What does the standard model of elementary particles describe. The Standard Model of Elementary Particles for Beginners. Standard Model of Particles and Interactions

All matter consists of quarks, leptons and particles - carriers of interactions.

The standard model today is called the theory that best reflects our understanding of the source material from which the universe was originally built. It also describes exactly how matter is formed from these basic components, and the forces and mechanisms of interaction between them.

From a structural point of view, elementary particles that make up atomic nuclei ( nucleons), and in general all heavy particles - hadrons (baryons And mesons) - consist of even more simple particles which are called fundamental. In this role, the truly fundamental primary elements of matter are quarks, whose electric charge is equal to 2/3 or –1/3 of the unit positive charge of the proton. The most common and lightest quarks are called top And lower and denote, respectively, u(from English up) And d(down). Sometimes they are called proton And neutron quark due to the fact that the proton consists of a combination uud, and the neutron udd. The top quark has a charge of 2/3; lower - negative charge -1/3. Since the proton consists of two up and one down quarks, and the neutron consists of one up and two down quarks, you can independently verify that the total charge of the proton and neutron turns out to be strictly equal to 1 and 0, and make sure that the Standard Model adequately describes reality in this . The other two pairs of quarks are part of more exotic particles. Quarks from the second pair are called enchanted - c(from charmed) And strange - s(from strange). The third pair is true - t(from truth, or in English. traditions top) And Beautiful - b(from beauty, or in English. traditions bottom) quarks. Almost all particles predicted by the Standard Model and consisting of various combinations of quarks have already been discovered experimentally.

Another building set consists of bricks called leptons. The most common of the leptons - long known to us electron, which is part of the structure of atoms, but does not participate in nuclear interactions, being limited to interatomic ones. In addition to it (and its paired antiparticle called positron) leptons include heavier particles - the muon and the tau lepton with their antiparticles. In addition, each lepton is assigned its own uncharged particle with zero (or practically zero) rest mass; such particles are called, respectively, electron, muon or taon neutrino.

So, leptons, like quarks, also form three "family pairs". Such a symmetry has not escaped the observant eyes of theorists, but no convincing explanation has yet been offered for it. Be that as it may, quarks and leptons are the basic building blocks of the universe.

To understand the flip side of the coin - the nature of the forces of interaction between quarks and leptons - you need to understand how modern theoretical physicists interpret the very concept of force. An analogy will help us with this. Imagine two boatmen rowing on opposite courses on the River Cam in Cambridge. One rower out of generosity decided to treat a colleague with champagne and, when they sailed past each other, threw him a full bottle of champagne. As a result of the law of conservation of momentum, when the first rower threw the bottle, the course of his boat deviated from the straight line in the opposite direction, and when the second rower caught the bottle, its momentum was transferred to him, and the second boat also deviated from the straight line. straight course, but in the opposite direction. Thus, as a result of the exchange of champagne, both boats changed direction. According to the laws of Newtonian mechanics, this means that a force interaction has occurred between the boats. But the boats did not come into direct contact with each other, did they? Here we both see visually and understand intuitively that the force of interaction between the boats was transferred by the carrier of the impulse - a bottle of champagne. Physicists would call it carrier of interaction.

In exactly the same way, force interactions between particles occur through the exchange of particles-carriers of these interactions. In fact, we distinguish between the fundamental forces of interaction between particles only insofar as different particles act as carriers of these interactions. There are four such interactions: strong(this is what keeps the quarks inside the particles), electromagnetic, weak(which is what leads to some form of radioactive decay) and gravitational. Carriers of strong color interaction are gluons, which have neither mass nor electric charge. This type of interaction is described by quantum chromodynamics. Electromagnetic interaction occurs through the exchange of quanta of electromagnetic radiation, which are called photons and also devoid of mass . Weak interaction, on the contrary, is transmitted by massive vector or gauge bosons, which "weigh" 80-90 times more than a proton - in laboratory conditions they were first discovered only in the early 1980s. Finally, the gravitational interaction is transmitted through the exchange of non-self-mass gravitons- these intermediaries have not yet been experimentally detected.

Within the framework of the Standard Model, the first three types of fundamental interactions have been unified, and they are no longer considered separately, but are considered three different manifestations of the force of a single nature. Returning to the analogy, suppose that another pair of rowers, passing each other on the River Cam, exchanged not a bottle of champagne, but only a glass of ice cream. From this, the boats will also deviate from the course in opposite directions, but much weaker. It may seem to an outside observer that in these two cases different forces acted between the boats: in the first case, there was an exchange of liquid (I suggest not to take into account the bottle, since most of us are interested in its contents), and in the second - a solid body (ice cream). Now imagine that in Cambridge that day there was a summer heat rare for northern places, and the ice cream melted in flight. That is, some increase in temperature is enough to understand that, in fact, the interaction does not depend on whether the liquid or solid body acts as its carrier. The only reason we thought there were different forces acting between the boats was because the ice cream carrier was different in appearance, due to the temperature being too low to melt it. Raise the temperature - and the forces of interaction will appear visually united.

The forces acting in the Universe also fuse together at high energies (temperatures) of interaction, after which it is impossible to distinguish them. First unite(this is how it is usually called) weak nuclear and electromagnetic interactions. As a result, we get the so-called electroweak interaction observed even in the laboratory at the energies developed by modern accelerators elementary particles. In the early Universe, the energies were so high that in the first 10–10 seconds after big bang there was no line between weak nuclear and electromagnetic forces. Only after the average temperature of the Universe dropped to 10 14 K did all four force interactions observed today separate and take on a modern form. While the temperature was above this mark, only three fundamental forces acted: strong, combined electroweak and gravitational interactions.

The unification of the electroweak and strong nuclear interactions occurs at temperatures of the order of 10 27 K. Under laboratory conditions, such energies are currently unattainable. The most powerful accelerator currently under construction on the border of France and Switzerland, the Large Hadron Collider (Large Hadron Collider) will be able to accelerate particles to energies that are only 0.000000001% of what is needed to combine the electroweak and strong nuclear interactions. So, probably, we will have to wait a long time for experimental confirmation of this association. There are no such energies in the modern Universe, however, in the first 10–35 from its existence, the temperature of the Universe was above 10 27 K, and only two forces acted in the Universe - electrostrong and gravitational interaction. Theories describing these processes are called "Great Unification Theories" (GUTs). It is not possible to directly test the TVO, but they also give certain predictions about processes occurring at lower energies. To date, all TVO predictions for relatively low temperatures and energies are confirmed experimentally.

So, the Standard Model, in a generalized form, is a theory of the structure of the Universe, in which matter consists of quarks and leptons, and strong, electromagnetic and weak interactions between them are described by grand unification theories. Such a model is obviously not complete because it does not include gravity. Presumably, a more complete theory will eventually be developed ( cm. Universal Theories), and today the Standard Model is the best of what we have.

"Elements"

Regulations

The standard model consists of the following provisions:

• All matter consists of 24 fundamental quantum fields of spin ½, the quanta of which are fundamental particles - fermions, which can be combined into three generations of fermions: 6 leptons (electron, muon, tau lepton, electron neutrino, muon neutrino and tau neutrino), 6 quarks (u, d, s, c, b, t) and 12 corresponding antiparticles.
• Quarks participate in strong, weak, and electromagnetic interactions; charged leptons (electron, muon, tau-lepton) - in weak and electromagnetic; neutrinos - only in weak interactions.
• All three types of interactions arise as a consequence of the postulate that our world is symmetrical with respect to three types of gauge transformations. The particles-carriers of interactions are bosons:

• Unlike the electromagnetic and strong interactions, the weak interaction can mix fermions from different generations, which leads to the instability of all particles, except for the lightest ones, and to such effects as CP violation and neutrino oscillations.
• The external parameters of the standard model are:
  • the masses of leptons (3 parameters, neutrinos are assumed to be massless) and quarks (6 parameters), interpreted as interaction constants of their fields with the field of the Higgs boson,
  • parameters of the CKM quark mixing matrix - three mixing angles and one complex phase that breaks the CP symmetry - constants of interaction of quarks with an electroweak field,
  • two parameters of the Higgs field, which are uniquely related to its vacuum expectation value and the mass of the Higgs boson,
  • three interaction constants associated with the gauge groups U(1), SU(2), and SU(3), respectively, and characterizing the relative intensities of the electromagnetic, weak, and strong interactions.

Due to the discovery of neutrino oscillations, the standard model needs an extension that introduces an additional 3 neutrino masses and at least 4 parameters of the PMNS neutrino mixing matrix similar to the CKM quark mixing matrix, and possibly 2 more mixing parameters if neutrinos are Majorana particles. Also, the vacuum angle of quantum chromodynamics is sometimes included among the parameters of the standard model. It is noteworthy that a mathematical model with a set of 20-odd numbers is able to describe the results of millions of experiments carried out to date in physics.

Beyond the Standard Model

see also

Notes

Literature

• Emelyanov V. M. The standard model and its extensions. - M .: Fizmatlit, 2007. - 584 p. - (Fundamental and applied physics). - ISBN 978-5-922108-30-0

Links

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See what the "Standard Model" is in other dictionaries:

STANDARD MODEL, a model of ELEMENTARY PARTICLES and their interactions, which is the most Full description physical phenomena related to electricity. Particles are divided into HADRONS (turning into QUARKS under the influence of NUCLEAR FORCES), ... ... Scientific and technical encyclopedic dictionary

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THE STANDARD CONCEPT OF SCIENCE is a form of logical and methodological analysis of natural science theories, developed under the significant influence of the neopositivist philosophy of science. Within the framework of the standard concept of science, the properties of a theory (interpreted as ... ... Philosophical Encyclopedia

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Books

• Particle Physics - 2013. Quantum electrodynamics and the Standard Model, O. M. Boyarkin, G. G. Boyarkina. In the second volume of a two-volume book containing a modern course in elementary particle physics, quantum electrodynamics is considered as the first example of the theory of real interactions. ...

Today, the Standard Model is one of the most important theoretical constructions in elementary particle physics, describing the electromagnetic, weak and strong interaction of all elementary particles. The main provisions and components of this theory are described by the physicist, corresponding member of the Russian Academy of Sciences Mikhail Danilov

1

Now, on the basis of experimental data, a very perfect theory has been created that describes almost all the phenomena that we observe. This theory is modestly called the "Standard Model of Elementary Particles". It has three generations of fermions: quarks, leptons. It is, so to speak, a building material. Everything that we see around us is built from the first generation. It includes u- and d-quarks, an electron and an electron neutrino. Protons and neutrons are made up of three quarks: uud and udd, respectively. But there are two more generations of quarks and leptons, which to some extent repeat the first, but are heavier and eventually decay into particles of the first generation. All particles have antiparticles that have opposite charges.

2

The standard model includes three interactions. Electromagnetic interaction keeps electrons inside an atom and atoms inside molecules. The carrier of electromagnetic interaction is a photon. Strong interaction keeps protons and neutrons inside the atomic nucleus, and quarks inside protons, neutrons and other hadrons (this is how L.B. Okun proposed to call the particles participating in the strong interaction). Quarks and hadrons built from them, as well as carriers of the interaction itself - gluons (from the English glue - glue) take part in the strong interaction. Hadrons are either made up of three quarks, like the proton and neutron, or made up of a quark and an antiquark, like, say, a π+ meson, made up of u- and anti-d-quarks. The weak force leads to rare decays, such as the decay of a neutron into a proton, an electron, and an electron antineutrino. The carriers of the weak interaction are W- and Z-bosons. Both quarks and leptons take part in the weak interaction, but it is very small at our energies. This, however, is simply explained by the large masses of the W and Z bosons, which are two orders of magnitude heavier than protons. At energies greater than the mass of the W- and Z-bosons, the strengths of the electromagnetic and weak interactions become comparable, and they combine into a single electroweak interaction. It is assumed that at much b O higher energies and the strong interaction will unite with the rest. In addition to the electroweak and strong interactions, there is also the gravitational interaction, which is not included in the Standard Model.

W, Z-bosons

g - gluons

H0 is the Higgs boson.

3

The Standard Model can only be formulated for massless fundamental particles, i.e. quarks, leptons, W and Z bosons. In order for them to acquire mass, the Higgs field, named after one of the scientists who proposed this mechanism, is usually introduced. In this case, there must be another fundamental particle in the Standard Model - the Higgs boson. The search for this last brick in the slender building of the Standard Model is being actively conducted at the largest collider in the world - the Large Hadron Collider (LHC). Already received indications of the existence of the Higgs boson with a mass of about 133 proton masses. However, the statistical reliability of these indications is still insufficient. It is expected that by the end of 2012 the situation will clear up.

4

The Standard Model perfectly describes almost all experiments in elementary particle physics, although the search for phenomena that go beyond the SM is persistently pursued. The latest hint at physics beyond the SM was the discovery in 2011 in the LHCb experiment at the LHC of an unexpectedly large difference in the properties of the so-called charmed mesons and their antiparticles. However, apparently, even such a large difference can be explained in terms of the SM. On the other hand, in 2011 another confirmation of the SM was obtained, which had been sought for several decades, predicting the existence of exotic hadrons. Physicists from the Institute of Theoretical and Experimental Physics (Moscow) and the Institute nuclear physics(Novosibirsk) in the framework of the international BELLE experiment discovered hadrons consisting of two quarks and two antiquarks. Most likely, these are meson molecules predicted by the ITEP theorists M. B. Voloshin and L. B. Okun.

5

Despite all the successes of the Standard Model, it has many shortcomings. The number of free parameters of the theory exceeds 20, and it is completely unclear where their hierarchy comes from. Why is the mass of the t quark 100,000 times the mass of the u quark? Why is the coupling constant of t- and d-quarks, measured for the first time in the international ARGUS experiment with the active participation of ITEP physicists, 40 times less than the coupling constant of c- and d-quarks? SM does not answer these questions. Finally, why do we need 3 generations of quarks and leptons? Japanese theorists M. Kobayashi and T. Maskawa in 1973 showed that the existence of 3 generations of quarks makes it possible to explain the difference in the properties of matter and antimatter. The hypothesis of M. Kobayashi and T. Maskawa was confirmed in the BELLE and BaBar experiments with the active participation of physicists from the INP and ITEP. In 2008, M. Kobayashi and T. Maskawa were awarded the Nobel Prize for their theory

6

There are more fundamental problems with the Standard Model. We already know that the SM is not complete. It is known from astrophysical studies that there is matter that is not in the SM. This is the so-called dark matter. It is about 5 times more than the ordinary matter of which we are composed. Perhaps the main drawback of the Standard Model is its lack of internal self-consistency. For example, the natural mass of the Higgs boson, which arises in the SM due to the exchange of virtual particles, is many orders of magnitude greater than the mass needed to explain the observed phenomena. One solution, the most popular at the moment, is the supersymmetry hypothesis - the assumption that there is a symmetry between fermions and bosons. This idea was first expressed in 1971 by Yu. A. Gol'fand and EP Likhtman at the Lebedev Physical Institute, and now it enjoys tremendous popularity.

7

The existence of supersymmetric particles not only makes it possible to stabilize the behavior of the SM, but also provides a very natural candidate for the role of dark matter - the lightest supersymmetric particle. Although there are currently no reliable experimental evidence this theory, it is so beautiful and so elegant in solving the problems of the Standard Model that so many people believe in it. The LHC is actively searching for supersymmetric particles and other alternatives to the SM. For example, they are looking for additional dimensions of space. If they exist, then many problems can be solved. Perhaps gravity becomes strong at relatively large distances, which would also be a big surprise. There are other, alternative Higgs models, mechanisms for the emergence of mass in fundamental particles. The search for effects outside the Standard Model is very active, but so far without success. Much should become clear in the coming years.

“We wonder why a group of talented and dedicated people would dedicate their lives to chasing objects so tiny that they can't even be seen? In fact, in the classes of particle physicists, human curiosity and a desire to find out how the world in which we live works is manifested. ” Sean Carroll

If you are still afraid of the phrase quantum mechanics and still do not know what the standard model is - welcome to cat. In my publication, I will try to explain the basics of the quantum world, as well as elementary particle physics, as simply and clearly as possible. We will try to figure out what are the main differences between fermions and bosons, why quarks have such strange names, and finally, why everyone was so eager to find the Higgs Boson.

What are we made of?

Well, we will begin our journey into the microcosm with a simple question: what do the objects around us consist of? Our world, like a house, consists of many small bricks, which, when combined in a special way, create something new, not only in appearance, but also in terms of its properties. In fact, if you look closely at them, you will find that there are not so many different types of blocks, it’s just that each time they are connected to each other in different ways, forming new forms and phenomena. Each block is an indivisible elementary particle, which will be discussed in my story.

For example, let's take some substance, let it be the second element periodic system Mendeleev, inert gas, helium. Like other substances in the universe, helium is made up of molecules, which in turn are formed by bonds between atoms. But in this case, for us, helium is a little bit special because it's just one atom.

What is an atom made of?

The helium atom, in turn, consists of two neutrons and two protons, which make up atomic nucleus around which two electrons revolve. The most interesting thing is that the only absolutely indivisible here is electron.

An interesting moment of the quantum world

How less the mass of an elementary particle, the more she takes up space. It is for this reason that electrons, which are 2000 times lighter than a proton, take up much more space than the nucleus of an atom.

Neutrons and protons belong to the group of so-called hadrons(particles subject to strong interaction), and to be even more precise, baryons.

Hadrons can be divided into groups

• Baryons, which are made up of three quarks
• Mesons, which consist of a pair: particle-antiparticle

The neutron, as its name implies, is neutrally charged, and can be divided into two down quarks and one up quark. The proton, a positively charged particle, is divided into one down quark and two up quarks.

Yes, yes, I'm not kidding, they are really called upper and lower. It would seem that if we discovered the top and bottom quarks, and even the electron, we would be able to describe the entire Universe with their help. But this statement would be very far from the truth.

The main problem is that the particles must somehow interact with each other. If the world consisted only of this trinity (neutron, proton and electron), then the particles would simply fly through the vast expanses of space and would never gather into larger formations, like hadrons.

Fermions and Bosons

Quite a long time ago, scientists invented a convenient and concise form of representation of elementary particles, called the standard model. It turns out that all elementary particles are divided into fermions, of which all matter is composed, and bosons, which carry various kinds of interactions between fermions.

The difference between these groups is very clear. The fact is that according to the laws of the quantum world, fermions need some space to survive, while their counterparts, bosons, can easily live right on top of each other in trillions.

Fermions

A group of fermions, as already mentioned, creates visible matter around us. Whatever we see, wherever, is created by fermions. Fermions are divided into quarks, which interact strongly with each other and are trapped inside more complex particles like hadrons, and leptons, which freely exist in space independently of their counterparts.

Quarks are divided into two groups.

• Top type. Up quarks, with a charge of +23, include: up, charm and true quarks
• Lower type. Down-type quarks, with a charge of -13, include: down, strange and charm quarks

True and lovely are the largest quarks, while up and down are the smallest. Why quarks were given such unusual names, and more correctly, "flavors", is still a subject of controversy for scientists.

Leptons are also divided into two groups.

• The first group, with a charge of "-1", includes: an electron, a muon (heavier particle) and a tau particle (the most massive)
• The second group, with a neutral charge, contains: electron neutrino, muon neutrino and tau neutrino

Neutrino is a small particle of matter, which is almost impossible to detect. Its charge is always 0.

The question arises whether physicists will find several more generations of particles that will be even more massive than the previous ones. It is difficult to answer it, but theorists believe that the generations of leptons and quarks are limited to three.

Don't find any similarities? Both quarks and leptons are divided into two groups, which differ from each other in charge per unit? But more on that later...

Bosons

Without them, fermions would fly around the universe in a continuous stream. But exchanging bosons, fermions tell each other some kind of interaction. The bosons themselves do not interact with each other.

The interaction transmitted by bosons is:

• electromagnetic, particles - photons. These massless particles transmit light.
• strong nuclear, particles are gluons. With their help, quarks from the nucleus of an atom do not decay into separate particles.
• Weak nuclear, particles - W and Z bosons. With their help, fermions are transferred by mass, energy, and can turn into each other.
• gravitational , particles - gravitons. An extremely weak force on the scale of the microcosm. Becomes visible only on supermassive bodies.

A reservation about gravitational interaction.
The existence of gravitons has not yet been experimentally confirmed. They exist only in the form of a theoretical version. In the standard model, in most cases, they are not considered.

That's it, the standard model is assembled.

Trouble has just begun

Despite the very beautiful representation of the particles in the diagram, two questions remain. Where do particles get their mass and what is Higgs boson, which stands out from the rest of the bosons.

In order to understand the idea of ​​using the Higgs boson, we need to turn to quantum field theory. talking plain language, it can be argued that the whole world, the whole Universe, does not consist of the smallest particles, but of many different fields: gluon, quark, electronic, electromagnetic, etc. In all these fields, slight fluctuations constantly occur. But we perceive the strongest of them as elementary particles. Yes, and this thesis is highly controversial. From the point of view of corpuscular-wave dualism, the same object of the microcosm in different situations behaves like a wave, sometimes like an elementary particle, it depends only on how it is more convenient for a physicist observing the process to model the situation.

Higgs field

It turns out that there is a so-called Higgs field, the average of which does not want to go to zero. As a result, this field tries to take some constant non-zero value throughout the Universe. The field makes up the ubiquitous and constant background, as a result of which the Higgs Boson appears as a result of strong fluctuations.
And it is thanks to the Higgs field that particles are endowed with mass.
The mass of an elementary particle depends on how strongly it interacts with the Higgs field constantly flying inside it.
And it is because of the Higgs boson, and more specifically because of its field, that the standard model has so many similar groups of particles. The Higgs field forced the creation of many additional particles, such as neutrinos.

Results

What I have been told is the most superficial understanding of the nature of the Standard Model and why we need the Higgs Boson. Some scientists still hope deep down that a particle found in 2012 that looks like the Higgs boson at the LHC was just a statistical error. After all, the Higgs field breaks many of the beautiful symmetries of nature, making the calculations of physicists more confusing.
Some even believe that the standard model is living its life. last years because of its imperfection. But this has not been experimentally proven, and the standard model of elementary particles remains a valid example of the genius of human thought.

standard model- This modern theory structures and interactions of elementary particles, repeatedly verified experimentally. This theory is based on a very small number of postulates and allows you to theoretically predict the properties of thousands of different processes in the world of elementary particles. In the vast majority of cases, these predictions are confirmed by experiment, sometimes with exceptionally high accuracy, and those rare cases when the predictions of the Standard Model disagree with experience become the subject of heated debate.

The Standard Model is the boundary that separates the reliably known from the hypothetical in the world of elementary particles. Despite its impressive success in describing experiments, the Standard Model cannot be considered the ultimate theory of elementary particles. Physicists are sure that it must be part of some deeper theory of the structure of the microworld. What kind of theory this is is not yet known for certain. Theorists have developed big number candidates for such a theory, but only an experiment should show which of them corresponds to the real situation that has developed in our Universe. That is why physicists are persistently looking for any deviations from the Standard Model, any particles, forces or effects that are not predicted by the Standard Model. Scientists collectively call all these phenomena "New physics"; exactly search for New Physics and is the main task of the Large Hadron Collider.

Main Components of the Standard Model

The working tool of the Standard Model is quantum field theory - a theory that replaces quantum mechanics at speeds close to the speed of light. The key objects in it are not particles, as in classical mechanics, and not "particle-waves", as in quantum mechanics, but quantum fields: electronic, muon, electromagnetic, quark, etc. - one for each variety of "entities of the microworld".

Both vacuum, and what we perceive as separate particles, and more complex formations that cannot be reduced to separate particles - all this is described as different states of fields. When physicists use the word "particle", they actually mean these states of the fields, and not individual point objects.

The standard model includes the following main ingredients:

• A set of fundamental "bricks" of matter - six kinds of leptons and six kinds of quarks. All of these particles are spin 1/2 fermions and very naturally organize themselves into three generations. Numerous hadrons - compound particles involved in the strong interaction - are composed of quarks in various combinations.
• Three types of forces acting between fundamental fermions - electromagnetic, weak and strong. Weak and electromagnetic interactions are two sides of the same electroweak interaction. The strong force stands apart, and it is this force that binds quarks into hadrons.
• All these forces are described on the basis of gauge principle- they are not introduced into the theory “forcibly”, but seem to arise by themselves as a result of the requirement that the theory be symmetrical with respect to certain transformations. Separate types of symmetry give rise to strong and electroweak interactions.
• Despite the fact that there is an electroweak symmetry in the theory itself, in our world it is spontaneously violated. Spontaneous breaking of electroweak symmetry- a necessary element of the theory, and in the framework of the Standard Model, the violation occurs due to the Higgs mechanism.
• Numerical values ​​for about two dozen constants: these are the masses of fundamental fermions, the numerical values ​​of the coupling constants of interactions that characterize their strength, and some other quantities. All of them are extracted once and for all from comparison with experience and are no longer adjusted in further calculations.

In addition, the Standard Model is a renormalizable theory, that is, all these elements are introduced into it in such a self-consistent way that, in principle, allows calculations to be carried out with the required degree of accuracy. However, often calculations with the desired degree of accuracy turn out to be unbearably complex, but this is not a problem of the theory itself, but rather of our computational abilities.

What the Standard Model Can and Cannot Do

The Standard Model is, in many ways, a descriptive theory. It does not give answers to many questions that begin with “why”: why are there so many particles and exactly these? where did these interactions come from and exactly with such properties? Why did nature need to create three generations of fermions? Why are the numerical values ​​of the parameters exactly the same? In addition, the Standard Model is unable to describe some of the phenomena observed in nature. In particular, it has no place for neutrino masses and dark matter particles. The Standard Model does not take into account gravity, and it is not known what happens to this theory on the Planck scale of energies, when gravity becomes extremely important.

If, however, the Standard Model is used for its intended purpose, to predict the results of collisions of elementary particles, then it allows, depending on the specific process, to perform calculations with varying degrees of accuracy.

• For electromagnetic phenomena (electron scattering, energy levels) the accuracy can reach parts per million or even better. The record here is anomalous magnetic moment electron, which is calculated with an accuracy better than one billionth.
• Many high-energy processes that proceed due to electroweak interactions are calculated with an accuracy better than a percent.
• Worst of all is the strong interaction at not too high energies. The accuracy of calculating such processes varies greatly: in some cases it can reach percent, in other cases, different theoretical approaches can give answers that differ by several times.

It is worth emphasizing that the fact that some processes are difficult to calculate with the required accuracy does not mean that the “theory is bad”. It's just that it's very complicated, and the current mathematical techniques are not yet enough to trace all its consequences. In particular, one of the famous mathematical Millennium Problems concerns the problem of confinement in quantum theory with non-Abelian gauge interaction.

Additional literature:

• Basic information about the Higgs mechanism can be found in the book by L. B. Okun "Physics of elementary particles" (at the level of words and pictures) and "Leptons and quarks" (at a serious but accessible level).