Neutrino oscillations. Examples of possible manifestations and applications

The beginning of the XXI century was the time of sensational discoveries in the field of neutrino physics. The results obtained so far initiate further experimental and theoretical research properties of neutrinos in two main directions:

1. Studying the characteristics of ultrahigh-energy neutrinos as the only particles that can provide science with information about the distant regions of our Universe.
2. Study of interconversions of neutrinos of different flavors - the so-called "oscillations" of neutrinos.

This article is devoted to the presentation of the main results achieved in this second direction of research.
Neutrinos are fundamental fermions (see table). All particles indicated in the table have spin J / ћ. Twelve fundamental fermions correspond to 12 fundamental antifermions.

The existence of three types of neutrinos, differing in the quantum number "aroma ( flavor) ". They correspond to three types of antineutrinos. The names of different neutrinos come from the names of their charged "partners" in the group of leptons: electron, muon and tau-lepton, the rest masses of which are 0.511 MeV, 106 MeV and 1777 MeV, respectively.
In 1930, Wolfgang Pauli suggested that the continuous nature of the β-decay electron spectrum can be explained by the fact that, together with the electron during β-decay, a chargeless particle with a half-integer spin escapes, which is not detected by conventional detectors. The study of β-spectra showed that the mass of this particle should be very small - much less than the mass of an electron. (The name of this particle is neutrino = "neutron" belongs to E. Fermi and was introduced in 1932 after the discovery of the neutron).
First experimental confirmation the existence of neutrinos was obtained by measuring the kinetic energy of the Li nucleus formed in the process of electron capture by the beryllium nucleus:

7 Be + e - → 7 Li + ν e.

Among the many problems associated with neutrino physics, the problem of neutrino (antineutrino) mass has attracted special attention.
The study of the shape of the β-decay spectra made it possible to assert that the neutrino mass is very small, and the estimate of this value has been decreasing more and more over the years. Investigations were carried out for those decays where the total energy of an electron and an antineutrino (or a positron and a neutrino) is small. This decay is the decay of tritium:

How is the difference between the properties of neutrinos and antineutrinos proved? The sun (like other stars) is a source of electronic neutrino due to the deuteron fusion reaction:

p + p → d + e + + ν e.

Any nuclear reactor is a powerful source of electronic antineutrino arising from neutron decays:

n → p + e- + e.

R. Davis's attempts to register neutrinos from nuclear reactor by reaction
e + 17 Cl → 17 Ar + e - were unsuccessful. So it was experimentally proved that neutrinos and antineutrinos are different particles.
In a large series of experiments carried out by R. Davis, the intensity of the reaction ν e + 17 Cl → 17 Ar + e - initiated by a flux of neutrinos born on the Sun, was investigated. Davis's experiments, which were carried out for 30 years, showed that the magnitude of the measured flux of solar neutrinos is much less than it should be according to the model of the sun. Measurements of electron neutrino fluxes from the Sun, carried out at other facilities, also invariably showed their deficit.
Possible explanation this phenomenon is transformation of one kind of neutrino into others - the so-called. neutrino oscillations... The idea of ​​neutrino oscillations was first proposed by B.M. Pontecorvo.
The difference between neutrinos (and antineutrinos) of different flavors is manifested in reactions in which neutrinos are involved. The difference in reactions caused by leptons with different flavors prompted the introduction of three different quantum numbers, called "lepton charges": L e, L μ, L τ. Leptons of the first generation (see table) have a lepton charge L e = 1, L μ = L τ = 0, the second L e = 0, L μ = 1, L τ = 0, the third L e = L μ = 0, L τ = 1. The signs of the lepton charges of antiparticles are opposite to those of the particles. Before the establishment of neutrino oscillations as an experimental fact, it was believed that these quantum numbers are conserved in all reactions. For example, in the decay π + → μ + + ν μ, a pion having no lepton charge decays into a positive muon with L μ = –1 and a muonic neutrino ν μ with L μ = +1. Thus, the lepton charge is conserved in the decay. In muon decays
μ + → e + + ν e + μ lepton charges are also conserved. Indeed, the lepton charge of a positive muon is equal to L μ = –1, just like a muonic antineutrino. The electron lepton charges of a positron and an electron neutrino are equal in magnitude and opposite in sign. These facts led to the conclusion about the existence of exact conservation laws for each of the "sorts" of lepton charges separately. Experimental confirmation of the hypothesis of the exact conservation of each of their types of lepton charges separately was the experiments carried out at accelerators to search for decays of muons into an electron (positron) and a γ-quantum: μ - → e - + γ,
μ + → e + + γ. The fact that these decays were not detected is explained by the manifestation of the law of conservation of lepton charges.
However, the observation of neutrino oscillations - i.e. transformations of neutrinos of one flavor into neutrinos of another flavor proves that these conservation laws can be violated. Oscillations of neutrinos - and their existence has already been proven - lead to another interesting consequence: the neutrinos indicated in the table of fundamental fermions do not have a rigidly defined mass! The wave functions characterizing them are superpositions of the wave functions of particles with certain masses, and oscillations are a manifestation of the quantum-wave nature of these particles. (It should be recalled that particle physics has already encountered a similar phenomenon in the study of decays of neutral K-mesons). Let us consider a simplified example of the quantum physics of neutrino oscillations.

Quantum physics of neutrino oscillations

If the lepton numbers L e, L μ, L τ are not absolutely conserved quantum numbers, and if neutrinos have not zero, but finite masses, then the transformation of neutrinos of one "generation" into neutrinos of another "generation" is possible. This process can be described in terms of quantum physics as oscillations of neutrinos (see for example).
Let us consider the process of neutrino oscillations for two neutrinos: electron and muon. (Generalization to three types of neutrinos would be too cumbersome). The wave functions of the electron and muon neutrino are functions of time and obey the Schrödinger equation:

The transition from neutrino states ν 1 (t), ν 2 (t) to ν e (t), ν μ (t) and vice versa is carried out by a unitary matrix, which is conveniently represented in terms of cos θ and sin θ of the angle θ, which will hereinafter be called "Mixing angle":

	(4)
	(5)

If the mixing angle is 0, there is no mixing and ν 1 (t), ν 2 (t) coincide with ν e (t), ν μ (t). (A similar situation arises for θ = π / 2 - but ν 1 (t), ν 2 (t) in this case coincide, respectively, with ν μ (t), ν e (t)).
Let us consider the situation when at the initial moment of time there are neutrinos of only one type, for example, electron ν μ (t) = 0; ν e (t) = 1. Then it follows from (4) that ν 1 (0) = cos θ; ν 2 (0) = sin θ.
According to equation (3)

(In transformation (7) trigonometric relations are used:)
From (7) we obtain the intensity of the electron neutrino flux as a function of time:

(The calculation of the probability of detecting electron neutrinos in a beam primarily consisting of muon neutrinos is carried out in the same way and gives the same result.)
Thus, the probability of neutrino oscillations depends on three arguments:

1) from mixing angle associated with the value of the interaction Hamiltonian H int;

2) on the value of the difference

(10)

3) from the time elapsed since the birth of a particular type of neutrino.

Consider the influence of each of the arguments on neutrino oscillations:

1. Mixing of neutrino wave functions is maximal at θ = π / 4, since int ~ sin 2θ.

2. When deriving formula (10), we used the fact that the neutrino mass is much less than its kinetic energy. The formula for the total energy of a particle E = (p 2 c 2 + m 2 c 4) 1/2 in the system ћ = c = 1 looks like E = (p 2 + m 2) 1/2. Provided m<< p

Condition m<< p соответствует «почти релятивистской» кинематике нейтрино. При этом импульсы разных нейтрино совпадают и E 2 – E 1 = m 2 /2p

When masses coincide, i.e. at , no oscillations.

3. The quantity determines the argument of the second of the multipliers in formula (9). Usually this quantity is presented in such a way as to use the values ​​of the neutrino energy (E ν) in MeV, the values ​​of Δm 2 in (eV) 2, and the distance to the neutrino source (L) in meters (m). Using conversion constant

ћc = 197 MeV · fm ≡ 1.97 · 10 -7 eV · m = 1; 1 eV = 10 7 / 1.97 m,

get for

(11)

Thus, if the mass difference of the "primary" neutrinos is small, noticeable results in the study of oscillations can be achieved only if the length L is large. This is especially important if the neutrino energies are high.

Experimental studies of neutrino oscillations

At present, several experimental complexes for the study of neutrino oscillations are operating or are being created.
The first indications of neutrino oscillations were obtained in measurements with the SuperKamiokande water Cherenkov detector in 1998.
The detector is a stainless steel tank 42 m high and 40 m in diameter, filled with 50 thousand tons of specially purified water. It is located at a depth of 1.6 km (2.7 km water equivalent) in Japan (Kamioka mine). On the walls of the tank there are 11146 PMTs (internal detector + 1885 8 ”PMT (external detector).
The detector made it possible to reliably distinguish between electron and muon neutrinos.
One of the tasks set by the researchers was to measure atmospheric neutrino fluxes.
Neutrinos are born in the atmosphere as a result of the interaction of high-energy protons emitted by the Sun with the nuclei of the atmosphere. The result of these reactions is mainly the production of charged and neutral π-mesons. The decay of charged π-mesons creates the following chain of transformations:

π + → μ + + ν μ ; π - → + μ ; μ + → e + + ν e + μ; μ - → e - + e + ν μ.

(12)

Measurements at this facility have shown that the number of detected muon neutrinos is comparable to the number of electron neutrinos, although it follows from (12) that the number of muon neutrinos should be twice as large. The fact that the observed anomaly is a consequence of oscillations is confirmed by the dependence of the muon neutrino flux on the distance traveled. For vertically falling neutrinos, this path is only 20 km, and for neutrinos entering the detector from below from under the Earth, about 13,000 km. The stream coming from the bottom was much smaller than the one coming from the top.
These results, together with Davis's data, initiated the creation of special experimental complexes for studying the problem of neutrino oscillations. (In the same experimental complex (K2K), the registration of muon neutrinos, born as a result of the reactions of protons obtained at the KEK accelerator, is currently being carried out. The path length of muon neutrinos from the KEK accelerator to SuperKamiokande is 240 km.)
Even more convincing evidence of neutrino oscillations was obtained at the Sudbury neutrino telescope.

The Sudbury Neutrino Observatory (Canada) was built in a mine at a depth of 2070 m and contains SNO, a heavy water Cherenkov detector. 1000 tons of ultrapure heavy water (D 2 O) are poured into an acrylic vessel with a diameter of 12 meters. Cherenkov radiation is recorded by 9600 photomultipliers mounted on a sphere with a diameter of 17 meters, surrounding a vessel with heavy water. The detector is immersed in ultrapure ordinary water, which is located in a barrel-shaped cavity 22 meters in diameter and 34 meters high, dug into the rock. The detector registered about 10 neutrino events per day.

In Sudbury, fluxes of "boric" neutrinos formed on the Sun

The first reaction (CC), which occurs with the participation of charged currents, is sensitive only to electron neutrinos (ν e), the second (NC), which occurs with the participation of neutral currents, is sensitive to all neutrinos (x - e, μ, τ). Elastic scattering (ES) is sensitive to all neutrino flavors, but to a lesser extent to muonic and tau flavors. Thus, if neutrinos can pass from one flavor to another, the neutrino flux measured using the reaction (CC) F CC (ν e) should be less than the flux measured using the reaction (ES) F ES (ν x).
In the first series of measurements, which was carried out using the reaction (CC), a deficit of electron neutrinos was recorded.
The next year, the neutrino fluxes were estimated using the reaction (NC).
Experimental data obtained in Sudbury made it possible to estimate the solar neutrino flux from reaction (13) and prove that it agrees with the standard model of the Sun. Thus, the deficit of electron neutrinos recorded by Davis is a consequence of oscillations.
In addition to measuring the oscillations of atmospheric muon neutrinos, experiments with so-called "distant" accelerator neutrinos are planned and are already being carried out. In these experiments, muon neutrinos formed as a result of the interaction of protons accelerated up to several GeV with a converter target, having passed a long distance underground, are recorded by a detector. The MINOS experiment (Fermi Laboratories (USA)) uses two neutrino detectors. One of them is located near the target-converter, the other is at a distance of 725 km. Comparison of the number of muon neutrinos that should have reached the "far" detector in the absence of oscillations with the measured result proves the presence of oscillations.
The main result of all the experiments carried out is proof of the existence of oscillations and estimation of the neutrino mixing parameters ν 1, ν 2, ν 3. According to

(15)

Although studies of neutrino oscillations and the mixing angles corresponding to this phenomenon have already achieved good accuracy for ν 1, ν 2 (15), the mixing parameters ν 2 , ν 3 are known much less well, and reliable estimates of the neutrino mixing parameters ν 1, ν 3 have not yet been obtained.
The results of studies of neutrino oscillations are reflected in the above diagram: rectangles correspond to neutrinos ν 1, ν 2, ν 3 (from bottom to top); approximate estimates of the contributions of neutrinos of different flavors to them are shown. At this time, only the mass difference ν 1, ν 2 has been established with good accuracy: it is about 0.09 eV. Such small differences in the masses ν 1, ν 2, together with the data of experiments on studying the shape of β-spectra, make it possible to estimate the neutrino masses m (ν 1), m (ν 2)<2 эВ.

Literature:

1. R. Davis Jr. Half a century with solar neutrinos. UFN 174 408 (2004)
2. D. Perkins - Introduction to High Energy Physics, M., 1991
3. M. Koshiba. The birth of neutrino astrophysics. UFN, 174 4183(2004)

The theory of neutrino oscillations emerged as a possible solution to the problem of solar neutrino deficit. The crux of the problem was that in the sun, according to the standard model, neutrinos are mainly produced by the reaction of the proton-proton cycle:

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 is the -decay of 8 B isotopes, which arise in the 7 Be (p,) 8 B reaction (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. For 30 years, radiochemical experiments have been carried out based on the reaction 37 Cl + e 37 Ar + e -. According to the theory, the main contribution to this reaction should be made by neutrinos from 8 V decay. Research on the direct registration of neutrinos from 8 V decay with measuring 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 carried out 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 thermonuclear furnace in real time. In all experiments, a deficit in solar neutrino fluxes is observed in comparison with the predictions of the Standard Solar Model.
A possible solution to the problem of the deficit of solar neutrinos is neutrino oscillations - the transformation of electron neutrinos into muonic and tau neutrinos.
The first thing to pay attention to when starting a discussion of the properties of neutrinos is the existence of their various types.
As you know, at the present time we can definitely talk about three such varieties:
ν e, ν μ, ν τ and, accordingly, their antineutrinos. When exchanging a charged W-boson, an electron neutrino passes into an electron, and a muonic one - 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 the electron and muon neutrino. Namely, neutrino beams generated at accelerators consist mainly of the decay products of charged π-mesons:

π + μ + + ν
π − μ − + ν

If the neutrino does not distinguish between the types of leptons, then the neutrinos obtained in this way will produce electrons and muons with equal probability when interacting with the nuclei of matter. If each lepton corresponds to its own kind of neutrino, then in the decays of pions only its muonic kinds are generated. Then the neutrino beam from the accelerator will in the overwhelming majority of cases give muons, not electrons. It is this phenomenon that was registered experimentally.
After clarifying the difference between the types of neutrinos, 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 kind (flavor) of quarks. For example, the following chain of transitions is possible:

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

m (e)< 5.1 эВ,

while the electron mass is 0.51099906 ± 0.00000015 MeV
In the overwhelming majority of cases, we can assume that the masses of all three neutrinos are equal to zero. If they are exactly zero, it is impossible to notice the effects of possible mixing of different types of neutrinos. It is only if neutrinos have nonzero masses that mixing takes on a physical meaning. Note that we are not aware of any fundamental reasons leading to the strict equality of the neutrino masses to zero. Thus, the question of whether mixing of different neutrinos exists is a problem that should be solved by physical methods, primarily experimental. For the first time, B.M. Pontecorvo.

Mixing of neutrino states

Consider the problem of two types of neutrinos: e, ν μ,. For mixing effects, consider how states develop over time. The evolution in time is determined by the Schrödinger equation

From this point on, we use the system of units h = c = 1, which is usually used in particle physics. This system is convenient in that it contains only one dimensional quantity, for example, energy. The momentum and mass now have the same dimensions with energy, and the x coordinate and time t have the dimension of the reciprocal energy. Applying this relation to the case of neutrinos under consideration, 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). Here the value is very important, the difference of which from zero leads to mixing effects. If it does not exist, the system decays into two independent equations and neutrinos, electron and muonic, exist separately with their own masses.
So, H 0. Then we will seek 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, have the form (3). For what follows, it is important to note that at small 0, 1 is an almost pure electron neutrino, and at / 2, it is almost completely muonic. 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 the 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 at 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 us 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 considered state (we omit the common factor e -ikt)

(13)

Let us introduce the notation m 2 = m 1 2 - m 2 2. We see that along with the initially existing electron neutrino, the state of the muonic neutrino also appears here. The probability of its occurrence according to the rules of quantum mechanics is the square of the modulus of the amplitude, 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 the squares of the masses m 2 in square electronvolts. Of course, we take into account the smallness of the neutrino masses, so that L = ct. The muon component has a characteristic oscillating dependence; this phenomenon is called neutrino oscillations. What should be observed as the effect of neutrino oscillations? We know that electron neutrinos give an electron as a result of the reaction with the exchange of W, and muons give, respectively, a muon. Consequently, the beam, initially consisting of electron neutrinos, when passing through the recording equipment, gives not only electrons, but also muons with a probability depending on the distance to the starting point described by formula (14). Simply put, one should look for the production 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 m2. 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. In these experiments, the neutrino flux from decays of particles produced in the upper layers of the atmosphere by high-energy cosmic rays was studied. Depending on the angles of inclination to the horizon at which the investigated neutrinos come to the device, they cover distances from several tens of kilometers (directly above) to many thousands of kilometers (directly below). The result of continuous one and a half year measurements turned out to be incompatible with the calculations according to the theory without oscillations. At the same time, the introduction of oscillations leads to excellent agreement with experiment. In this case, the transitions ν μ e are necessary:

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

that is, explicitly nonzero values ​​are required. So far, scientific public opinion is not inclined towards the final recognition of the discovery of neutrino oscillations and is awaiting confirmation of the result. Experiments are continuing, and meanwhile it turned out that even richer information can be obtained from the study of neutrino oscillations taking into account their interaction with matter.

Oscillations of neutrinos in matter

Elucidation of the possibilities associated with the effects of neutrino propagation in matter is associated with the works of L. Wolfenstein and S.P. Mikheeva and A. Yu. Smirnov.
Consider again the case of two neutrinos - electron and muon. In matter, there are 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 in comparison with propagation in vacuum. The situation is completely different with the scattering of neutrinos by electrons. The muonic neutrino can interact with the electron only due to the exchange of the neutral boson Z, while the exchange of the charged boson W contributes to the scattering of the electron neutrino (and antineutrino) by the electron. Indeed, for example, W - goes over into the pair e, so that the process scattering follows the scheme

When antineutrinos are scattered by an electron, they merge into W, and when neutrinos are scattered, an exchange of W occurs, in which the original neutrino gives an electron and W +, which is absorbed by the original electron, giving the final neutrino. For a muonic neutrino, such transitions are impossible.
So, an electron neutrino has an additional interaction with an electron, which is described by an 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 an electron neutrino by electrons due to the exchange W. Electroweak theory gives a simple expression

,

(17)

where G F = (1.16637 + 0.00002). 10 -5 GeV -2 is the well-known Fermi constant characterizing weak interactions, and N e- the density of electrons in a 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 quantity can be represented as (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 oscillations of neutrinos in matter. Let the mixing of neutrinos in a 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 oscillations is also clearly manifested in the dependence of the neutrino masses in matter on the density (16). Indeed, we begin with expression (16) with a minus sign, which, in accordance with Eqs. (15), describes the initial electron neutrino (since it contains its characteristic interaction with electrons V W). Let the density change 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 a resonance, the type of neutrino changes completely.
It should be noted that if instead of neutrinos we consider antineutrinos, 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 or 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 an electron neutrino, but not an 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 transmitting a neutrino beam to a certain object, for example a planet, a star, etc., based on the composition of the neutrino beam at the output, it is possible to obtain a picture of the density distribution inside the illuminated object. One can draw attention to a 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 registered experimentally, however, there are indications of their existence, and they are associated precisely with possible resonance phenomena. The fact is that detection methods are mainly sensitive to electron neutrinos (antineutrinos), since muonic and even more so tau neutrinos with energies of several megaelectronvolts cannot give reactions, for example

37 Cl + 37 Ar + e -.

which is used in the chlorine-argon neutrino detection method. This is due to the fact that for the production of a muon it is necessary to spend more than 100 MeV energy (and even more for the production of tau). At the same time, a similar reaction with electron neutrinos can occur. Nuclear reactions in the Sun are precisely the source of electron (anti-) neutrinos, so the method used seemed to be quite adequate. However, if an oscillation occurred on the way from the point of birth to the device and the neutrino turned, for example, into a muonic one, then the reaction does not occur, the neutrino becomes “sterile”. This could explain the deficit of solar neutrinos.
At first, they tried to use the usual (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. Turning to formula (14), we can conclude that the fraction of such sterile neutrinos on Earth

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

Thus, it is generally possible to achieve the suppression of the neutrino flux from the Sun by half, generally speaking, but this requires maximum mixing sin 2 = 1. Searches for oscillations show that such a large mixing is excluded by experiment for a wide range of neutrino masses. In addition, this explanation provides the same suppression of the neutrino flux for all neutrino energies, while the experimental results indicate an energy dependence of the effect.
An explanation with the help of resonant oscillations in the matter of the Sun turns out to be more adequate. For a resonant neutrino transition to a sterile state to occur, condition (20) must be satisfied on a certain layer of the Sun's matter. Let the mixing angle be very small, so cos 21. Take as an example the parameter values

Z / A = 1.05, = 10 g / cm 2, E = 1 MeV,

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

It is precisely this order of the neutrino mass 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 is as follows: if the existing experimental data are finally confirmed, then no other explanation, except for the resonant oscillation, will be offered. This will be the most important result, opening the way to a further understanding of the structure of the physical world. In addition, we will get a new method of X-ray transmission of celestial bodies, including our Earth. Indeed, bearing in mind that the densities of terrestrial rocks are 3-6 g / cm 3 in the mantle and 9-12 g / cm 3 in the core, we are convinced that with a neutrino mass (22), the resonance conditions are achieved for neutrinos with energies of the order of several megaelectronvolt. By forming such beams and carrying out a program of scanning the Earth with registration of the effect on the network of neutrino stations, it is possible to obtain tomograms of the earth's thickness. In the future, this can lead both to clarification of the details of the structure of the Earth, and to practical results, for example, in the application to the search for deep-lying minerals.

On Tuesday, October 6, it became known that the Japanese Takaaki Kajita and the Canadian Arthur MacDonald were awarded the Nobel Prize in Physics for 2015 for the discovery of neutrino oscillations.

This is already the fourth "Nobel" in physics, which is awarded for the work on the study of these mysterious particles. What is the mystery of neutrinos, why they are so difficult to detect and what neutrino oscillations are, we will describe in this article in a simple and accessible language.

The birth of a neutron

In the late 19th century, French physicist Henri Becquerel, while studying how luminescence and X-rays are related, accidentally discovered radioactivity. It turned out that one of the uranium salts itself emits invisible and mysterious radiation that is not X-ray. Then it turned out that radioactivity is inherent in uranium, and not in the compounds into which it enters, after which the radioactivity of other elements, such as thorium, radium, and so on, was discovered.

A few years later, the British physicist Ernest Rutherford decided to pass the as yet unexplored radioactive radiation through a magnetic field and found that it can be divided into three parts. Some beams deflected in a magnetic field just as if they were composed of positively charged particles, others as composed of negative ones, and still others did not deflect at all.

As a result, it was decided to call the first alpha rays, the second beta rays, and the third gamma rays. Subsequently, it turned out that gamma rays are high-frequency electromagnetic radiation (or a stream of high-energy photons), alpha rays are a stream of helium nuclei, that is, particles composed of two protons and two neutrons, and beta rays are a stream of electrons. although there are also positron beta rays (this depends on the type of beta decay).

If you measure the energy of alpha particles and gamma particles arising from the corresponding type of radioactive decay, it turns out that it can only take on some discrete values. This fits well with the laws of quantum mechanics. However, the situation was different with electrons emitted during beta decay - their energy spectrum was continuous. In other words, an electron could carry absolutely any energy, limited only by the type of decaying isotope. Moreover, in most cases it turned out that the electron energy is less than that predicted by the theory. In addition, the energy of the nucleus formed after radioactive decay also turned out to be less than predicted.

It turned out that during beta decay, energy literally disappeared, violating a fundamental physical principle - the law of conservation of energy. Some scientists, among whom was Niels Bohr himself, were already ready to admit that the law may not work in the microworld, but the German physicist Wolfgang Pauli proposed to solve this problem in a simple and rather risky way - to assume that the missing energy is carried away by some particle, which does not have an electric charge, interacts extremely weakly with matter and therefore has not been discovered until now.

A few years later, this hypothesis was adopted by the Italian physicist Enrico Fermi for a theoretical explanation of beta decay. By this time, the neutron had already been discovered and physicists knew that the atomic nucleus consists not only of protons. It was known that the so-called strong interaction holds protons and neutrons in the nucleus. However, it was still not clear why, during beta decay, the nucleus emits an electron, which, in principle, is not there.

Fermi suggested that beta decay is similar to the emission of a photon by an excited atom and that an electron appears in the nucleus precisely during the decay process. One of the neutrons in the nucleus decays into three particles: a proton, an electron and that very invisible particle predicted by Pauli, which Fermi called in Italian a "neutrino", that is, a "neutron", or a small neutron. Like a neutron, a neutrino has no electric charge, nor does it take part in strong nuclear interactions.

Fermi's theory turned out to be successful. It was discovered that another hitherto unknown interaction - the weak nuclear one - is responsible for beta decay. This is the very interaction in which, in addition to gravitational, neutrinos participate. But due to the fact that the intensity and radius of this interaction is very small, the neutrino remains mostly invisible to matter.

You can imagine a neutrino of not too high energy, which flies through a sheet of iron. In order for this particle to be trapped by a sheet with one hundred percent probability, its thickness must be approximately 10 ^ 15 kilometers. For comparison: the distance between the Sun and the center of our Galaxy is only one order of magnitude greater - about 10 16 kilometers.

This elusiveness of the neutrino greatly complicates its observation in practice. Therefore, the existence of neutrinos was experimentally confirmed only 20 years after the theoretical prediction - in 1953.

Three generations of neutrinos

Beta decay can occur in two ways: with the emission of an electron or a positron. An antineutrino is always emitted together with an electron, and a neutrino is always emitted together with a positron. In the middle of the twentieth century, the question arose before physicists: is there any difference between neutrinos and antineutrinos? For example, a photon is an antiparticle for itself. But the electron is not at all identical to its antiparticle - the positron.

The identity of the neutrino and antineutrino was indicated by the absence of an electric charge in the particle. However, with the help of careful experiments, it was possible to find out that neutrinos and antineutrinos are still different. Then, to distinguish between the particles, it was necessary to introduce their own charge sign - the lepton number. By agreement of scientists, leptons (particles that do not participate in strong interactions), which include electrons with neutrinos, are assigned a lepton number of +1. And antileptons, among which there are also antineutrinos, the number -1 is assigned. In this case, the lepton number should always be conserved - this explains the fact that a neutrino always appears only in a pair with a positron, and an antineutrino with an electron. They seem to balance each other, leaving unchanged the sum of the lepton numbers of each particle from the entire system.

In the middle of the twentieth century, the physics of elementary particles experienced a real boom - scientists one after another discovered new particles. It turned out that there are more leptons than was thought - in addition to the electron and neutrino, the muon (heavy electron), as well as the muon neutrino, were discovered. Subsequently, scientists discovered a third generation of leptons - even heavier tau leptons and tau neutrinos. It became clear that all leptons and quarks form three generations of fundamental fermions (particles with half-integer spin that make up matter).

To distinguish between three generations of leptons, it was necessary to introduce the so-called flavor lepton charge. Each of the three generations of leptons (electron and neutrino, muon and muonic neutrino, tau lepton and tau neutrino) has its own flavor lepton charge, and the sum of the charges makes up the total lepton number of the system. For a long time it was believed that the lepton charge should also always be conserved. It turned out that this does not happen in the case of neutrinos.

Right-handed and left-handed neutrinos

Each elementary particle has such a quantum mechanical characteristic as spin. Spin can be thought of as the amount of rotational motion of a particle, although this description is very arbitrary. The spin can be directed in a certain direction relative to the momentum of the particle - parallel to it or perpendicularly. In the second case, it is customary to talk about the transverse polarization of the particle, in the first case, about the longitudinal polarization. With longitudinal polarization, two states are also distinguished: when the spin is directed together with the momentum, and when it is directed opposite to it. In the first case, the particle is said to have right-handed polarization, in the second, left-handed.

For a long time in physics, the parity conservation law was considered indisputable, which says that strict mirror symmetry should be observed in nature and particles with right polarization should be completely equivalent to particles with left. According to this law, in any neutrino beam one could find the same number of right-handed and left-handed particles.

There was no limit to the surprise of scientists when it turned out that the law of parity is not observed for neutrinos - there are no right-handed neutrinos and left-handed antineutrinos in nature. All neutrinos are left-handed and antineutrinos are right-handed. This is proof of the amazing fact that the weak nuclear interaction, which is responsible for beta decay, in which neutrinos are born, is chiral - its laws change with mirror reflection (we have already written about this in detail separately).

From the point of view of the physics of elementary particles in the middle of the twentieth century, the situation with strict polarization indicated that the neutrino is a massless particle, since otherwise it would be necessary to admit the violation of the law of conservation of the lepton charge. Based on this, it was believed for a long time that the neutrino really has no mass. But today we know that this is not the case.

Elusive mass

Neutrinos in huge quantities sweep through the thickness of the Earth and right through our body. They are born in thermonuclear reactions on the Sun and other stars, in the atmosphere, in nuclear reactors, even inside ourselves, as a result of the radioactive decay of some isotopes. Until now, relic neutrinos, born after the Big Bang, fly through the Universe. But their extremely weak interaction with matter determines the fact that we do not notice them at all.

Nevertheless, over the years of researching neutrinos, physicists have learned to register them using clever methods. And when observing the flux of neutrinos born on the Sun, scientists discovered a strange fact - from the luminary of these particles arrives about three times less than the theory predicts. Here it is necessary to clarify that we are talking about just one type of neutrino - electron neutrinos.

To explain this fact, they tried to attract various hypotheses about the internal structure of the Sun, which is capable of retaining missing neutrinos, but these attempts were unsuccessful. The fact remained only one theoretical explanation - on the way from the Sun to the Earth, particles turn from one type of neutrino to another. A particle born as an electron neutrino undergoes oscillations on its way, manifesting itself with a certain periodicity as a muon or tau neutrino. Therefore, not only electron neutrinos, but also muonic and tau neutrinos arrive from the Sun to the Earth. The hypothesis of neutrino oscillations was put forward by the Soviet-Italian physicist Bruno Pontecorvo back in 1957. Such transformations of neutrinos from one type to another presupposed one necessary condition - the presence of mass in neutrinos. All experiments carried out with neutrinos showed that the mass of this particle is negligible, but rigorous proof that it is equal to zero has not been obtained. This means that the possibility for neutrino oscillations really remained.

Opening oscillations

Confirmation of the existence of neutrino oscillations was obtained through observations of solar and atmospheric neutrinos at the Superkamiokande experimental facility in Japan and at the Sudbury neutrino observatory in Canada.

To register neutrinos, the Japanese have built an impressive structure - a huge tank (40 by 40 meters) made of stainless steel, filled with 50 thousand tons of the purest water. The reservoir was surrounded by more than 11 thousand photomultipliers, which were supposed to register the smallest bursts of Cherenkov radiation, generated when electrons are knocked out of atoms by some neutrinos. Considering that neutrino interacts extremely weakly with matter, only a few out of billions of particles flying through the reservoir are registered. Considering also the fact that researchers have to weed out these events from a large background (after all, a lot of completely different particles still fly through the huge reservoir), the work they did was colossal.

The Japanese detector was able to distinguish between electron and muon neutrinos by the nature of the radiation they cause. In addition, scientists knew that most muonic neutrinos are born in the atmosphere when air particles collide with cosmic rays. Thanks to this, they discovered the following pattern: the longer the neutrino beams cover the distance, the fewer muon neutrinos are among them. This meant that along the way, some of the muon neutrinos were transformed into other neutrinos.

The final proof of the existence of neutrino oscillations was obtained in 1993 in an experiment in Sudbury. In fact, the Canadian installation was similar to the Japanese one - a huge and equally impressive underground water reservoir and many Cherenkov radiation detectors. However, she was already able to distinguish all three types of neutrinos: electron, muon and tau neutrinos. As a result, it was found that the total number of neutrinos arriving from the Sun does not change and is in good agreement with theory, and the lack of electron neutrinos is caused precisely by their oscillation. Moreover, according to statistical data, neutrinos experience oscillations to a greater extent when passing through matter than through a vacuum, since a greater number of electron neutrinos arrived at the detector during the day than at night, when particles born on the Sun had to overcome the entire thickness of the Earth.

According to current ideas, neutrino oscillations are evidence of the mass of these particles, although the exact value of the mass is still unknown. Physicists know only its upper limit - a neutrino is at least a thousand times lighter than an electron. Finding out the exact mass of neutrinos is the next big task of physicists working in this direction, and it is possible that the next "Nobel" for neutrinos will be awarded precisely for this achievement.

Neutrinos - just like charged leptons (electron, muon, tau), up-type quarks (up, charmed, true) and down-type (down, strange, adorable) - are of three types. But they can be divided into types in different ways. Moreover, due to the quantum nature of our world, only one of them can be used at a time. In this article, I will explain why this happens, and how this fact leads to such an interesting and scientifically important fact as neutrino oscillations.

You may think that every particle has a certain mass - for example, the energy of the mass of electrons is (E = mc 2) 0.000511 GeV - and from one possible point of view, the three types of neutrinos are no exception. We can classify three neutrinos by their masses (which are not yet known for sure), and call them, from lightest to heaviest, neutrino-1, neutrino-2 and neutrino-3. We will call such division mass classification, and such types of neutrinos - mass types.


Rice. 1

Another way to classify neutrinos is by their relationship to charged leptons (electron, muon, and tau). This is mentioned in the article on what particles would look like if the Higgs field were zero. The best way to understand this is to focus on how neutrinos are affected by the weak nuclear force, which is reflected in their interactions with particle W. Particle W is very heavy, and if you produce it, it can decay (Fig. 1) into one of three charged antileptons and one of the three neutrinos. If W decays into anti-tau, then a tau neutrino will appear. Similarly, if W decays into an anti-muon, a muonic neutrino will appear. (Critically for creating a neutrino beam, a pion decays using weak interactions, and an anti-muon and a muon neutrino are obtained from positively charged pions.) And if W decays into a positron, an electron neutrino will appear. Let's call this a weak classification, and these neutrinos are weak type neutrinos, since they are determined by the weak interaction.

So what's the problem here? We constantly use different classifications when applied to people. We are talking about the fact that people are young, adult and old; they are tall, medium height and short. But people can be further divided at will, for example, into nine categories: young and tall, young and medium height, adults and short, elderly and short, and so on. But quantum mechanics forbids us to do the same with neutrino classifications. There are no neutrinos that are both muonic neutrinos and neutrino-1; there is no tau-neutrino-3. If I tell you the mass of a neutrino (and therefore whether it belongs to the neutrino group 1, 2, or 3), I simply cannot tell you whether it is an electron, a muon, or a tau neutrino. A neutrino of a certain mass type is a mixture, or "superposition" of three weak type neutrinos. Each mass-type neutrino - neutrino-1, neutrino-2 and neutrino-3 - is a precise but different mixture of electron, muon and tau neutrinos.

The converse is also true. If I see a pion decay into an anti-muon and a neutrino, I will immediately know that the resulting neutrino will be a muonic neutrino - but I will not be able to find out its mass, since it will be a mixture of neutrino-1, neutrino-2 and neutrino-3 ... The electron neutrino and the tau neutrino are also exact, but different mixtures of three neutrinos of certain masses.

The relationship between these massive and weak types is more similar (but does not exactly match) the relationship between the classifications of American highways as going "north-south" and "west-east" (the US government divides them in this way, assigning odd numbers of C / S and even simple roads W / E), and dividing them into roads going from "northeast to southwest" and from "southeast to northwest". There are advantages to using any classification: the N / S - W / E classification is suitable if you are concentrating on latitude and longitude, and the NE / SW - SE / NW will be more convenient near the coast, since it runs from the southwest to the north East. But both classifications cannot be used at the same time. The road going northeast is partly north and partly east; it cannot be said that she is either this or that. And the north road is a mixture of north-east and north-west. So it is with neutrinos: mass-type neutrinos are a mixture of weak-type neutrinos, and weak-type neutrinos are a mixture of mass neutrinos. (The analogy will stop working if you decide to use the improved classification of the N / S - NE / SW - E / W - SE / NW roads; for neutrinos, this option does not exist).

The inability to classify neutrinos by assigning them to a certain mass type and to a certain weak type is an example of the uncertainty principle, similar to an oddity that forbids simultaneously knowing the exact position and exact speed of a particle. If you know exactly one of these properties, you have no idea about the other. Or you can learn something about both properties, but not everything. Quantum mechanics tells you exactly how to balance your knowledge and ignorance. Incidentally, these problems do not apply only to neutrinos. They are related to other particles as well, but are especially important in the context of neutrino behavior.

A few decades ago, everything was simpler. Then it was believed that neutrinos have no mass, so it was enough to use a weak classification. If you look at old works or old books for ordinary people, you will only see names such as electron neutrino, muon neutrino and tau neutrino. However, after the discoveries of the 1990s, this is no longer enough.

And now the fun begins. Let's say you have a high energy electron type neutrino, that is, a certain mixture of neutrino-1, neutrino-2 and neutrino-3. A neutrino moves through space, but its three different mass types move at slightly different speeds, very close to the speed of light. Why? Because the speed of an object depends on its energy and mass, and three mass types have three different masses. The difference in their speeds is extremely small for any neutrino we can measure - it has never been observed - but its effect is surprisingly strong!

Difference of neutrino velocities - some formulas

The speed of a particle v in Einstein's theory of relativity can be written in terms of the particle's mass m and energy E (this is the total energy, i.e. the energy of motion plus the energy of the mass E = mc 2), and the speed of light c, as:

If the particle has a very high speed and its total energy E is much greater than the energy of mass mc 2, then

Recall the raised 1/2 means “take-the-square-root”. If the particle has very high velocity and its total energy E is much, much larger than its mass-energy mc2, then

Where the dots remind that this formula is not exact, but a good approximation to large E. In other words, the speed of a particle moving almost at the speed of light differs from the speed of light by an amount equal to half the square of the ratio of the energy of the particle's mass to its total energy ... It can be seen from this formula that if two neutrinos have different masses m 1 and m 2, but the same high energy E, then their velocities differ very little.

Let's see what this means. All measured neutrinos from a supernova that exploded in 1987 arrived on Earth in a 10-second interval. Let's say an electron neutrino was emitted by a supernova with an energy of 10 MeV. This neutrino was a mixture of neutrino-1, neutrino-2 and neutrino-3, each of which was moving at a slightly different speed! Would we have noticed this? We do not know exactly the masses of neutrinos, but let us assume that the mass energy of neutrino-2 is 0.01 eV, and that of neutrino-1 the mass energy is 0.001 eV. Then their two speeds, given that their energies are equal, will differ from the speed of light and from each other by less than one part of a hundred thousand trillion:

(the error of all equations does not exceed 1%). Such a difference in speed means that the parts of neutrino-2 and neutrino-1 of the original electron neutrino would arrive on Earth with a difference of a millisecond - such a difference cannot be detected for many technical reasons.

And now we move from the interesting to the really weird things.

This tiny difference in speed causes the precise mixture of neutrino-1, neutrino-2, and neutrino-3 that makes up an electron neutrino to gradually change as it moves through space. This means that the electron neutrino with which we started, eventually ceases to be itself and to correspond to one specific mixture of neutrino-1, neutrino-2 and neutrino-3. Different masses of neutrinos of three mass types convert the initial electron neutrino as it travels into a mixture of electron neutrinos, muonic neutrinos and tau neutrinos. The percentages of the mixture depend on the difference in velocities, and, therefore, on the energy of the initial neutrino, as well as on the difference in masses (more precisely, on the difference in the squared masses) of the neutrinos.

Rice. 2

At first, the effect increases. But, interestingly, as shown in Fig. 2, this effect is not just constantly growing. It grows, and then decreases again, and then grows again, decreases again, again and again, as the neutrino moves. This is called neutrino oscillations. How exactly they occur depends on what masses the neutrinos have and how mass neutrinos and weak neutrinos are mixed there.

The effect of oscillations can be measured due to the fact that an electron neutrino in a collision with a nucleus (and this is how a neutrino can be detected) can turn into an electron, but not a muon and not a tau, while a muonic electrino can turn into a muon, but not into electron or tau. So, if we started with a beam of a muon neutrino, and after moving a certain distance, some neutrinos collided with nuclei and turned into electrons, this means that oscillations occur in the beam, and muon neutrinos turn into electron neutrinos.

One very important effect complicates and enriches this story. Since ordinary matter is made of electrons, but not muons and tau, electron neutrinos interact with it differently than muonic or tau. These interactions, occurring through weak interactions, are extremely small. But if a neutrino passes through a large thickness of matter (say, through a tangible fraction of the Earth or the Sun), these small effects can accumulate and strongly affect the oscillations. Fortunately, we know enough about the weak nuclear interaction to predict these effects in detail, and calculate the entire chain backwards, from measurements in an experiment to elucidating the properties of neutrinos.

This is all done using quantum mechanics. If this is not intuitive for you, relax; for me it is also not intuitive. I got all my intuition from the equations.

It turns out that careful measurement of neutrino oscillations is the fastest way to study the properties of neutrinos! This work has already been awarded the Nobel Prize. This whole story emerged from the classic interaction of experiment and theory, stretching from the 1960s to the present day. I will mention the most important measurements taken.

For starters, we can study electron neutrinos produced at the center of the sun, in its well-studied nuclear furnace. These neutrinos travel through the Sun and through empty space to Earth. It has been found that when they arrive on Earth, they are as likely to be of the muonic or tau type as they are to the electron neutrino type. This in itself serves as evidence of neutrino oscillations, and the exact distribution gives us detailed information about neutrinos.

We also have muon neutrinos arising from the decay of pions arising in cosmic rays. Cosmic rays are high-energy particles that arrive from space and collide with atomic nuclei in the upper atmosphere. The resulting particle cascades often contain pions, many of which decay into muonic neutrinos and anti-muons, or into muonic antineutrinos and muons. We detect some of these neutrinos (and antineutrinos) in our detectors, and we can measure how much of them belongs to electron neutrinos (and antineutrinos), depending on how much of the Earth they passed before entering the detector. This again gives us important information about the behavior of neutrinos.

These "solar" and "atmospheric" neutrinos have taught us a lot about the properties of neutrinos over the past twenty years (and the first hint of something interesting happened almost 50 years ago). And to these natural sources of energy are added various studies done with neutrino beams, such as those used in the OPERA experiment, as well as with neutrinos from conventional nuclear reactors. Each of the measurements is largely consistent with the standard interpretation of solar and atmospheric neutrinos, and allows more accurate measurements of mixtures of mass types and weak types of neutrinos and differences in the mass squared neutrinos of the mass type.

As you would expect, there are small discrepancies in the experiments with theoretical expectations, but none of them have been confirmed, and most, if not all, are just statistical coincidences or problems at the experimental level. So far, not a single contradiction with understanding neutrinos and their behavior has been confirmed in several experiments. On the other hand, this whole picture is quite new and rather poorly tested, so it is quite possible, although unlikely, that it could have completely different interpretations. Indeed, quite serious alternatives have already been proposed. So clarifying the details of the properties of neutrinos is an actively developing area of ​​research, in which there is much agreement, but some questions still remain open - including the complete and irrevocable determination of neutrino masses.

Particles of a certain type, depending on the time passed from the moment of particle creation.

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 problem of solar neutrinos.

Oscillations in a vacuum

It is assumed that such transformations are a consequence of the presence of mass in neutrinos or (for the case of neutrino-antineutrino transformations) nonconservation of the lepton charge at high energies.

Experiments

Oscillations were observed for:

• solar neutrinos (the Davis chlorine-argon experiment, the SAGE, GALLEX / GNO gallium-germanium experiments, the Kamiokande and SNO water-Cherenkov experiments), the BOREXINO scintillation experiment;
• atmospheric neutrinos (Kamiokande, IMB) arising from the interaction of cosmic rays with the nuclei of atoms of atmospheric gases in the atmosphere;
• reactor antineutrinos (KamLAND scintillation experiment, Daya Bay, Double Chooz, RENO);
• accelerator neutrinos (experiment K2K (rus. KEK To Kamioka) observed a decrease in the number of muon neutrinos after passing 250 km in the thickness of matter, the OPERA experiment discovered in 2010 oscillations of muon neutrinos in tau neutrinos with the subsequent production of tau leptons);

Oscillations with the transformation of muon neutrinos, as well as antineutrinos, into electronic ones are currently being investigated in the MiniBooNE experiment, set up according to the conditions of the LSND experiment. The preliminary results of the experiment may indicate a difference in the oscillations of neutrinos and antineutrinos.

see also

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Literature

• S. M. Bilenky// Phys. - 2003 .-- T. 173. - S. 1171-1186. - DOI: 10.3367 / UFNr.0173.200311b.1171.
• Yu. G. Kudenko// Phys. - 2011 .-- T. 181. - S. 569-594. - DOI: 10.3367 / UFNr.0181.201106a.0569.
• Yu. G. Kudenko// Phys. - 2013 .-- T. 183. - S. 1225-1230. - DOI: 10.3367 / UFNr.0183.201311d.1225.
• Yuri Kudenko.... elementy.ru, "Trinity Option" No. 13 (82) (July 5, 2011). Retrieved January 18, 2013.
• G. Bellini, L. Ludhova, G. Ranucci, F.L. Villante Neutrino oscillations (eng.). - 2013 .-- arXiv: 1310.7858.

Excerpt Characterizing Neutrino Oscillations

Dolokhov chuckled.
“You better not worry. I will not ask for what I need, I will take it myself.
- Well, I am so ...
- Well, I am.
- Goodbye.
- Be healthy…
... and high and far,
On the home side ...
Zherkov touched the horse with his spurs, which three times, getting hot, kicked him, not knowing where to start, coped and galloped, overtaking the company and catching up with the carriage, also to the beat of the song.

Returning from the inspection, Kutuzov, accompanied by the Austrian general, went into his office and, having called the adjutant, ordered to submit to himself some papers related to the state of the arriving troops, and letters received from Archduke Ferdinand, who commanded the advanced army. Prince Andrey Bolkonsky entered the commander-in-chief's office with the required papers. In front of the plan laid out on the table sat Kutuzov and an Austrian member of the Hofkrigsrat.
"Ah ..." said Kutuzov, looking back at Bolkonsky, as if by this word inviting the adjutant to wait, and continued the conversation that had begun in French.
“I’m only saying one thing, General,” Kutuzov said with a pleasant grace of expression and intonation that made him listen attentively to every leisurely spoken word. It was evident that Kutuzov himself was listening to himself with pleasure. - I only say one thing, General, that if the matter depended on my personal desire, then the will of His Majesty the Emperor Franz would have been fulfilled long ago. I would have joined the Archduke long ago. And believe my honor, that for me personally to transfer the higher command of the army to a more knowledgeable and skillful general, which Austria is so abundant, and to give up all this heavy responsibility for me personally would be a delight. But circumstances are stronger than we are, General.
And Kutuzov smiled with such an expression, as if he were saying: “You have every right not to believe me, and even I do not care whether you believe me or not, but you have no reason to tell me this. And that's the whole point. "
The Austrian general looked displeased, but could not answer Kutuzov in the same tone.
“On the contrary,” he said in a grumpy and angry tone that so contradicted the flattering meaning of the words spoken, “on the contrary, your Excellency's participation in a common cause is highly valued by His Majesty; but we believe that a real slowdown is depriving the glorious Russian troops and their commanders-in-chief of those laurels that they are used to reaping in battles, - he finished the apparently prepared phrase.
Kutuzov bowed without changing his smile.
- And I am so convinced and, based on the last letter that His Highness Archduke Ferdinand honored me with, I suppose that the Austrian troops, under the command of such a skilled assistant as General Mac, have now won a decisive victory and no longer need our help, - said Kutuzov.
The general frowned. Although there was no positive news of the defeat of the Austrians, there were too many circumstances confirming the general unfavorable rumors; and therefore the assumption of Kutuzov about the victory of the Austrians was very similar to a mockery. But Kutuzov smiled meekly, all with the same expression that said that he had the right to assume this. Indeed, the last letter he received from Mac's army informed him of the victory and the most advantageous strategic position of the army.
“Give me this letter here,” said Kutuzov, addressing Prince Andrey. “If you please, see. - And Kutuzov, with a mocking smile at the ends of his lips, read in German to the Austrian general the following passage from the letter of Archduke Ferdinand: “Wir haben vollkommen zusammengehaltene Krafte, nahe an 70,000 Mann, um den Feind, wenn er den Lech passirte, angreifen und schl konnen. Wir konnen, da wir Meister von Ulm sind, den Vortheil, auch von beiden Uferien der Donau Meister zu bleiben, nicht verlieren; mithin auch jeden Augenblick, wenn der Feind den Lech nicht passirte, die Donau ubersetzen, uns auf seine Communikations Linie werfen, die Donau unterhalb repassiren und dem Feinde, wenn er sich gegen unsere treue Allirte mit ganzer Macht, wenden wollte Wir werden auf solche Weise den Zeitpunkt, wo die Kaiserlich Ruseische Armee ausgerustet sein wird, muthig entgegenharren, und sodann leicht gemeinschaftlich die Moglichkeit finden, dem Feinde das Schicksal zuzubereiten. So erdient [We have a fully concentrated force, about 70,000 people, so that we can attack and defeat the enemy in the event of a crossing over Leh. Since we already own Ulm, we can retain the benefit of commanding both banks of the Danube, therefore, every minute, if the enemy does not cross the Lech, cross the Danube, rush to his line of communication, below cross the Danube and the enemy, if he decides to turn all his power on our faithful allies, not to allow his intention to be fulfilled. Thus, we will cheerfully await the time when the imperial Russian army is completely ready, and then together we will easily find an opportunity to prepare the enemy for the fate he deserves. "]
Kutuzov sighed heavily, having finished this period, and carefully and affectionately looked at the member of the Hofkrigsrat.
“But you know, Your Excellency, a wise rule that presupposes the worst,” said the Austrian general, apparently wanting to end the jokes and get down to business.
He involuntarily glanced back at the adjutant.
“Excuse me, General,” Kutuzov interrupted him and also turned to Prince Andrey. - That's what, my dear, you take all the reports from our spies at Kozlovsky. Here are two letters from Count Nostitz, here is a letter from His Highness Archduke Ferdinand, here's another one, ”he said, handing him several papers. - And out of all this, neatly, in French, compose a memorandum, a note, for the visibility of all the news that we had about the actions of the Austrian army. Well, then, and introduce it to His Excellency.
Prince Andrey bowed his head as a sign that he understood from the first words not only what was said, but also what Kutuzov would like to tell him. He collected the papers, and, giving a general bow, quietly walking on the carpet, went out into the waiting room.