Particles, antiparticles and their annihilation

Antiparticles are often more mystical and mysterious than they really are, thanks to science fiction and other writings like Dan Brown’s “ Angels and Demons ”.

Each type of particle has an antiparticle. This is usually a separate particle, but it happens that the antiparticle and the particle are one and the same. Only particles that satisfy certain conditions (for example, electrically neutral) can be antiparticles themselves. A small list of examples of such particles is photons, Z-particles, gluons and gravitons. Perhaps three neutrinos. All other particles have individual antiparticles that have the same mass but the opposite electric charge. The neutron is an example of an electrically neutral particle that is not an antiparticle itself. Like a proton, there are more quarks in a neutron than antiquarks, while an antineutron has more antiquarks than quarks.

For particles that are different from antiparticles, the names of antiparticles are usually quite obvious (upper antiquark, antineutrino, antitau), with the exception of the anti-electron, which is usually called the positron.
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What is so famous antimatter, because of what it sounds so mysterious? All this is due to the statement "matter and anti-matter annihilate to pure energy." This statement sounds cool, but it is not serious. It is not entirely wrong, but not true. The reality is more complex and not so amazing.

Often, for simplicity, physicists omit the prefix "anti" when it is obvious from the context. Examples:

• In many processes, muon and antimuon appear. Physicists sometimes call this the "muon pair."
• A W-particle decays into an upper quark and a lower antiquark, and it is often said that it disintegrates "into quarks."

Annihilation of particles and antiparticles

The annihilation of particles and antiparticles devote a lot of materials - it sounds mysterious, scary and fantastic - but these are the main processes taking place in the heart of particle physics, and such a description of them leads to frequent misunderstandings. I want to describe some basic rules that determine whether a particle and an antiparticle of one type will turn into another pair of particles and antiparticles, approaching each other. This is not a complete history of particle and antiparticle annihilation, but a good start.

In a world like ours, governed by quantum mechanics and Einstein's relativity, there is a mathematical theorem: for each type of particle there is a corresponding type of antiparticle with exactly the same mass. This is not just a theorem — for all known particles, antiparticles were obtained experimentally, so there’s nothing to argue about.

However, some particles coincide with antiparticles: an antiparticle for a photon (particles of light) and there will be a photon. The same will be for the Z-particle and the Higgs particle. On the other hand, an electron with a negative (by definition) electric charge has an antiparticle, an antielectron, or a positron, with a positive charge. Almost all known particles have this: the muon has an anti-muon, the upper quark has an upper antiquark, the W-particle with a positive charge has an antiparticle W with a negative one.

If you bring together a particle and an antiparticle, almost all of their properties will be mutually destroyed. For example, the electric charge of a muon (a heavy cousin of an electron) plus the electric charge of an anti-muon will be zero. The first is negative, the second is positive, but they are equal in size. The only thing that is not destroyed is their mass and energy. True, this statement with a little dirty trick. Mass is not “preserved” - it can appear and disappear , which is very good for particle physics. The only thing that will not go anywhere is energy. Energy is saved: with what you started, with this and finish.

1. Muon and anti-muon turn into two photons

Suppose I have a shoebox, in which there is nothing but practically resting muon and anti-muon. Then the energy inside the box is equal to the energy of the mass of the muon and the energy of the mass of the anti-muon. [“Practically” - because I omit the electric field between the muon and the anti-muon, but this is a very tiny effect, which in our case can be ignored.] Suppose the muon mass is M, then the muon mass energy is M c ² , and the same true for antimuion. The momenta of both particles will be zero, since they do not move. Total energy E and momentum p in the box initially

$$

$$E_ {initial} = 2 M c ^ 2 \\ p_ {initial} = 0$$

Everything else in the box is zero: the total electric charge, angular momentum, etc. Only energy. And the mass - but they are related to each other.

Since almost everything is mutually destroyed, a particle and an antiparticle can be transformed through one of the four known interactions into another particle and its antiparticle. For example, a muon and an anti-muon can turn into a photon and a second photon (remember, the photon is an antiparticle to itself). Both photons will have energy - but how much? Well, the photons will be the same, and they will have the same energy, and since it is conserved, the total final energy will be the same as the total initial energy:

$$

$$E_ {photon} = 1/2 E_ {final} = 1/2 E_ {initial} = M c ^ 2 = E_ {muon}$$

Pay attention to what a cool thing just happened: we started with massive particles, each of which did not move, and did not have the energy of motion, but it had the energy of mass M c ² . And we ended up with two massless particles, without mass energy, but with an energy of motion equal to the mass energy of the muons:
M c ² . See fig. one.


Fig. one

Also, the photons will have pulses. But the pulses of the two photons will be multidirectional and mutually destroyed, so that the final pulse will be zero.

$$

$$p_ {final} = p_ {initial} = 0$$

Note that the energy is saved, the momentum is saved, and the mass is not. The final mass is zero, although the initial mass is 2 M.

2. Muon and anti-muon turn into electron and anti-electron

Simple reaction:

$$

$$particle_1 + antiparticle_1 \ rightarrow particle_2 + antiparticle_2$$

not only possible process for particle and antiparticle annihilation, but also very common. Let's look at another option for particle 2.


Fig. 2

Instead of becoming two photons, a muon and an antimuon can turn into an electron and a positron (antielectron), as in fig. 2. Both will have the same mass; let's call it m. The mass of an electron is about 200 times less than the mass of a muon M. What a muon and an antimuon will turn into photons or an electron / positron pair, determines randomness, but with the probability described by the equations of quantum mechanics.

The same logic as before leads us to the same conclusion. We will have symmetry, an electron and a positron, with the same mass, the same energy, and thanks to the conservation law, the total energy should be the same as the initial energy of the muon.

$$

$$E_ {electron} = E_ {positron} = 1/2 E_ {final} = 1/2 E_ {initial} = M c2 = E_ {muon}$$

The situation is a bit different: we started with massive stationary particles that do not have the energy of motion and have the energy of mass M c ² . And they ended up with two massive particles, each of which has the energy of mass mc ² and a lot of energy of motion, and the total energy of the electron is equal to the energy of the mass of the muon M c ² . Again, the electron momentum is mutually annihilated with the positron momentum:

$$

$$p_ {final} = 0$$

Of course, their electric charges are mutually destroyed. Before the transformation of the charge in the box was not there and after it. The energy is again conserved, the impulse is conserved, the charge is conserved, and the mass is not. The initial mass was 2M, and the final mass was 2m.


Fig. 3

3. Electron and anti-electron turn into two photons.

The resting electron and positron can turn into two photons, just like muon and antimuon. All calculations can be carried out by reducing the problem to the case of muons, simply replacing M with m everywhere. There is no difference (compare Fig. 1 and Fig. 3).

4. Can an electron and an antielectron turn into a muon and an antimuon?

No and yes. The answer depends on the question:

• No, if the electron and positron are initially resting. They do not have enough energy to create a muon and antimuon, so this process will not happen.
• Yes, if the electron and positron have great energies of motion and collide very strongly. The process can occur as long as they have enough energy.

First, let's make sure that if the electron and the positron are at rest - they do not have the energy of motion - they will not be able to turn into muon and antimuon. The logic is simple - we just need to return to the previous problem, in which the muon and anti-muon turned into an electron and positron, and replace everywhere the muon with an electron, the anti-muon with a positron, M with m. It turns out:

$$

$$E_ {muon} = E_ {anti-muon} = 1/2 E_ {final} = 1/2 E_ {initial} = m c ^ 2 = E_ {electron}$$

But this is impossible! Muon has an energy of mass M c ² , plus a positive energy of motion. M> m. It turns out a contradiction:

$$

$$E_ {muon} = M c ^ 2 + "motion energy" ≥ M c ^ 2> m c ^ 2$$

The muon energy can not be equal to mc ² , as required by the conservation of energy, since M> m. We have to admit that this process cannot happen.


Fig. four

However, this is precisely why this attempt does not work, and tells us how to achieve the desired. No need to consider the resting electron and positron. Let's accelerate them - almost to the speed of light, so that their energies of motion become very large, and the total energies (energy of mass and energy of motion) were significantly greater than mc ² . For simplicity, let us imagine that their initial energy has become equal to M c ² . Then the total initial energy in the box will be 2 M c ² , and in order for the process to go, the conservation law requires:

$$

$$E_ {muon} = E_ {anti-muon} = 1/2 E_ {final} = 1/2 E_ {initial} = M c2 = E_ {electron}$$

What does not contradict the requirements of the previous equation

$$

$$E_ {muon} = M c ^ 2 + "motion energy" ≥ M c ^ 2> m c ^ 2$$

The energy of the electron and positron is barely enough to create a resting muon and antimuon (Fig. 5).


Fig. five

If we make the energies of the electron and the positron even more, we can create a muon and an antimuon. The excess energy will turn into the energy of motion of the muon and anti-muon, see fig. 6

Note that mass is again not conserved, although energy is conserved. In this case, the mass increased from 2m to 2M. This is very important for particle physics! This is one of the main techniques we use to discover new particles. We collide a particle and an antiparticle with very large energies of motion, hoping that they will turn into a heavy particle, unprecedented before, together with its antiparticle.


Fig. 6

Total

• A stationary particle and its antiparticle can annihilate, generating a particle and an antiparticle, if the initial particle is heavier than the final one.
• A fixed particle and an antiparticle cannot annihilate, giving rise to a particle and an antiparticle, if the final particle is heavier than the initial one.
• A particle moving relative to each other and its antiparticle can annihilate, producing a heavier particle and an antiparticle, if they have enough energy to move.
• If the sum of the energy of the mass and the energy of motion of the particle is equal to the energy of the mass of the heavier particle, then the resulting heavy particle and antiparticle will be fixed.
• If the sum of the energy of the mass and the energy of motion of the particle is greater than the energy of the mass of the heavier particle, then the excess energy will turn into the energy of motion of the heavier particles and antiparticle.