (2006 - 2015), in the light of the latest achievements of New Physics, four decisions out of ten were WRONG (except for those indicated, 2008 “For the discovery of the source of symmetry violation, which made it possible to predict the existence in nature according to at least three generations of quarks" - but quarks have not been found in nature and neither have their fractional electric charge; 2011 "For the discovery of the accelerated expansion of the Universe through the observation of distant supernovae" - but the presence of the expansion of the Universe itself has not been proven by physics: red shift, based on which this hypothesis was put forward allows for other alternative interpretations). The result of the activities of the Nobel Committee on Physics over the past 5 years is even more depressing: 60% of the decisions of the Nobel Committee on Physics turned out to be erroneous, while the Nobel Committee openly ignored the warnings of New Physics, for which they paid with erroneous decisions. Those. The current composition of the Nobel Physics Committee makes the right decisions with a probability of 40-60%. Maybe the officials from the Nobel Committee on Physics are satisfied with this indicator of the success of their work, but it does not suit physics at all, on whose behalf they make decisions - physics did not give them such powers. Something is wrong in the activities of the current (2005-2015) composition of the Nobel Committee “on Physics” - it does not represent the interests of PHYSICS today.

I present the rationale for the 2015 Nobel Prize in Physics “for the discovery of neutrino oscillations, showing that neutrinos have mass,” taken from the Wikipedia website.

In the first part of the article, as well as the article “Electron Neutrino”, I proved the impossibility of Neutrino oscillations in nature as contradicting the laws of nature - but apparently the laws of nature do not matter for the current composition of the Nobel Committee on Physics.

Different types of neutrinos have different sets of quantum numbers, which will correspond to different structures of electromagnetic fields and, accordingly, different internal energies - these are the basics of Field Physics. The transformation of one elementary particle into another contradicts the laws of electromagnetism and the law of conservation of energy - this is at a minimum. The field cannot spontaneously become different - the fields are transformed according to the laws of the field: electromagnetic fields - according to the laws of electromagnetism. Well, the fact that the transformation of some types of neutrinos into others is also a mockery of the law of conservation of energy - unfortunately, this has become the norm of behavior of some modern “theories” that do not bother themselves with the need to take into account the laws of nature and reality. The world of capitalism, built on lies, has such a “science” as it deserves.

Neutrinos can transform into each other only as a result of their reactions (decay or collisions, if there is sufficient kinetic energy).

If the Nobel Committee on Physics believes that the laws of nature have now ceased to apply, only because they think so, and what the storytellers want from science, palming off their mathematical theories-FAIRY TALES, then someone can provide experimental evidence of this. The lies of the authors of experiments presenting their hypotheses as laws of nature will not be taken into account - evidence is required, and confirmed by other experiments.

Now let’s see what we actually saw in the experiments awarded the 2015 Nobel Prize in Physics.

4.1 Error 1 of the 2015 Nobel Committee in Physics.

Each neutrino detector, including those awarded the Nobel Prize in Physics (Kamiokande, Super-Kamiokande, SNO), has an energy threshold. If the corresponding neutrino has a kinetic energy below the energy threshold, it will pass through the detector UNDETECTED - and then pseudoscientific tales appear about miraculous transformations allegedly discovered in the experiment, violating the laws of nature. All I needed was a little brain work.

The energy thresholds for the considered detectors, as well as the classical neutrino accumulation detector SAGE, are given in the table taken from Wikipedia:

SuperKamiokande does not have a threshold energy listed in the table. But SuperKamiokande is just a continuation of the Kamiokande experiment with more water and better statistics. But, as is known, increasing the amount of water used improves the statistics, but does not reduce the energy threshold of the neutrino detector, therefore, it can be considered the same at the level of 7.5 MeV.

I specifically added a classic gallium detector so that you could see how many times its energy threshold (threshold energy) is lower than that of Chereknov detectors, which take a large amount of excess purified simple or heavy water, receive a large number of recorded events, and can even determine the direction ( where the particle came from), but the question is: what part of the spectrum do they record? The gain in quantity turned into a loss in quality. But even the gallium detector was unable to catch solar electron neutrinos passing through the molten lava of our planet, which these neutrinos have maintained in a molten state for billions of years. What then can we say about neutrino detectors, whose energy threshold is tens of times higher?

4.2 Error 2 of the 2015 Nobel Committee in Physics.

The statement that the Earth is transparent to neutrinos is an unfounded statement of the Standard Model that does not correspond to reality. Quantum “theory” and the Standard Model consider only one version of interaction, when a reaction occurs with the participation of an elementary particle, but nature is structured differently and there are also interactions “not noticed” by these mathematical constructions.

Any elementary particle with a non-zero rest mass, including any neutrino, has electromagnetic fields, the internal energy of which creates its rest mass. According to the laws of classical electrodynamics, the action of which in nature has not yet been canceled by the decision of the “Divine” Nobel Committee on Physics, the electromagnetic fields of elementary particles still interact with each other. The result of such interaction is the exchange of kinetic energy, in accordance with the LAWS OF NATURE. Consequently, the dipole electric field of any neutrino (the existence of which physics of the 20th century did not even suspect) interacts with free electric charge carriers of the substance through which this neutrino flies. Free electric charge carriers include free electrons (not within the atom) and ions. Both are contained in gigantic quantities in molten lava located inside our planet under the earth’s crust. This molten state of the Earth's matter is maintained by the flow of kinetic energy from solar electron neutrinos. Therefore, when passing through the molten lava of the Earth’s substance, any of the neutrinos will gradually lose their kinetic energy - this is a consequence of classical electrodynamics, such an unloved quantum “theory” - a fairy tale.

Now look at paragraph 2.1 and you will see the corollary of paragraph 2.2: A neutrino that has lost a sufficient amount of kinetic energy, when passing through the molten lava of the Earth’s substance, becomes INVISIBLE for a neutrino detector.

Vladimir Gorunovich

Ministry of Education of the Republic of Belarus

Grodno University named after. Ya. Kupala

Department of Theoretical Physics

Course work

Topic: Neutrino oscillations.

Completed by: 5th year student Sharkunova V.A.

Checked by: Senko Anna Nikolaevna

The work shows that to explain these experiments, one can make an assumption about the existence of neutrino oscillations, and therefore neutrino masses. The theory of neutrino oscillations is considered. Neutrinos are considered within the framework of the left-right model. In the two-flavor approximation, possible hierarchies of neutrino masses are obtained.

Annotation................................................. ........................................................ ... 2

Introduction........................................................ ........................................................ ...... 4

1. Neutrino oscillations................................................... ........................... 7

1.1. Vacuum neutrino oscillations.................................................... ........................................................ ........................... 7

1.2. Neutrino oscillations in a continuous medium.................................................... ........................................................ .................. eleven

2. Indication of non-zero neutrino mass.................................................... 15

2.1. The problem of solar neutrinos........................................................ ........................................................ ................................. 15

2.2. Atmospheric neutrinos................................................... ........................................................ ............................................... 19

2.3. Results of the LSND (Los Alamos liquid scintillation neutrino detector) experiment................................................... 21

2.4. Hot dark matter of the Universe.................................................... ........................................................ ........................... 22

2.5. Double β-decay.................................................... ........................................................ ........................................................ ......... 23

3. Some experiments on detecting neutrinos.................................... 26

3.1. Solar neutrino detectors................................................................... ........................................................ ........................... 26

3.2. Homestake experiment................................................... ........................................................ ............................................... 28

3.3. Experiments Kamiokande and Super-Kamiokande.................................................... ........................................................ .... 29

3.4. Gallex and SAGE experiments.................................................... ........................................................ .................................... 31

4. Mass hierarchy of Majorana neutrinos in the left-right model.. 32

Conclusion................................................. ................................................... 35

Literature................................................. ........................................................ 36

Neutrino is an elementary particle produced in certain nuclear reactions. There are several powerful sources of neutrinos in the Universe.

1) The Sun and other stars are in a stable state.

2) Supernovae, which lose some of their energy in a few seconds in the form of neutrinos.

3) Some massive astrophysical objects (quasars, active galactic nuclei...), which are sources of high-energy neutrinos, which constitute an important part of cosmic rays.

There are atmospheric neutrinos - these are neutrinos born during the collision of cosmic rays with the nuclei of the earth's atmosphere, as well as neutrinos born during the beta decay of nuclei in atomic reactors and terrestrial neutrinos. We are immersed in relic neutrinos (about 500 per cubic centimeter) created during the Big Bang 15 billion years ago.

Figure 1. Neutrino flux from various sources.

There are three types, or flavors, of neutrinos: electron, muon and tauon. It is still not clear whether a neutrino differs from an antineutrino. There are theories in which they are different. In this case, they talk about Dirac neutrinos. In other theories, neutrinos and antineutrinos are not distinguished, and then neutrinos are called Majorana neutrinos.

Regardless of whether neutrinos are Majornian or Dirac, we do not know whether neutrinos have mass and magnetic moment. The experiment so far provides upper limits. However, there are indications that neutrinos have masses. To explain some experiments, a hypothesis about neutrino oscillations is put forward. Neutrino oscillations are the interconversion of different types of neutrinos. Currently, there are three experimental facts in support of neutrino oscillations.

1) Solar flow

appears to be greatly suppressed compared to the predictions of existing solar models.

2) The theoretical ratio of the fluxes of atmospheric muon and electron neutrinos to those measured experimentally is in conflict with the experimental results.

3) Study of decays of moving

mesons LSND collaboration shows the presence of both and .

For the existence of neutrino oscillations, it is necessary (but not sufficient) that neutrinos have nonzero masses.

In the minimum standard model, there are no right-handed neutrinos, and therefore the lepton number is not conserved. Thus, the neutrino has neither Majorana nor Dirac masses. Any evidence for a non-zero mass or mixing angle is evidence outside the standard model. Additionally, the masses and mixing angles are fundamental parameters that will be explained in the final fermion mass theory. The left-right model predicts the existence of neutrino mass and leads to mixing between states of a certain mass both within and between neutrino generations.

1. Neutrino oscillations.

Neutrino oscillations can be represented similarly to the more well-known example of spin precession in a transverse magnetic field. Suppose there are particles of spin ½ whose spins are polarized along z (or “up”). The beam passes through the region where a magnetic field is created in the y direction. Spin up is not the ground state in this magnetic field. Because of this, the beam undergoes oscillations (precession). If we examine the beam after traveling a certain distance, we can find that the beam is a superposition of spins “up” and “down”.

You can reformulate the last statement differently. We started with a spin-up beam, but after traveling a certain distance, the probability of finding spin-up in the beam is less than one. In other words, there is spin-up depletion. Neutrino oscillations represent depletion, such as solar

in the same way, i.e. it is postulated that the states that are created or observed are not the underlying propagation states.

1.1. Vacuum neutrino oscillations.

Electron neutrino

- a state that arises in decay, where a positron is also born. Muon neutrino is a state obtained in decay together with the muon. We will also name flavor states. It is not obvious from this definition that these flavor states are physical particles. In general, any of them can be a superposition of various physical particles. In other words, the state obtained in decay must have some probability of the existence of a particle and some probability of the existence of a particle. We will call these states and as particles or physical states. Let us introduce the following notation: (1.1)