What a stupid name for the most accurate scientific theory of all known to mankind. More than a quarter of the Nobel Prizes in physics in the last century have been awarded to works that are either directly or indirectly related to the Standard Model. Her name, of course, is such that for a couple of hundred rubles you can buy an improvement. Any theoretical physicist would prefer "an amazing theory of almost everything", which, in fact, it is.
Many remember the excitement among scientists and in the media caused by the discovery of the Higgs boson in 2012. But his discovery didn't come as a surprise or out of nowhere - it marked the fiftieth anniversary of the Standard Model's string of victories. It includes every fundamental force except gravity. Any attempt to disprove it and demonstrate in the laboratory that it needs to be completely reworked - and there have been many - has failed.
In short, the Standard Model answers this question: what is everything made of, and how does everything hold together?
The smallest building blocks
Physicists love simple things. They want to break everything down to its very essence, to find the most basic building blocks. Do it with hundreds chemical elements not so easy. Our ancestors believed that everything consists of five elements - earth, water, fire, air and ether. Five is much easier than one hundred and eighteen. And also wrong. You certainly know that the world around us is made up of molecules, and molecules are made up of atoms. The chemist Dmitri Mendeleev figured this out in the 1860s and presented atoms in the table of elements that is taught in schools today. But there are 118 of these chemical elements. Antimony, arsenic, aluminum, selenium ... and 114 more.
In 1932, scientists knew that all these atoms are made up of just three particles - neutrons, protons and electrons. Neutrons and protons are closely related to each other in the nucleus. Electrons, thousands of times lighter than them, circle the nucleus at a speed close to the speed of light. The physicists Planck, Bohr, Schrödinger, Heisenberg and others presented new science- quantum mechanics - to explain this movement.
It would be great to stop there. There are only three particles. It's even easier than five. But how do they stick together? Negatively charged electrons and positively charged protons are held together by the forces of electromagnetism. But the protons clump together in the nucleus and their positive charges should push them away. Even neutral neutrons will not help.
What binds these protons and neutrons together? "Divine Intervention"? But even a divine being would have trouble keeping track of each of the 1080 protons and neutrons in the universe, holding them by willpower.
Expanding the Particle Zoo
Meanwhile, nature desperately refuses to keep only three particles in its zoo. Even four, because we need to take into account the photon, the particle of light described by Einstein. Four became five when Anderson measured the positively charged electrons - positrons - that hit the Earth from outer space. Five became six when the pion holding the nucleus as a whole was discovered and predicted by Yukawa.
Then came the muon - 200 times heavier than the electron, but otherwise its twin. It's already seven. Not so easy.
By the 1960s, there were hundreds of "fundamental" particles. Instead of a well-organized periodic table, there were only long lists of baryons (heavy particles like protons and neutrons), mesons (like Yukawa pions), and leptons (light particles like the electron and elusive neutrinos), without any organization or principles of design.
And in this abyss, the Standard Model was born. There was no illumination. Archimedes didn't jump out of the tub shouting "Eureka!" No, instead, in the mid-1960s, several smart people put forward important assumptions that turned this quagmire first into simple theory and then at fifty experimental verification and theoretical development.
Quarks. They got six options that we call flavors. Like flowers, but not as delicious. Instead of roses, lilies and lavender, we got up and down, strange and enchanted, lovely and true quarks. In 1964, Gell-Mann and Zweig taught us how to mix three quarks to make a baryon. A proton is two up and one down quark; neutron - two lower and one upper. Take one quark and one antiquark and you get a meson. A pion is an up or down quark associated with an up or down antiquark. All matter we deal with is made up of up and down quarks, antiquarks, and electrons.
Simplicity. Not exactly simple, though, because keeping quarks bound is not easy. They are connected together so tightly that you will never find a quark or an antiquark wandering around on its own. The theory of this connection and the particles that take part in it, namely gluons, is called quantum chromodynamics. This is an important part of the Standard Model, mathematically complex, and in some places even unsolvable for basic mathematics. Physicists do their best to make calculations, but sometimes the mathematical apparatus is not developed enough.
Another aspect of the Standard Model is the "lepton model". This is the title of a landmark 1967 paper by Steven Weinberg that combined quantum mechanics with the essential knowledge of how particles interact and organized them into a single theory. He turned on electromagnetism, connected it with " weak force”, which leads to certain radioactive decays, and explained that these are different manifestations of the same force. This model included the Higgs mechanism, which gives mass to fundamental particles.
Since then, the Standard Model has predicted outcome after outcome, including the discovery of several varieties of quarks and W and Z bosons, heavy particles that play the same role in weak interactions as the photon does in electromagnetism. The possibility that neutrinos have mass was missed in the 1960s, but confirmed by the Standard Model in the 1990s, a few decades later.
The discovery of the Higgs boson in 2012, long predicted by the Standard Model and long awaited, did not come as a surprise, however. But it was another important victory of the Standard Model over the dark forces that particle physicists regularly wait on the horizon. Physicists don't like the fact that the Standard Model doesn't fit their idea of a simple model, they're worried about its mathematical inconsistencies, and they're also looking for a way to include gravity in the equation. Obviously, this translates into different theories of physics, which may be after the Standard Model. This is how grand unification theories, supersymmetries, technocolor and string theory appeared.
Unfortunately, theories outside the Standard Model have not found successful experimental confirmations and serious gaps in the Standard Model. Fifty years later, it is the Standard Model that comes closest to being the theory of everything. An amazing theory of just about everything.
The Standard Model of elementary particles is considered the greatest achievement of physics in the second half of the 20th century. But what lies beyond it?
The Standard Model (SM) of elementary particles, based on gauge symmetry, is a magnificent creation of Murray Gell-Mann, Sheldon Glashow, Steven Weinberg, Abdus Salam and a whole galaxy of brilliant scientists. The SM perfectly describes the interactions between quarks and leptons at distances of the order of 10−17 m (1% of the proton diameter), which can be studied at modern accelerators. However, it begins to slip already at distances of 10-18 m, and even more so does not provide advancement to the coveted Planck scale of 10-35 m.
It is believed that it is there that all fundamental interactions merge in quantum unity. The SM will someday be replaced by a more complete theory, which, most likely, will also not be the last and final one. Scientists are trying to find a replacement for the Standard Model. Many believe that a new theory will be built by expanding the list of symmetries that form the foundation of the SM. One of the most promising approaches to solving this problem was laid not only out of connection with the problems of the SM, but even before its creation.
Particles obeying Fermi-Dirac statistics (fermions with half-integer spin) and Bose-Einstein (bosons with integer spin). In the energy well, all bosons can occupy the same lower energy level, forming a Bose-Einstein condensate. Fermions, on the other hand, obey the Pauli exclusion principle, and therefore two particles with the same quantum numbers (in particular, unidirectional spins) cannot occupy the same energy level.
Mixture of opposites
In the late 1960s, Yury Golfand, senior researcher at the FIAN theoretical department, suggested to his graduate student Evgeny Likhtman that he generalize the mathematical apparatus used to describe the symmetries of the four-dimensional space-time of the special theory of relativity (Minkowski space).
Lichtman found that these symmetries could be combined with the intrinsic symmetries of quantum fields with non-zero spins. In this case, families (multiplets) are formed that unite particles with the same mass, having integer and half-integer spin (in other words, bosons and fermions). This was both new and incomprehensible, since both obey different types quantum statistics. Bosons can accumulate in the same state, and fermions follow the Pauli principle, which strictly forbids even pair unions of this kind. Therefore, the emergence of bosonic-fermion multiplets looked like a mathematical exoticism that had nothing to do with real physics. This is how it was perceived in FIAN. Later, in his Memoirs, Andrei Sakharov called the unification of bosons and fermions a great idea, but at that time it did not seem interesting to him.
Beyond the standard
Where are the boundaries of the SM? “The Standard Model is consistent with almost all data obtained at high energy accelerators. - explains the leading researcher of the Institute for Nuclear Research of the Russian Academy of Sciences Sergey Troitsky. “However, the results of experiments that testify to the presence of mass in two types of neutrinos, and possibly in all three, do not quite fit into its framework. This fact means that the SM needs to be expanded, and in which one, no one really knows. Astrophysical data also point to the incompleteness of the SM. Dark matter, which accounts for more than a fifth of the mass of the universe, consists of heavy particles that do not fit into the SM. By the way, it would be more accurate to call this matter not dark, but transparent, since it not only does not emit light, but also does not absorb it. In addition, the SM does not explain the almost complete absence of antimatter in the observable universe.”
There are also aesthetic objections. As Sergei Troitsky notes, the SM is very ugly. It contains 19 numerical parameters that are determined by experiment and, from the point of view of common sense, take on very exotic values. For example, the vacuum mean of the Higgs field, which is responsible for the masses of elementary particles, is 240 GeV. It is not clear why this parameter is 1017 times less than the parameter that determines the gravitational interaction. I would like to have a more complete theory, which will make it possible to determine this relationship from some general principles.
Nor does the SM explain the huge difference between the masses of the lightest quarks, which make up protons and neutrons, and the mass of the top quark, which exceeds 170 GeV (in all other respects, it is no different from the u-quark, which is almost 10,000 times lighter). Where seemingly identical particles with such different masses come from is still unclear.
Lichtman defended his dissertation in 1971, and then went to VINITI and almost abandoned theoretical physics. Golfand was fired from FIAN due to redundancy, and for a long time he could not find a job. However, employees of the Ukrainian Institute of Physics and Technology, Dmitry Volkov and Vladimir Akulov, also discovered the symmetry between bosons and fermions, and even used it to describe neutrinos. True, neither Muscovites nor Kharkovites gained any laurels at that time. Only in 1989 did Golfand and Likhtman receive the I.E. Tamm. In 2009 Volodymyr Akulov (now teaching physics at the Technical College of the City University of New York) and Dmitry Volkov (posthumously) were awarded the National Prize of Ukraine for scientific research.
The elementary particles of the Standard Model are divided into bosons and fermions according to the type of statistics. Composite particles - hadrons - can obey either Bose-Einstein statistics (such include mesons - kaons, pions), or Fermi-Dirac statistics (baryons - protons, neutrons).
The birth of supersymmetry
In the West, mixtures of bosonic and fermionic states first appeared in a nascent theory that represented elementary particles not as point objects, but as vibrations of one-dimensional quantum strings.
In 1971, a model was constructed in which each bosonic-type vibration was combined with its paired fermion vibration. True, this model worked not in the four-dimensional space of Minkowski, but in the two-dimensional space-time of string theories. However, already in 1973, the Austrian Julius Wess and the Italian Bruno Zumino reported to CERN (and published an article a year later) on a four-dimensional supersymmetric model with one boson and one fermion. She did not claim to describe elementary particles, but demonstrated the possibilities of supersymmetry in a clear and extremely physical example. Soon these same scientists proved that the symmetry they discovered was an extended version of the symmetry of Golfand and Lichtman. So it turned out that within three years, supersymmetry in the Minkowski space was independently discovered by three pairs of physicists.
The results of Wess and Zumino prompted the development of theories with boson-fermion mixtures. Because these theories relate gauge symmetries to space-time symmetries, they were called supergauge and then supersymmetric. They predict the existence of many particles, none of which have yet been discovered. So the supersymmetry of the real world is still hypothetical. But even if it exists, it cannot be strict, otherwise the electrons would have charged bosonic cousins with exactly the same mass, which could be easily detected. It remains to be assumed that the supersymmetric partners of known particles are extremely massive, and this is possible only if supersymmetry is broken.
The supersymmetric ideology came into force in the mid-1970s, when the Standard Model already existed. Naturally, physicists began to build its supersymmetric extensions, in other words, to introduce symmetries between bosons and fermions into it. The first realistic version of the Supersymmetric Standard Model, called the Minimal Supersymmetric Standard Model (MSSM), was proposed by Howard Georgi and Savas Dimopoulos in 1981. In fact, this is the same Standard Model with all its symmetries, but each particle has a partner added, whose spin differs from its spin by ½, a boson to a fermion and a fermion to a boson.
Therefore, all SM interactions remain in place, but are enriched by the interactions of new particles with old ones and with each other. More complex supersymmetric versions of the SM also arose later. All of them compare the already known particles with the same partners, but they explain the violations of supersymmetry in different ways.
Particles and superparticles
The names of fermion superpartners are constructed using the prefix "s" - electron, smuon, squark. The superpartners of bosons acquire the ending "ino": photon - photino, gluon - gluino, Z-boson - zino, W-boson - wine, Higgs boson - higgsino.
The spin of the superpartner of any particle (with the exception of the Higgs boson) is always ½ less than its own spin. Consequently, the partners of an electron, quarks, and other fermions (as well as, of course, their antiparticles) have zero spin, while the partners of a photon and vector bosons with unit spin have half. This is due to the fact that the number of states of a particle is greater, the greater its spin. Therefore, replacing subtraction by addition would lead to the appearance of redundant superpartners.
On the left is the Standard Model (SM) of elementary particles: fermions (quarks, leptons) and bosons (interaction carriers). On the right are their superpartners in the Minimal Supersymmetric Standard Model, MSSM: bosons (squarks, sleepons) and fermions (superpartners of force carriers). The five Higgs bosons (marked with a single blue symbol in the diagram) also have their superpartners, the Higgsino quintuple.
Let's take an electron as an example. It can be in two states - in one, its spin is directed parallel to the momentum, in the other, it is antiparallel. From the SM point of view, these are different particles, since they do not quite equally participate in weak interactions. A particle with a unit spin and a non-zero mass can exist in three different states (as physicists say, it has three degrees of freedom) and therefore is not suitable for partners with an electron. The only way out is to assign one spin-zero superpartner to each of the states of the electron and consider these electrons to be different particles.
Superpartners of bosons in the Standard Model are somewhat trickier. Since the mass of a photon is equal to zero, even with a unit spin it has not three, but two degrees of freedom. Therefore, photino, a half-spin superpartner, which, like an electron, has two degrees of freedom, can be easily assigned to it. Gluinos appear according to the same scheme. With Higgs, the situation is more complicated. The MSSM has two doublets of Higgs bosons, which correspond to four superpartners - two neutral and two oppositely charged Higgsinos. Neutrals mix in various ways with photino and zino and form a four of physically observable particles with the common name neutralino. Similar mixtures with the name chargino, which is strange for the Russian ear (in English - chargino), form superpartners of positive and negative W-bosons and pairs of charged Higgs.
The situation with neutrino superpartners also has its own specifics. If this particle had no mass, its spin would always be in the opposite direction of momentum. Therefore, a massless neutrino would have a single scalar partner. However, real neutrinos are still not massless. It is possible that there are also neutrinos with parallel momenta and spins, but they are very heavy and have not yet been discovered. If this is true, then each type of neutrino has its own superpartner.
According to University of Michigan physics professor Gordon Kane, the most universal mechanism for breaking supersymmetry has to do with gravity.
However, the magnitude of its contribution to the masses of superparticles has not yet been clarified, and the estimates of theorists are contradictory. In addition, he is hardly the only one. Thus, the Next-to-Minimal Supersymmetric Standard Model, NMSSM, introduces two more Higgs bosons that contribute to the mass of superparticles (and also increases the number of neutralinos from four to five). Such a situation, notes Kane, dramatically multiplies the number of parameters incorporated in supersymmetric theories.
Even a minimal extension of the Standard Model requires about a hundred additional parameters. This should not be surprising since all these theories introduce many new particles. As more complete and consistent models emerge, the number of parameters should decrease. As soon as the detectors of the Large Hadron Collider capture superparticles, new models will not keep you waiting.
Particle Hierarchy
Supersymmetric theories make it possible to eliminate a number of weaknesses in the Standard Model. Professor Kane brings to the fore the riddle of the Higgs boson, which is called the hierarchy problem..
This particle acquires mass in the course of interaction with leptons and quarks (just as they themselves acquire mass when interacting with the Higgs field). In the SM, the contributions from these particles are represented by divergent series with infinite sums. True, the contributions of bosons and fermions have different signs and in principle can almost completely cancel each other out. However, such an extinction should be almost ideal, since the Higgs mass is now known to be only 125 GeV. It's not impossible, but highly unlikely.
For supersymmetric theories, there is nothing to worry about. With exact supersymmetry, the contributions of ordinary particles and their superpartners must completely compensate each other. Since supersymmetry is broken, the compensation turns out to be incomplete, and the Higgs boson acquires a finite and, most importantly, calculable mass. If the masses of the superpartners are not too large, it should be measured in the range of one to two hundred GeV, which is true. As Kane emphasizes, physicists began to take supersymmetry seriously when it was shown to solve the hierarchy problem.
The possibilities of supersymmetry do not end there. It follows from the SM that in the region of very high energies, the strong, weak, and electromagnetic interactions, although they have approximately the same strength, never combine. And in supersymmetric models at energies of the order of 1016 GeV, such a union takes place, and it looks much more natural. These models also offer a solution to the problem of dark matter. Superparticles during decays give rise to both superparticles and ordinary particles - of course, of a smaller mass. However, supersymmetry, in contrast to the SM, allows for the rapid decay of the proton, which, fortunately for us, does not actually occur.
Proton, and with it the whole the world can be salvaged by assuming that processes involving superparticles conserve the R-parity quantum number, which is equal to one for ordinary particles and minus one for superpartners. In such a case, the lightest superparticle must be completely stable (and electrically neutral). By definition, it cannot decay into superparticles, and the conservation of R-parity forbids it from decaying into particles. Dark matter can consist precisely of such particles that emerged immediately after the Big Bang and avoided mutual annihilation.
Waiting for experiments
“Shortly before the discovery of the Higgs boson, based on M-theory (the most advanced version of string theory), its mass was predicted with an error of only two percent! Professor Kane says. — We also calculated the masses of electrons, smuons and squarks, which turned out to be too large for modern accelerators — on the order of several tens of TeV. The superpartners of the photon, gluon, and other gauge bosons are much lighter, and therefore have a chance of being detected at the LHC.”
Of course, the correctness of these calculations is not guaranteed by anything: M-theory is a delicate matter. And yet, is it possible to detect traces of superparticles on accelerators? “Massive superparticles should decay immediately after birth. These decays occur against the background of the decays of ordinary particles, and it is very difficult to single them out unambiguously,” explains Dmitry Kazakov, Chief Researcher of the Laboratory of Theoretical Physics at JINR in Dubna. “It would be ideal if superparticles manifest themselves in a unique way that cannot be confused with anything else, but the theory does not predict this.
One has to analyze many different processes and look among them for those that are not fully explained by the Standard Model. These searches have so far been unsuccessful, but we already have limits on the masses of superpartners. Those of them that participate in strong interactions should pull at least 1 TeV, while the masses of other superparticles can vary between tens and hundreds of GeV.
In November 2012, at a symposium in Kyoto, the results of experiments at the LHC were reported, during which for the first time it was possible to reliably register a very rare decay of the Bs meson into a muon and an antimuon. Its probability is approximately three billionths, which is in good agreement with the predictions of the SM. Since the expected probability of this decay, calculated from the MSSM, may be several times greater, some have decided that supersymmetry is over.
However, this probability depends on several unknown parameters, which can make both a large and a small contribution to the final result, there is still a lot of uncertainty here. Therefore, nothing terrible happened, and rumors about the death of MSSM are greatly exaggerated. But that doesn't mean she's invincible. The LHC is not yet operating at full capacity, it will reach it only in two years, when the proton energy will be brought up to 14 TeV. And if then there are no manifestations of superparticles, then the MSSM will most likely die a natural death and the time will come for new supersymmetric models.
Grassmann numbers and supergravity
Even before the creation of MSSM, supersymmetry was combined with gravity. Repeated application of transformations connecting bosons and fermions moves the particle in space-time. This makes it possible to link supersymmetries and deformations of the space-time metric, which, according to the general theory of relativity, is the cause of gravity. When physicists realized this, they began to build supersymmetric generalizations of general relativity, which are called supergravity. This area of theoretical physics is actively developing now.
At the same time, it became clear that supersymmetric theories needed exotic numbers, invented in the 19th century by the German mathematician Hermann Günter Grassmann. They can be added and subtracted as usual, but the product of such numbers changes sign when the factors are rearranged (therefore, the square and, in general, any integer power of the Grassmann number is equal to zero). Naturally, functions of such numbers cannot be differentiated and integrated according to the standard rules mathematical analysis, completely different methods are needed. And, fortunately for supersymmetric theories, they have already been found. They were invented in the 1960s by the outstanding Soviet mathematician from Moscow State University Felix Berezin, who created a new direction - supermathematics.
However, there is another strategy that is not related to the LHC. While the LEP electron-positron collider was operating at CERN, they were looking for the lightest of charged superparticles, whose decays should give rise to the lightest superpartners. These precursor particles are easier to detect because they are charged and the lightest superpartner is neutral. Experiments at LEP have shown that the mass of such particles does not exceed 104 GeV. This is not much, but they are difficult to detect at the LHC due to the high background. Therefore, there is now a movement to build a super-powerful electron-positron collider for their search. But this is a very expensive car, and it certainly won't be built anytime soon."
Closings and openings
However, according to Mikhail Shifman, professor of theoretical physics at the University of Minnesota, the measured mass of the Higgs boson is too large for MSSM, and this model is most likely already closed:
“True, they are trying to save her with the help of various superstructures, but they are so inelegant that they have little chance of success. It is possible that other extensions will work, but when and how is still unknown. But this question goes beyond pure science. The current funding for high energy physics rests on the hope of discovering something really new at the LHC. If this does not happen, funding will be cut, and there will not be enough money to build new generation accelerators, without which this science will not be able to really develop.” So, supersymmetric theories still show promise, but they can't wait for the verdict of the experimenters.
What is the structure of the Standard Model? What are the properties of particles in the Standard Model? Is the existence of the fourth generation of elementary particles possible? Doctor of Physical and Mathematical Sciences Dmitry Kazakov answers these and other questions.
The last third of the 20th century was marked by the fact that it was created, experimentally confirmed, accepted and crowned Nobel Prize Standard model of fundamental interactions. What it is?
First of all, it is a model that describes the fundamental particles of matter and all their interactions. This model is a model quantum theory fields and is formulated as Lagrangian quantum field theory. This is a theory that is described as the quantum mechanics of fields, the quanta of which are elementary particles, and includes all the fundamental particles of matter. There are not so many such particles - these are six quarks and six leptons. They are involved in three types: strong, weak and electromagnetic. In this case, we ignore the gravitational interaction due to its smallness, and it is not included in the Standard Model. So, three types of interactions and six types of particles.
The Standard Model has a structure, this structure is usually associated with symmetry groups. Three types of interactions - three symmetry groups. All these groups belong to the same class - these are the so-called unitary groups. Electromagnetic interactions are described by the SU (1) symmetry group, unitary groups with one parameter, and, accordingly, one particle-carrier of electromagnetic interactions is a photon. Weak interactions have a symmetry group SU (2), there are already three parameters here, and, accordingly, there are three particles-carriers of weak interactions - these are W- and Z-bosons. Strong interactions are described by the SU (3) group, there are already eight parameters and, accordingly, eight interaction carrier fields - they are called gluons. This is about carriers of interactions.
The particles of matter themselves also belong to the representations of symmetry groups. From the point of view of the group of strong interactions - and only quarks participate in them - quarks appear in the Standard Model in the form of triplets, that is, they have quantum numbers that take on three values, often called the word "color": blue, red, green. In weak interactions, all particles act as doublets - this is the lowest representation of the symmetry group of weak interactions. We have up and down quarks, an electron and a neutrino - these are examples of two doublets.
Interestingly, quarks and leptons repeat each other, this is called generations. There are first generation, second generation and third generation of the Standard Model. Generally speaking, it is not very clear why nature chose three generations. There is the first generation of particles that make up the entire observable world, there is a copy - the second generation, and there is a third copy - this is the third generation. The Standard Model includes . These particles are fundamental in the sense that we do not see any structure in these particles.
Generally speaking, an absolute statement cannot be made, since earlier the proton also seemed to be a particle without structure, and then this structure was discovered. Therefore, it cannot be said that those particles that we now consider to be structureless are always so.
Perhaps in the future something will be revealed to us that is not known now. But today, those particles that make up the Standard Model are structureless point particles - these are quarks and leptons, they are represented as point particles of the Standard Model. If we want to describe some process that occurs in nature, as a rule, not quarks themselves participate in it, but particles made up of quarks, that is, hadrons. Leptons - electron, muon, taon - are still observed in the form of free or interacting particles in nature. Therefore, the processes that are described with leptons are directly described by the Standard Model, with hadrons - indirectly.
One way or another, any interactions and any transformations that we observe in nature, both at small and large distances, are described by the Standard Model.
In this sense, the Standard Model crowns the entire edifice of particle physics and, in a sense, the entire edifice of fundamental physics, as it describes the most fundamental laws of nature that are known today.
What are the properties of the particles included in the Standard Model? First of all, we are accustomed to describe the quantum world with the help of so-called quantum numbers. An example of a quantum number is an electric charge. Electric charge is a characteristic of the particle that we understand. Particles are positively charged, negatively charged, not charged at all, and electric charge is actually a quantum number that is conserved in nature. The conservation of electric charge in the Standard Model is described by relevant group symmetry, the conservation of electric charge follows from the theory of symmetry.
But this is not the only characteristic of particles, since, as is well known, there are three symmetry groups in the Standard Model. Strong interactions describe colored objects. Color, of course, is a conditional concept, just a quantum number that takes on three values, it is convenient to designate it with color for clarity. So, the color charge also has a symmetry group and is also a conserved quantity, the color charge of quarks is conserved. Weak interactions have their own charge, they call it left because of the spin - a slightly complicated name that has historical reason, but this is also a characteristic of weak interactions, this is also a charge that is conserved. Thus, all particles have quantum numbers, quantum charges, which are conserved, as follows from the symmetry of the Standard Model.
There are properties in the Standard Model that are not very clear at first glance. For example, when we talk about quarks, we say that quarks cannot be observed in a free state. That is, we are so sure that quarks exist inside hadrons that the fact that we cannot directly observe them does not seem strange to us. But the properties possessed by these particles are very well manifested in the experiment, and therefore, in the experiment, we confirm all the properties of the Standard Model.
There are characteristics that are not obvious. For example, the Standard Model describes the masses of particles and the transitions of one kind of particles into others, while maintaining the desired symmetries. An interesting example weak interaction, in which there is a violation of a number of symmetries, in particular, violation of spatial parity or violation of charge conjugation, when particles are replaced by antiparticles.
What else is included in the Standard Model? In addition to quarks and leptons, the Standard Model includes the Higgs boson. arose in theory for the reason that it was necessary to find a mechanism that would give mass to all particles of the Standard Model. This was achieved by the spontaneous discovery of symmetry, by introducing into the theory an additional scalar field, that is, with spin zero, which is called the Higgs boson.
Thereby full squad The fields of the Standard Model consist of six quarks, six leptons, one Higgs boson, and carriers of all three kinds of interactions. All these particles are experimentally discovered. The Higgs boson was the last particle discovered in 2012. All the others were discovered back in the 20th century, the last one was the neutrino, which is called the taon neutrino, the third neutrino, and it was discovered in 2000. Thus, the 20th century completed the Standard Model with the exception of the Higgs boson, and all particles were experimentally confirmed.
The question arises: does the story end here, or maybe there are some other particles that have not yet entered the Standard Model, but will have to enter there? Or maybe there is something completely different that is not described by the Standard Model? There are various answers to all these questions, we do not yet know the truth.
First of all, if we talk about new particles such as new quarks and new leptons, which have not yet been discovered, as I said, there are three generations of these particles in the Standard Model. The question is: is there a fourth generation? Experimentally, the fourth generation is not visible. Moreover, there are indirect data related both to particle physics experiments and cosmology, which, perhaps, the fourth generation does not exist. The fact is that in the Standard Model there is a so-called: how many quarks, so many leptons. But for leptons (more precisely, for neutrinos), that the number of independent neutrino fields is three. There is a small loophole for a fourth, but in all likelihood, that too will soon be closed.
If the number of neutrinos is three and there is a quark-lepton symmetry, then the number of generations of all other particles is also three, and thus we complete the Standard Model.
There is only one Higgs boson. Could there be two, or four, or more? The answer is the same: maybe. Perhaps there are other Higgs bosons, perhaps we have discovered only one so far. But the theory allows the presence a large number Higgs bosons. Whether they exist or not is a matter for experiment. In this sense, it may turn out that the Standard Model is not yet complete, new particles will still be discovered. But maybe not - one boson is enough to give mass to all particles.
New interactions - we talked about three types of interactions that are included in the Standard Model, all of them are realized as an exchange of carriers, gauge fields with spin one. In a certain sense, the Higgs boson can also be considered as the carrier of the fourth interaction, when it acts as the carrier of the interaction with zero spin. But is there more? Are there any new interactions or some new symmetry groups that are wider than the Standard Model? Isn't the Standard Model included as component into some more general theory? This question is also open. It is possible that this is so, it is possible that it is included in a more general theory, but this is not yet clear.
It must be said that when we talk about the triumphant completion of the Standard Model, we are talking about the fact that, without exception, all the experiments that are carried out on accelerators, in underground physics, in space - they are all brilliant, completely with enviable accuracy, with an accuracy sometimes up to ten ten-thousandth digits, are described by the Standard Model. In this sense, this is a completely unique model that allows you to describe a huge part of inanimate nature using very simple universal mathematical formulas.
The modern understanding of particle physics is contained in the so-called standard model
. The Standard Model (SM) of particle physics is based on quantum electrodynamics, quantum chromodynamics and the quark-parton model.
Quantum electrodynamics (QED) - a high-precision theory - describes the processes occurring under the influence of electromagnetic forces, which are studied with a high degree of accuracy.
Quantum chromodynamics (QCD), which describes the processes of strong interactions, is constructed by analogy with QED, but to a greater extent is a semi-empirical model.
The quark-parton model combines the theoretical and experimental results of studying the properties of particles and their interactions.
So far, no deviations from the Standard Model have been found.
The main content of the Standard Model is presented in Tables 1, 2, 3. The constituents of matter are three generations of fundamental fermions (I, II, III), whose properties are listed in Table. 1. Fundamental bosons - carriers of interactions (Table 2), which can be represented using the Feynman diagram (Fig. 1).
Table 1: Fermions − (half-integer spin in units of ћ) constituents of matter
| Leptons, spin = 1/2 | Quarks, spin = 1/2 | |||||
| Aroma | Weight, GeV/s 2 |
Electric charge, e |
Aroma | Weight, GeV/s 2 |
Electric charge, e |
|
| I | v e | < 7·10 -9 | 0 | u, up | 0.005 | 2/3 |
| e, electron | 0.000511 | -1 | d, down | 0.01 | -1/3 | |
| II | ν μ | < 0.0003 | 0 | c, charm | 1.5 | 2/3 |
| μ, muon | 0.106 | -1 | s, strange | 0.2 | -1/3 | |
| III | ν τ | < 0.03 | 0 | t, top | 170 | 2/3 |
| τ, tau | 1.7771 | -1 | b, bottom | 4.7 | -1/3 | |
Table 2: Bosons - carriers of interactions (spin = 0, 1, 2 ... in units of ћ)
| carriers interactions |
Weight, GeV/s2 |
Electric charge, e |
| Electroweak interaction | ||
| γ, photon, spin = 1 | 0 | 0 |
| W - , spin = 1 | 80.22 | -1 |
| W + , spin = 1 | 80.22 | +1 |
| Z 0 , spin = 1 | 91.187 | 0 |
| Strong (color) interaction | ||
| 5, gluons, spin = 1 | 0 | 0 |
| Undiscovered bosons | ||
| H 0 , Higgs, spin = 0 | > 100 | 0 |
| G, graviton, spin = 2 | ? | 0 |
Table 3: Comparative characteristics fundamental interactions
The strength of the interaction is indicated relative to the strong one.
Rice. 1: Feynman diagram: A + B = C + D, a is the interaction constant, Q 2 = -t - 4-momentum that particle A transfers to particle B as a result of one of four types of interactions.
1.1 Fundamentals of the Standard Model
- Hadrons are made up of quarks and gluons (partons). Quarks are fermions with spin 1/2 and mass m 0; gluons are bosons with spin 1 and mass m = 0.
- Quarks are classified in two ways: flavor and color. There are 6 flavors of quarks and 3 colors for each quark.
- Flavor is a characteristic that is preserved in strong interactions.
- A gluon is made up of two colors - a color and an anticolor, and all other quantum numbers for it are equal to zero. When a gluon is emitted, a quark changes color, but not flavor. There are 8 gluons in total.
- Elementary processes in QCD are constructed by analogy with QED: bremsstrahlung of a gluon by a quark, production of quark-antiquark pairs by a gluon. The process of gluon production by a gluon has no analogue in QED.
- The static gluon field does not tend to zero at infinity, i.e. the total energy of such a field is infinite. Thus, quarks cannot fly out of hadrons; confinement takes place.
- Attractive forces act between quarks, which have two unusual properties: a) asymptotic freedom at very small distances and b) infrared trapping - confinement, due to the fact that the potential energy of interaction V(r) grows indefinitely with increasing distance between quarks r, V(r ) = -α s /r + ær, α s and æ are constants.
- Quark-quark interaction is not additive.
- Only color singlets can exist as free particles:
meson singlet, for which the wave function is given by
and baryon singlet with wave function
where R is red, B is blue, G is green.
- There are current and constituent quarks, which have different masses.
- The cross sections of the process A + B = C + X with the exchange of one gluon between the quarks that make up the hadrons are written as:
ŝ = x a x b s, = x a t/x c .
Symbols a, b, c, d denote quarks and variables related to them, symbols А, В, С – hadrons, ŝ, , , – quantities related to quarks, – distribution function of quarks a in a hadron A (or, respectively, - quarks b in hadron B), is the fragmentation function of quark c into hadrons C, d/dt is the elementary cross section qq of the interaction.
1.2 Search for deviations from the Standard Model
At existing energies of accelerated particles, all provisions of QCD, and even more so of QED, hold well. In the planned experiments with higher particle energies, one of the main tasks is to find deviations from the Standard Model.
Further development of high energy physics is associated with the solution of the following problems:
- Search for exotic particles with a structure different from that accepted in the Standard Model.
- Search for neutrino oscillations ν μ ↔ ν τ and the related problem of the neutrino mass (ν m ≠ 0).
- Search for the decay of a proton whose lifetime is estimated as τ exp > 10 33 years.
- Search for the structure of fundamental particles (strings, preons at distances d< 10 -16 см).
- Detection of deconfined hadronic matter (quark-gluon plasma).
- Study of CP violation in the decay of neutral K-mesons, D-mesons and B-particles.
- Study of the nature of dark matter.
- The study of the composition of the vacuum.
- Search for the Higgs boson.
- Search for supersymmetric particles.
1.3 Unresolved questions of the Standard Model
The fundamental physical theory, the Standard Model of electromagnetic, weak and strong interactions of elementary particles (quarks and leptons) is a generally recognized achievement of physics of the 20th century. It explains all the known experimental facts in the physics of the microworld. However, there are a number of questions that the Standard Model does not answer.
- The nature of the mechanism of spontaneous violation of the electroweak gauge invariance is unknown.
- Explanation of the existence of masses for W ± - and Z 0 -bosons requires the introduction into the theory of scalar fields with a ground state, vacuum, that is non-invariant with respect to gauge transformations.
- The consequence of this is the emergence of a new scalar particle - the Higgs boson.
- The SM does not explain the nature of quantum numbers.
- What are charges (electric; baryon; lepton: Le, L μ , L τ : color: blue, red, green) and why are they quantized?
- Why are there 3 generations of fundamental fermions (I, II, III)?
- The SM does not include gravity, hence the way of including gravity in the SM is a new hypothesis about the existence of additional dimensions in the space of the microworld.
- There is no explanation why the fundamental Planck scale (M ~ 10 19 GeV) is so far from the fundamental scale of electroweak interactions (M ~ 10 2 GeV).
Currently, there is a way to solve these problems. It consists in the development of a new idea of the structure of fundamental particles. It is assumed that the fundamental particles are objects that are commonly called "strings". The properties of strings are considered in the rapidly developing Superstring Model, which claims to establish a connection between phenomena occurring in particle physics and in astrophysics. This connection led to the formulation of a new discipline - the cosmology of elementary particles.
“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 CarrollIf 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 the 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 worldHow 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 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 that carry different kinds 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, and for bosons, the presence of free space is almost not important.
Fermions
A group of fermions, as already mentioned, creates visible matter around us. Whatever we see anywhere 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. Top quarks, with a charge of +2/3, include: up, charm and true quarks
- Lower type. Down-type quarks, with a charge of -1\3, include: down, strange and charm quarks
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
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 practically do not interact with each other.In fact, some bosons still interact with each other, but this will be discussed in more detail in the following articles on the problems of the microcosm.
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 are ±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. In simple terms, 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 either like a wave, or 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 are the most superficial concepts about 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.
