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.
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) non-conservation of lepton charge at high energies.
see also
- Matrix Pontecorvo - Maki - Nakagawa - Sakata
- Oscillations of neutral kaons
- B-meson oscillations
Notes
Literature
- Yu. G. Kudenko, “Study of neutrino oscillations in long-baseline accelerator experiments”, Advances in Physical Sciences, vol. 6, 2011.
- S. M. Bilenky, “Mass, mixing and oscillations of neutrinos”, Advances in Physical Sciences 173 1171-1186 (2003)
Wikimedia Foundation. 2010.
See what “Neutrino oscillations” are in other dictionaries:
Neutrino oscillations of the transformation of a neutrino (electron, muon or taon) into a neutrino of a different type (generation), or into an antineutrino. The theory predicts the existence of a law of periodic change in the probability of detecting a particle... ... Wikipedia
- (v), a light (possibly massless) electrically neutral particle with spin 1/2 (in units ћ), participating only in weak and gravitational. exposures. N. belongs to the class of leptons, and according to statistics. Holy revelation to you fermion. Three types of N. are known: ... ... Physical encyclopedia
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
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), |
(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 installation. 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.
On Tuesday, October 6, it became known that Japanese Takaaki Kajita and Canadian Arthur MacDonald were awarded the 2015 Nobel Prize in Physics for their discovery of neutrino oscillations.
This is the fourth “Nobel” in physics, which is awarded for 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 explain in this article in simple and accessible language.
The birth of a neutron
At the end of the 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-rays. Then it turned out that radioactivity is inherent precisely in uranium, and not in the compounds in which it is included, after which the radioactivity of other elements was discovered - such as thorium, radium, and so on.
A few years later, British physicist Ernest Rutherford decided to pass as yet unexplored radioactive radiation through a magnetic field and discovered that it could be divided into three parts. Some rays were deflected in a magnetic field as if they were composed of positively charged particles, others as if they were composed of negative ones, and still others were not deflected 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 nuclei of helium atoms, 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 we measure the energy of alpha particles and gamma particles arising from the corresponding type of radioactive decay, it turns out that it can take only some discrete values. This agrees well with the laws of quantum mechanics. However, with electrons emitted during beta decay, the situation was different - 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 was less than what the theory predicted. 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 microcosm, but the German physicist Wolfgang Pauli proposed solving this problem in a simple and rather risky way - to assume that the missing energy is carried away by some particle, which has no electrical charge, interacts extremely weakly with matter and therefore has not yet been discovered.
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 of more than just protons. It was known that protons and neutrons in the nucleus are held together by the so-called strong interaction. However, it was still unclear why, during beta decay, the nucleus emits an electron that is not there in principle.
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 same invisible particle predicted by Pauli, which Fermi in Italian called a “neutrino”, that is, a “neutron”, or a small neutron. Like the neutron, the neutrino has no electrical charge, and it also does not take part in the strong nuclear interaction.
Fermi's theory was successful. It was discovered that another hitherto unknown interaction, the weak nuclear interaction, is responsible for beta decay. This is the very interaction in which, in addition to the gravitational one, neutrinos participate. But because the intensity and radius of this interaction are so small, the neutrino remains largely invisible to matter.
You can imagine a neutrino of not too high energy flying through a sheet of iron. In order for this particle to be retained by the sheet with one hundred percent probability, its thickness should 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 makes it very difficult to observe it 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 along with an electron, and a neutrino is always emitted along with a positron. In the middle of the twentieth century, physicists were faced with the question: is there any difference between neutrinos and antineutrinos? For example, a photon is its own antiparticle. But the electron is not at all identical to its antiparticle – the positron.
The identity of neutrinos and antineutrinos was indicated by the absence of an electric charge on 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 particles, it was necessary to introduce their own sign of charge - the lepton number. By agreement of scientists, leptons (particles that do not participate in strong interactions), which include electrons and neutrinos, are assigned the lepton number +1. And antileptons, among which there are antineutrinos, are assigned the number -1. In this case, the lepton number must always be conserved - this explains the fact that a neutrino always appears only in pairs 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, particle physics experienced a real boom - scientists discovered new particles one after another. It turned out that there are more leptons than thought - in addition to the electron and neutrino, the muon (heavy electron) was discovered, as well as the muon neutrino. Subsequently, scientists discovered a third generation of leptons - even heavier tau lepton and tau neutrino. 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 muon neutrino, tau lepton and tau neutrino) has its own flavor lepton charge, and the sum of the charges constitutes 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 and left neutrinos
Each elementary particle has a quantum mechanical characteristic called 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 perpendicular. In the second case, it is customary to talk about the transverse polarization of the particle, in the first – about the longitudinal one. With longitudinal polarization, two states are also distinguished: when the spin is directed along 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 polarization.
For a long time in physics, the law of conservation of parity was considered indisputable, which states that strict mirror symmetry must be observed in nature and particles with right-hand polarization must be completely equivalent to particles with left-hand polarization. According to this law, in any neutrino beam one could find the same number of right-handed and left-handed polarized particles.
The surprise of scientists knew no bounds when it turned out that the parity law for neutrinos is not observed - right-handed neutrinos and left-handed antineutrinos do not exist in nature. All neutrinos have left-handed polarization, and antineutrinos have right-handed polarization. This is proof of the amazing fact that the weak nuclear interaction, responsible for beta decay, in which neutrinos are born, is chiral - with mirror reflection, its laws change (we have already written about this in detail separately).
From the point of view of elementary particle physics of the mid-twentieth century, the situation with strict polarization indicated that the neutrino is a massless particle, since otherwise one would have to admit that the law of conservation of lepton charge was not observed. Based on this, it was believed for a long time that neutrinos really have no mass. But today we know that this is not so.
Elusive mass
Neutrinos rush in huge numbers through the thickness of the Earth and directly through our body. They are born in thermonuclear reactions in the Sun and other stars, in the atmosphere, in nuclear reactors, even within ourselves, as a result of the radioactive decay of certain isotopes. Relic neutrinos born after the Big Bang are still flying through the Universe. But their extremely weak interaction with matter means that we do not notice them at all.
However, over the years of studying neutrinos, physicists have learned to register them using clever methods. And while observing the flow of neutrinos born on the Sun, scientists discovered a strange fact: approximately three times fewer of these particles arrive from the sun than the theory predicts. Here it is necessary to clarify that we are talking about exactly one type of neutrino – electron neutrinos.
To explain this fact, they tried to involve various hypotheses about the internal structure of the Sun, which is capable of trapping missing neutrinos, but these attempts were unsuccessful. There was only one theoretical explanation left for the fact: 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 experiences oscillations along its path, manifesting itself with a certain periodicity as a muon or tau neutrino. Therefore, not only electron neutrinos, but also muon and tau neutrinos fly to Earth from the Sun. 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 neutrino mass. All experiments carried out with neutrinos showed that the mass of this particle is negligibly small, but no strict proof was obtained that it is equal to zero. This means that the possibility for neutrino oscillations really remained.
Discovery of 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.
The Japanese built an impressive structure to register neutrinos - a huge tank (40 by 40 meters) made of stainless steel, filled with 50 thousand tons of pure water. The reservoir was surrounded by more than 11 thousand photomultiplier tubes, which were supposed to record the smallest flashes of Cherenkov radiation generated when electrons are knocked out of atoms by some neutrino. Considering that neutrinos interact extremely weakly with matter, out of the billions of particles flying through the tank, only a few are registered. Considering also the fact that researchers have to sift out these events from a large background (after all, there are still many completely different particles flying through the huge reservoir), they did a colossal amount of work.
The Japanese detector was able to distinguish electron and muon neutrinos by the nature of the radiation they caused. In addition, scientists knew that most muon neutrinos are created in the atmosphere when air particles collide with cosmic rays. Thanks to this, they discovered the following pattern: the longer neutrino beams travel distances, the fewer muon neutrinos among them. This meant that along the way, some of the muon neutrinos turned into other neutrinos.
Final proof of the existence of neutrino oscillations was obtained in 1993 in an experiment in Sudbury. In essence, the Canadian installation was similar to the Japanese one - a huge and no less impressive tank of water underground and many Cherenkov radiation detectors. However, she was already able to distinguish between 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 the 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 vacuum, since a larger 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 today's understanding, neutrino oscillations are evidence that these particles have mass, 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 for physicists working in this direction, and it is possible that the next Nobel for neutrinos will be awarded for this achievement.
Neutrinos - just like charged leptons (electron, muon, tau), up quarks (up, charm, true) and down quarks (down, strange, charm) - come in 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 one 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 might think that every particle has a certain mass - for example, the mass energy of electrons is (E = mc 2) 0.000511 GeV - and from one possible point of view, the three types of neutrinos are no exceptions. We can classify the three neutrinos by their masses (which are not yet known exactly), and call them, from lightest to heaviest, neutrino-1, neutrino-2 and neutrino-3. We will call this division mass classification, and these types of neutrinos – mass types.
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Another way to classify neutrinos is by their association with charged leptons (electron, muon and tau). This is mentioned in the article about 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 the W particle. The W particle is very heavy, and if you produce it, it can decay (Figure 1) into one of three charged antileptons and one of three neutrinos. If W decays into anti-tau, a tau neutrino will appear. Similarly, if W decays into an antimuon, a muon neutrino will appear. (Critical for the creation of a neutrino beam, the pion decays through weak interactions, and positively charged pions produce an antimuon and a muon neutrino). 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 because they are determined by the weak interaction.
Well, what's the problem here? We constantly use different classifications to apply to people. We talk about the fact that people are young, adults 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 average height, adults and short, elderly and short, and so on. But quantum mechanics prohibits us from doing the same with neutrino classifications. There are no neutrinos that are both muon 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 neutrinos of a weak type. Each mass neutrino—neutrino 1, neutrino 2, and neutrino 3—is a precise but distinct mixture of electron, muon, and tau neutrinos.
The opposite is also true. If I see a pion decay into an antimuon and a neutrino, I will immediately know that the resulting neutrino will be a muon neutrino - but I will not be able to know its mass, since it will be a mixture of neutrino 1, neutrino 2 and neutrino 3 . An electron neutrino and a tau neutrino are also precise but different mixtures of three neutrinos of certain masses.
The relationship between these massive and weak types is more similar to (but not exactly the same as) the relationship between the classifications of American highways as "north-south" and "west-east" (the US government divides them this way, assigning odd numbers to highways N/ S and even simple W/E roads), and dividing them into roads running from “northeast to southwest” and from “southeast to northwest”. There are advantages to using either classification: the N/S – W/E classification is suitable if you are concentrating on latitude and longitude, while the NE/SW – SE/NW classification will be more useful near the coast, as it runs from the southwest to the northwest. East. But both classifications cannot be used at the same time. The road running northeast is partly north and partly east; You can’t say that she is either this or that. And the northern road is a mixture of northeast and northwest. It’s the same with neutrinos: mass-type neutrinos are a mixture of weak-type neutrinos, and weak-type neutrinos are a mixture of mass ones. (The analogy breaks down if you decide to use the improved road classification N/S - NE/SW - E/W - SE/NW; there is no such option for neutrinos).
The inability to classify neutrinos into a certain mass type and a certain weak type is an example of the uncertainty principle, similar to the strangeness that prohibits knowing the exact position and exact speed of a particle at the same time. If you know exactly one of these properties, you have no idea about the other. Or you may learn something about both properties, but not everything. Quantum mechanics tells you exactly how to balance your knowledge and ignorance. By the way, these problems do not apply only to neutrinos. They are also associated with other particles, but are especially important in the context of the behavior of neutrinos.
A few decades ago, everything was simpler. At that time it was believed that neutrinos had no mass, so it was enough to use a weak classification. If you look at old papers 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 high-energy electron-type neutrinos, that is, a certain mixture of neutrino-1, neutrino-2 and neutrino-3. Neutrinos move through space, but their 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 the 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 large!
Neutrino speed difference - some formulas
The speed of a particle v in Einstein’s theory of relativity can be written through the mass of the particle m and the 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 mass energy 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 you that this formula is not an 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 particle's mass energy to its total energy . From this formula it is clear that if two neutrinos have different masses m 1 and m 2, but the same high energy E, then their speeds differ very little.
Let's see what this means. All measured neutrinos from the supernova that exploded in 1987 arrived on Earth within 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 moving at a slightly different speed! Would we notice this? We don’t know the exact masses of neutrinos, but let’s assume that neutrino-2 has a mass energy of 0.01 eV, and neutrino-1 has a mass energy of 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 one hundred thousand trillion:
(the error of all equations does not exceed 1%). This difference in speed means that the Neutrino-2 and Neutrino-1 portions of the original electron neutrino would arrive on Earth within a millisecond of each other—a difference that, for a variety of technical reasons, is impossible to detect.
And now we move on from the interesting to the really strange things.
This tiny difference in speed causes the precise mixture of neutrino-1, neutrino-2 and neutrino-3 that makes up the electron neutrino to gradually change as it moves through space. This means that the electron neutrino with which we started, over time, ceases to be itself and correspond to one specific mixture of neutrino-1, neutrino-2 and neutrino-3. Different masses of neutrinos of three mass types transform the initial electron neutrino in the process of movement into a mixture of electron neutrinos, muon neutrinos and tau neutrinos. The percentages of the mixture depend on the difference in speeds, and, therefore, on the energy of the initial neutrino, as well as on the difference in masses (more precisely, on the difference in the squares of the masses) of the neutrino.
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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, when colliding with a nucleus (and this is how a neutrino can be detected), can turn into an electron, but not into a muon or tau, while a muonic electrino can turn into a muon, but not into electron or tau. So, if we started with a beam of muon neutrinos, and after traveling a certain distance, some neutrinos collided with nuclei and turned into electrons, this means that oscillations occur in the beam, and the muon neutrinos turn into electron neutrinos.
One very important effect complicates and enriches this story. Because ordinary matter is made of electrons but not muons or tau, electron neutrinos interact with it differently than muons or tau. These interactions, which occur through the weak force, are extremely small. But if a neutrino passes through a large thickness of matter (say, through a noticeable fraction of the Earth or the Sun), these small effects can accumulate and greatly affect the oscillations. Fortunately, we know enough about the weak nuclear interaction to predict these effects in detail, and to calculate the entire chain backwards, from experimental measurements to elucidating the properties of neutrinos.
All this is done using quantum mechanics. If this is not intuitive for you, relax; It's not intuitive for me either. I got all the intuition I had from the equations.
It turns out that carefully measuring neutrino oscillations is the fastest way to study the properties of neutrinos! This work has already received a Nobel Prize. This whole story emerges from the classic interaction between 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 discovered that when they arrive on Earth they are just as likely to be of the muon or tau type as they are of the electron neutrino type. This in itself provides evidence of neutrino oscillation, and the precise distribution gives us detailed information about the neutrino.
We also have muon neutrinos, which are produced by the decay of pions produced in cosmic rays. Cosmic rays are high-energy particles coming from outer space that collide with atomic nuclei in the upper atmosphere. The resulting particle cascades often contain pions, many of which decay into muon neutrinos and antimuons, or muon antineutrinos and muons. We detect some of these neutrinos (and antineutrinos) in our detectors, and we can measure how much of them are electron neutrinos (and antineutrinos) depending on how much of the Earth they passed through before hitting 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 energy sources are added various studies carried out using neutrino beams, such as those used in the OPERA experiment, as well as using neutrinos from conventional nuclear reactors. Each of the measurements is largely consistent with the standard interpretation of solar and atmospheric neutrinos, and allows for more precise measurements of mixtures of mass-type and weak-type neutrinos and differences in the squared masses of mass-type neutrinos.
As might be expected, there are small discrepancies with theoretical expectations in the experiments, but none have been confirmed and most, if not all, are merely statistical flukes or problems at the experimental level. So far, no contradiction to the understanding of neutrinos and their behavior has been confirmed in several experiments. On the other hand, this whole picture is quite new and poorly tested, so it is quite possible, although unlikely, that there could be 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 for the most part there is agreement, but some questions still remain open - including a complete and irrevocable determination of neutrino masses.