Most particles decay and some do not.

Original author: Matt Strassler
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Although most particles disintegrate, or disintegrate, into other particles, some of them do not behave this way. But why?

There are many types of particles in the world, some of them look elementary, others can be built from elementary ones - for example, protons, neutrons and the atomic nucleus - but most of them decay in a small fraction of a second. In a previous article, I explained why they break up; in fact, this is a form of dispersion, of which we have an intuitive idea that comes from our experience associated with waves and vibrations. But why don't several types of particles decay at all, or at least live much longer than 13.7 billion years, longer than the age of the Universe?

The only stable particles known in nature are an electron (and an antielectron), the lightest of the three types of neutrinos (and its antiparticle), a photon, and a supposed graviton (both of which are antiparticles of their own accord). Other neutrinos, a proton, and many atomic nuclei (and their antiparticles - here I stop mentioning antiparticles, it will be implied) are probably unstable, but they live very, very, very long. Protons, for example, live so long that a very small number of them decayed from the Big Bang, so that from all practical points of view they are stable. Another long-lived particle is a neutron, which in itself, outside the atomic nucleus, lives only about 15 minutes. But inside atomic nuclei, neutrons can live longer than the age of the universe. Finally, it’s worth adding that if dark matter is made up of particles,

Why are these particles stable? It turns out that in the microworld there are rules for the behavior of particles, unknown to us from everyday life, filled with waves and vibrations. These laws prevent the decay of particles, both fast and slow. Fundamental rules are conservation laws that state that certain quantities of the universe do not change in any physical processes. Among them are energy, momentum, electric charge and several others. There are also some approximate conservation laws, suggesting that some quantities change very rarely. These laws did not appear from anywhere and were not invented by theoreticians from scratch. They are associated with other properties of the world. For example, if the laws of nature do not change over time, it follows from this (thanks to the theorem mathematician Emmy Noether) that the energy is conserved. We will see that the stability of the matter of which you and I are composed makes it possible to test these laws well.

The combination of these laws with the properties of particles gives us several simple rules that determine when particles simply cannot decay, or can decay very rarely. And these rules are (almost) enough to explain the stability of the particles of which we are composed, and the particles with which we most often interact.

Fermions and bosons


In a world in which Einstein's theory of relativity works, space has three dimensions and quantum mechanics works, all particles must be either fermions (named after the Italian physicist Enrico Fermi ) or bosons (in honor of the Indian physicist Satyendra Nat Bose ). This statement is a mathematical theorem, not the result of observations. But the data from the last 100 years of observations support it - all the particles known in the Standard Model are either fermions or bosons.

An example of a boson is a photon. Two or more bosons (of the same type of particles) are allowed to do the same thing. For example, a laser is a machine for creating a large number of photons that do exactly the same thing, and produces very bright light with a very precisely defined color and propagating in a certain direction. All photons in the beam are synchronized.

It is impossible to make a laser from fermions. An example of a fermion is an electron. Two fermions (of the same type of particles) cannot do the same thing at the same time. Since an electron is a fermion, two electrons cannot be in the orbit of an atom in the same way. This is due to the Pauli prohibition principle., which we teach in chemistry lessons, with enormous consequences for the periodic table of elements and for chemistry. Electrons in an atom occupy different orbits, in different shells around the atomic nucleus, because they cannot all fall into one orbit at the same time - fermions are forbidden to do this. More precisely, only two electrons can occupy one orbit, and only if they rotate in different directions around the axis, i.e. have different spin. If electrons were bosons, chemistry would not be recognizable!

Among the elementary particles known in our world there are many fermions: charged leptons, neutrinos, quarks, and many bosons: all the carriers of interactions and the Higgs particle.

Also, bosonic fields can, on average, differ significantly from zero. Fermion fields cannot do this. The Higgs field, non-zero in our Universe, giving mass to all elementary particles, is a boson field (and its particle is a boson, therefore it is called the Higgs boson).

In addition, a Bose-Einstein condensate, predicted by Einstein in the 1920s, but obtained only in the 1990s, in an experiment that received the Nobel Prize, can be formed from bosonic particles. In such experiments, condensate is produced, causing a large number of boson atoms to remain in the most “calm” state accessible to a quantum object, i.e. atoms are in the lowest possible quantum states, and then quantum effects begin to manifest themselves at the macroscopic level.

All this relates to quantum mechanics. Although Einstein did not like the consequences of quantum mechanics, you should not have the impression that he did not understand it. On the contrary, his work was critical for the development of some aspects of quantum theory.

The laws of nature for particles


Here are the main rules. The main consequences for our universe are marked in bold.

The laws of nature, which are considered for good reason, must be followed exactly


1) A particle must decay into two or more particles


Therefore, with each decay of particles in nature, two or more particles appear from a single particle. This follows from the law of nature, according to which the total energy and total momentum must remain constant in any physical process (physicists say that "energy and momentum are conserved"). And this is why the 1st rule follows from them:

Suppose a particle of type 1 can decay only into a particle of type 2. Let us prove that there is a contradiction here. Take particle 1 and place it in front of us in stillness. All her energy will be enclosed in her mass. Now, let's say it breaks up into particle 2. The law of conservation of energy states that
particle rest energy 1 = particle rest energy 2 + particle motion energy 2

Since the motion energy is positive, the rest energy of particle 2 can be less than or equal to the rest energy of particle 1. But the motion energy of particle 2 is positive, so if the rest energy of particle 2 is less than the rest energy of particle 1, then particle 2 must move. But particle 1 was at rest, so it did not have an impulse. Particle 2 moves, which means it has an impulse. But this is impossible - the momentum must be maintained. Therefore, such a decay is impossible, unless the masses of these particles are not equal to each other. But in this case, if particle 1 can decay into particle 2, the opposite is also true - particle 2 can decay into particle 1. But this is not decay - it’s just a confusion between the two types of particles.

2) The mass of the decaying particle must exceed the sum of the masses obtained during the decay of the particles


The total energy and total momentum during decay are conserved, but the total mass always decreases. A “parent” particle with mass m1 can decay only into “daughter” particles 2 and 3 if the sum of their masses is less than the mass of the parent: m2 + m3 <m1. This is a simple consequence of the law of nature - the total energy must remain constant in any physical process. Proof:

Imagine observing particle 1 at rest. All her energy is the rest energy, m 1 c 2 . Then it breaks up into particles 2 and 3. Each of them has a rest energy and an energy of motion. Since energy is conserved,
Particle rest energy 1 = Particle rest energy 2 + Particle rest energy 3 + Particle motion energy 2 + Particle motion energy 3

But the energy of motion is always greater than zero, therefore the initial rest energy exceeds the final rest energies, therefore m 1 c 2 > m 2 c 2 + m 3 c 2 , therefore m 1 > m 2 + m 3 .

Since the photon, as all experiments show, does not have mass, it cannot decay . Therefore, waves of light can pass through the entire room, all the space from the Sun to us, and the entire Universe, completely not disintegrating along the way. It is assumed that the graviton has the same properties.

3) The total charge before and after decay is maintained


Another remaining property is the electric charge. A W- particle, very heavy and negatively charged, with a charge –e, can decay into an electron with a negative charge –e and an antineutrino without a charge. But W- cannot decay into a positron with a positive charge + e and a neutrino without a charge, since the total charge would change from –e to + e. Also W- cannot decay into an electron with a negative charge and a positron (anti-electron) with a positive charge, since their combination would give a zero charge.

Since the electron is the lightest of particles with an electric charge, it cannot decay into anything else. Only neutrinos, photons, gluons, and gravitons are lighter than it, but they are electrically neutral, so any combination of them will have zero charge. Any unknown particle lighter than an electron must be electrically neutral, or we could easily find it in experiments. Therefore, the electron is stable .

4) The total number of fermions before and after decay can only change by an even number


The rule follows from the fact that the angular momentum, as well as energy and momentum, is conserved (which explains the tendency of rotating things, for example, the Earth, to maintain rotation). The rule forbids a neutron to decay into a proton and an electron. Such a decay would fall under laws 1, 2, and 3, but not under 4, since all these particles are fermions. The neutron decays into a proton, electron and antineutrino. Then we will initially have one fermion and three in the end, 3 - 1 = 2. There

are three types of neutrinos, and now it is believed that they all have mass (two are most likely, and the third is likely). The lightest neutrino is the lightest known fermion , but the only particles lighter than it into which it could decay are bosons (photon and graviton). Therefore, it does not break up: You cannot start with a fermion and end with bosons. In principle, it can be unstable if there are even lighter fermions that we have not yet encountered - they would interact even more weakly with ordinary matter than neutrinos. And we know that neutrinos live long enough, because we saw how they travel vast distances from remote explosions of supernova stars.

The laws of nature, which are thought to be for slightly less solid reasons, must be followed almost exactly


5) The difference between the total number of quarks and the total number of antiquarks during decay does not change


The proton contains three quarks, many gluons and pairs of antiquark quarks, so in the proton the number of quarks minus the number of antiquarks is three. There is also an overabundance of three quarks in the neutron. Therefore, a neutron, as a heavier particle, can decay into a proton without violating rule 5 - and it does so (generating an electron and an antineutrino).

But a proton is the lightest of particles containing more quarks than antiquarks, and this rule, together with rule 2, implies that it is stable. It is clear that a proton cannot decay into any combination of electrons, photons and neutrinos, because they do not contain quarks. There are several hadrons (particles consisting of quarks, antiquarks and gluons), in particular, pions, but they differ from protons and neutrons in that they contain an equal number of quarks and antiquarks. Therefore, a heavy proton cannot decay into any combination of pions and non-hadrons (photons, electrons, neutrinos), since daughter particles will have equal quarks and antiquarks, and this is not so for the parent particle. But peonies can decay without breaking the rules; for example, an electrically neutral pion (being a boson) can decay into two photons, and a positively charged pion can decay into neutrinos and an antimuon - which is very useful for creating neutrino rays.

Many theorists believe (although this was not confirmed by experiment) that this rule is slightly violated , and the proton is very, very, very slightly unstable, with an extremely long life. For more than ten years, observing the huge number of protons in a huge water tank in the Super Kamiokande experiment , and not having received a single decay, we know that a proton lives at least 10,000,000,000,000,000,000,000,000,000,000,000 years. I hope I haven’t missed a single zero. The age of the current phase of the Universe is approximately 13.7 billion, so in the future there will be a lot of protons.

There are other laws, but most of the effects we observe follow only from those listed.

Conclusion


Now we have rules to explain:
• why photons are stable,
• why electrons are stable,
• why protons are stable, or live very long,
• why at least one type of neutrino is stable or lives very long.

That is enough to explain ordinary matter, chemistry, sunlight, many other processes in life - except one. What about an unstable neutron?

The neutron is a very amazing thing. Nothing forbids it to decay, and it decays after about 15 minutes into a proton, electron and antineutrino. Why does he live so long? Partially due to the fact that the masses of the proton and neutron are very close. Although the neutron rest mass approaches GeV, it is only 0.0007 GeV larger than the sum of the rest masses of the proton, electron, and antineutrino. And the decay rate becomes very small when the total mass of daughter decay particles is very close to the mass of the parent particle. This is not surprising, since rule 2 postulates that decay should stop completely if the mass of daughter particles exceeds the mass of the parent.

But what is strange is that if you place a neutron in an atomic nucleus, it becomes stable! For example, in helium there are two protons and two neutrons. And although the neutron itself lives a quarter of an hour, the helium core can live as long as the universe exists, and even longer. This is true in general for all stable elements of the periodic table to them. Mendeleev and their neutrons. This fact is an extremely important consequence of the Einstein theory of relativity and some features of strong nuclear interaction, and without it our chemical world would not have any diversity. This feature deserves a separate article.

And by the way, if dark matter consists of unknown particles - why are they stable? No one knows for sure, but probably the laws I have described will not be enough for this. Most likely, there is another conservation law, exact or approximate, which remains to be discovered.

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