# Physics Tutorial: Particles and Antiparticles - Interaction and Laws of Conservation

In this Physics tutorial, you will learn:

• What are mesons and anti-mesons? What are some of their basic properties?
• What is antiproton? How is can be obtained?
• The same for antineutron and anti-photon.
• How neutrino and antineutrino are produced?
• What is baryon charge? What happens when baryon charge is conserved?
• The same for lepton charge.
• What is strangeness? Where is it observed?
• What does the law of strangeness conservation indicate in regard to a nuclear reaction?

## Introduction

How many elementary particles do you know so far? Do you think there exist others besides them?

What do you understand with antiparticle? What happens when particle and antiparticle enter in contact with each other?

How many laws of conservation do you know? Which are they? Do you think there are other laws of conservation beside them?

This tutorial introduces some other elementary particles besides those explained in the previous tutorial. Such elementary particles are useful in explaining the theory based on the well-known approach based on conservation laws, which makes the modern physics more reliable.

## Mesons and Anti-mesons

In the previous tutorial, we explained that muons and pions (both considered as mesons as their mass is in-between the mass of electron and nucleons) were identified and discovered in cosmic rays. The electric charge of muons and pions is the same as that of electron. The two types of muons (μ+ and μ- are antiparticles of each other. Each of them has a spin of 1/2 and a mass of 106 me = 54 MeV/c2.

Muons are unstable particles; their lifespan is 2.2 microseconds approximately. Muons transform into an electron (positron), a neutrino and an antineutrino according the scheme shown below:

μ+ → e+ + νe + vμ

and

μ- → e- + νμ + ve

As for pions, there are three types of pions, all of them having a zero spin. Two of them, π+ and π- have equal mass (273 me or 140 MeV/c2). These particles are also unstable; their lifespan is 26 nanoseconds (about 85 times shorter than the lifespan of muons).

The three possible reactions in which a pion splits in two other elementary particles are:

π+ → μ+ + νμ
π- → μ- + vμ
π0 → γ + γ

It is worth remembering that μ- and π- are the mesons while μ+ and π+ are their corresponding anti-mesons.

## Proton and Antiproton

After the discovery of positron as a kind of antielectron, scientists believed even more in the existence of antiproton - a particle with the same mass and spin as proton but with opposite charge. The antiproton must act in a powerful fashion when it falls in contact with the proton. As a result of this interaction there is a transformation of such a pair of particles in quants (γ-photons or π-mesons). This is why detecting antiproton in cosmic rays is very difficult. Antiprotons produced in cosmic rays encounter protons during their way and therefore they are annihilated without going to the observer. Based on the calculations, it was found that the energy needed to give the protons in order to obtain antiprotons is about 6 GeV (6 × 109 eV). This was made possible 1n 1955, when the discovery of antiproton took place. We use the symbol (p) to represent the antiproton. One of reactions that results in the generation of antiproton is:

p + p → p + p + p + p

When in contact, a proton and an antiproton are annihilated (despite not entirely, as there are antiparticles such as π-mesons obtained during this process). One of reactions that takes place during this process is:

p + p → π+ + π- + π0

## Neutron and Antineutron

One years after the discovery of antiproton, it was made possible the discovery of antineutron (n) as well. From these three antiparticles (antielectron, antiproton and antineutron) the antiatom and hence antimatter is obtained. This is a possible form of the existence of matter composed by antiparticles. Following this logic, the photon has its antiparticle (anti-photon) as well. We express the anti-photon with the symbol (γ).

## Neutrino and Antineutrino

As discussed in beta decay processes, neutrino and antineutrino are two antiparticles that are produced during these processes. The theoretical interpretation of beta minus decay with the presence of neutrino (or antineutrino in beta plus processes) was fully logical relying on the law of energy conservation. However, the practical identification of such particles relying on their interaction with other particles was very difficult.

According to theory, an antineutrino with sufficient energy can bring the following change when interacting with proton:

v + p → n + e+

The probability of such a process is very small, so the only possibility to observe this phenomenon is using a very intense beam of antineutrons. It is known that every nuclear fission process in a reactor brings the emission of some beta minus fissions, i.e. the emission of some neutrinos (antineutrinos). Hence, because of technical difficulties the process of antineutrino identification was made possible only in 1956, when the technology of nuclear accelerators was improved.

## Elementary Particles and Laws of Conservation

### a. Baryon Charge

From all elementary particles discussed so far, only the particles proton, electron, positrons, neutrino, antineutrino and photon (gamma quant) are stable while the other particles are radioactive. Thus, while the lifespan of neutron is 12 minutes, that of zero pion (π0) particle is about 10-16 s. According to the law of energy conservation, an isolated particle can split only in lighter particles. The balance of energies (or masses) is ensured by means of kinetic energy of fission products. However, particles like neutrino, antineutrino and photon have a zero rest mass, hence they cannot experience any fission. Likewise, electron (e-) and positron (e+) as the two lightest charged particles, are stable too (electric charge can neither increase nor decrease during the fission process).

In order to explain the stability of proton and antiproton from the experimental point of view, scientists associated a nucleonic number otherwise known as baryon charge B to each particle, in analogy with the electric charge e discussed in Electrostatics section. Baryon charge represents the amount of nucleons' attraction inside the atomic nucleus, i.e. it characterizes the strength of nucleons as sources of nuclear field. Hence, there is a full similarity between the baryon charge that produces the nuclear field and electric charge that produces the electric field.

The conservation of baryon charge implies the conservation of the number of baryons in a nucleus. Baryons are not only neutrons and protons but also some heavier elementary particles discovered recently (>Λ, Σ, ΞΩ - hyperons) which contain nuclear charge. In other words, the conservation of baryon charge also implies the conservation of nuclear material.

Each baryon bears a baryon number B as follows:

• For every nucleon (proton or neutron), B = +1
• For every antinucleon (antiproton or antineutron), B = -1
• For every meson, neutrino, electron or photon (and their corresponding antiparticles), B = 0

Knowing the baryon number of each particle or antiparticle helps us understand whether a certain nuclear reaction can occur or not (not all combinations of elementary particles are possible). It is not sufficient to have the law of electric charge conservation applied but the law of baryon charge conservation must also be applied for a nuclear reaction to occur. Let's clarify this point through an example.

#### Example 1

Determine whether the following nuclear reaction are possible or not.

##### Part a
p + p → p + p + p + e+
n → p + e- + v
##### Part c
p + e- + ν → n + γ + n

#### Solution 1

1. The electric charge of proton and positron is +q while the electric charge of electron and antiproton is -q. All the other elementary particles have zero electric charge. Thus, we have for the first reaction:
p + p → p + p + p + e+
( + q) + ( + q) → ( + q) + ( + q) + (-q) + ( + q)
( + 2q) → ( + 2q)
Thus, the electric charge is conserved. Now let's check whether the law of baryon charge conservation is applied in this reaction. We have
p + p → p + p + p + e+
( + 1) + ( + 1) → ( + 1) + ( + 1) + (-1) + 0
( + 2) → ( + 1)
Thus, the baryon charge is not conserved. That means the above nuclear reaction cannot occur.
2. First, let's check the law of conservation of electric charge. We have
n → p + e- + v
0 → ( + q) + (-q) + 0
0 → 0
Hence, the electric charge is conserved. Now let's check whether the baryon charge is conserved. We have
n → p + e- + v
( + 1) → ( + 1) + 0 + 0
( + 1) → ( + 1)
Hence, the baryon charge is also conserved, so this reaction can occur.
3. We use the same procedure as in the first two reactions. Thus, for electric charge we have
p + e- + ν → n + γ + n
( + q) + (-q) + 0 → 0 + 0 + 0
0q → 0q
As for the baryon charge, we have
p + e+ + ν → n + γ + n
( + 1) + 0 + 0 → ( + 1) + 0 + (-1)
( + 1) → 0

Thus, this nuclear reaction cannot occur, as the baryon charge is not conserved. The law of conservation of baryon charge is so far universal. It is similar to all laws of conservation such as the law of conservation of mass, energy, momentum, moment of impulse, electric charge etc.

### b. Lepton charge

Since there exist particles and antiparticles such as neutrino, antineutrino, mesons etc., which have neither electric nor baryon charge, this implies that these two types of charge are not the only that make the distinction between matter and antimatter. Obviously, neutrino and antineutrino must have other properties that make them different from (and opposite to) each other. For example, we see that in beta decay process, antineutrino is associated with electron while neutrino with positron. This is not a casual combination. It is impossible to find neutrino and antineutrino alone in space. This fact brought scientists in the conclusion that there exist another charge besides the electric and baryon ones in elementary particles as well as the law governing its behavior. This is known as a lepton charge - a type of charge that is also conserved in various nuclear reactions and radioactive decay processes.

The term "lepton" derives from Greek language (leptos = lightweight). The category of leptons (lightweight particles) includes electrons and positrons (e- and e+), muons and antimuon (μ- and μ+), tau particles - elementary particles similar to the electron, with negative electric charge and a spin of 1/2 (τ+ and τ-) and the three types of neutrinos (νμ, νe and μτ) each of them having in correspondence an antineutrino as well. In total, there are six leptons and six antileptons. All leptons have a spin of 1/2. The tau particles and muons are unstable; each tau particle splits into one muon and two neutrinos while one muon splits into one electron and two neutrinos. Tau particles have a large mass (1784 MeV/c2, i.e. about 3491 times heavier than electron). They belong to the category of leptons only because they don't produce a strong interaction.

As we discussed earlier, leptons obey to the laws of conservation. There are 3 lepton numbers according to the type of corresponding leptons (Le, Lμ and Lτ). Thus, electron e- and electronic neutrino νe have L = + 1 as well as μ-meson μ- and muon neutrino νμ (L = +1) while their antiparticles have L = -1. In all types of interaction, the lepton charge must be conserved in order to have a valid reaction. Let's explain this point through an example.

#### Example 2

Prove that the μ-meson reaction

μ- → e- + νe + vμ

does not violate the laws of conservation, hence it can occur.

#### Solution 2

We must see whether all three laws of charge conservation (of electric, baryon and lepton charge) are applied in this reaction. Thus, since the μ-meson (μ-) and electron (e-) have both a positive charge -q while the other two particles don't have any electric charge, we obtain:

μ- → e- + νe + vμ
(-q) → (-q) + 0 + 0
(-q) → (-q)

Thus, the electric charge is conserved. Now, let's check for the baryon charge. Since all the above elementary particles have a baryon charge equal to zero (only protons, neutrons and their corresponding antiparticles have a baryon charge different from zero, we have:

μ- → e- + νe + vμ
0 → 0 + 0 + 0
0 → 0

Hence, the baryon charge is also conserved in this reaction. At last, we have to check whether lepton charge is conserved or not. Thus, based on the lepton numbers given earlier, we have

μ- → e- + νe + vμ
( + 1) → ( + 1) + ( + 1) + (-1)
( + 1) → ( + 1)

Hence, the lepton charge is also conserved. Thus, since all three types of charge are conserved, this reaction can occur as it obeys the laws of conservation.

## Strangeness

The experimental data found during the second half of the last century enriched the world of elementary particles with new ones. Some of them didn't need to have known in the explanation of theory the structure of matter and fields or the known interactions involved. For this reason, scientists names these elementary particles "strange". The distinctive feature of such particles is their generation in pairs. For example, Σ-hyperon is produced together with K-mesons (K+, K-, K0) otherwise known as kaons. This generation is pairs is similar to those of electron-antineutrino or positron-neutrino pairs. Like all the other particles that are produced in pairs, the strange particles have a specific charge associated with, the law of conservation of which, allows us to determine whether a specific reaction involving such particles can occur or not. This new type of charge is known as Strangeness, S.

Nucleons, muons and π-mesons do not manifest any strange behavior or property. Therefore their strangeness is S = 0. On the other hand, two strange elementary particles that belong to the same pair have their strangeness equal and opposite. In this way, the algebraic sum of strangeness before and after the reaction takes place must be the same. Thus, the Λ0, Σ+, Σ- and Σ0 hyperons have S = -1 whereas their corresponding accompanying particles K0 and K+ have S = +1. The corresponding antiparticles of elementary particles mentioned above, have an opposite strangeness. Thus, Λ0, Σ+, Σ-, Σ0 have S = +1 while K0 and K- have S = -1.

The law of strangeness conservation is applicable only in strong interaction; it is not applied in weak interaction observed during radioactive decay processes.

### Example 3

Which of the following reactions can occur based on the law of strangeness conservation?

#### Part a

μ- → e- + νe + νμ

p + π- → p + K-

### Solution 3

1. Muons do don manifest any strange behavior, so S(μ-) = 0. This is also true for all particles that are obtained as products of μ- decomposition. Hence, we have
μ- → e- + νe + νμ
0 → 0 + 0 + 0
Hence, the reaction is possible due to the law of conservation of strangeness.
2. Neither π-meson nor proton do manifest any strange behavior. On the other hand, the strangeness of K- kaon is S = -1. Therefore, we have
p + π- → p + K-
0 + 0 → 0 + (-1)
0 → -1

It is clear that the strangeness is not conserved as the values in both sides are different. Hence, this reaction cannot occur.

## Summary

Muons are unstable elementary particles; their lifespan is 2.2 microseconds approximately. The electric charge of muons (and pions) is the same as that of electron. The two types of muons (μ+ and μ- are antiparticles of each other. Each of them has a spin of 1/2 and a mass of 106 me = 54 MeV/c2.

Muons are unstable particles; their lifespan is 2.2 microseconds approximately. Muons transform into an electron (positron), a neutrino and an antineutrino according the scheme

μ+ → e+ + νe + vμ

and

μ- → e- + νμ + ve

There are three types of pions, all of them having a zero spin. Two of them, π+ and π- have equal mass (273 me or 140 MeV/c2). These particles are also unstable; their lifespan is 26 nanoseconds (about 85 times shorter than the lifespan of muons).

The three possible reactions in which a pion splits in two other elementary particles are:

π+ → μ+ + νμ
π- → μ- + vμ
π0 → γ + γ

Antiproton (p) is a particle with the same mass and spin as proton but with opposite charge. It was found that the energy needed to give the protons in order to obtain antiprotons is about 6 GeV (6 × 109 eV).

One years after the discovery of antiproton, the discovery of antineutron (n) was made possible as well. From these three antiparticles (antielectron, antiproton and antineutron) the antiatom and hence antimatter is obtained. This is a possible form of the existence of matter composed by antiparticles. Following this logic, the photon has its antiparticle (anti-photon) as well. We express the anti-photon with the symbol (γ).

Neutrino and antineutrino are two other elementary particles that are produced during beta decay processes. According to theory, an antineutrino with sufficient energy can bring the following change when interacting with proton:

v + p → n + e+

In order to explain the stability of proton and antiproton from the experimental point of view, scientists associated a nucleonic number otherwise known as baryon charge B to each particle, in analogy with the electric charge e. Baryon charge represents the amount of nucleons attraction inside the atomic nucleus, i.e. it characterizes the strength of nucleons as sources of nuclear field.

The conservation of baryon charge implies the conservation of the number of baryons in a nucleus. Baryons are not only neutrons and protons but also some heavier elementary particles discovered recently (Λ, Σ, Ξ and Ω - hyperons) which contain nuclear charge. In other words, the conservation of baryon charge also implies the conservation of nuclear material.

Each baryon bears a baryon number B as follows:

• For every nucleon (proton or neutron), B = +1
• For every antinucleon (antiproton or antineutron), B = -1
• For every meson, neutrino, electron or photon (and their corresponding antiparticles), B = 0

It is impossible to find neutrino and antineutrino alone in space. This fact brought scientists in the conclusion that there exist another charge besides the electric and baryon ones in elementary particles as well as the law governing its behavior. This is known as a lepton charge - a type of charge that is also conserved in various nuclear reactions and radioactive decay processes.

The category of leptons (lightweight particles) includes electrons and positrons (e- and e+), muons and antimuon (μ- and μ+), tau particles - elementary particles similar to the electron, with negative electric charge and a spin of 1/2 (τ+ and τ-) and the three types of neutrinos (νμ, νe and μτ) each of them having in correspondence an antineutrino as well. In total, there are six leptons and six antileptons. The tau particles and muons are unstable; each tau particle splits into one muon and two neutrinos while one muon splits into one electron and two neutrinos. Tau particles have a large mass (1784 MeV/c2, i.e. about 3491 times heavier than electron). They belong to the category of leptons only because they don't produce a strong interaction.

Leptons obey to the laws of conservation. There are 3 lepton numbers according to the type of corresponding leptons (Le, Lμ and Lτ). Thus, electron e- and electronic neutrino νe have L = +1 as well as μ-meson μ- and muon neutrino νμ (L = +1) while their antiparticles have L = -1. In all types of interaction, the lepton charge must be conserved in order to have a valid reaction.

Some elementary particles don't need the structure of matter and fields known in the explanation of theory or the known interactions involved. For this reason, scientists called these elementary particles "strange". The distinctive feature of such particles is their generation in pairs. For example, Σ-hyperon is produced together with K-mesons (K+, K-, K0) otherwise known as kaons. Like all the other particles that are produced in pairs, the strange particles have a specific charge associated with, the law of conservation of which, allows us to determine whether a specific reaction involving such particles can occur or not. This new type of charge is known as Strangeness, S.

Nucleons, muons and π-mesons do not manifest any strange behavior or property. Therefore their strangeness is S = 0. Two strange elementary particles that belong to the same pair have their strangeness equal and opposite. The algebraic sum of strangeness before and after the reaction takes place must be the same. Thus, the Λ0, Σ+ , Σ- and Σ0 hyperons have S = -1 whereas their corresponding accompanying particles K0 and K+ have S = +1. The corresponding antiparticles of elementary particles mentioned above, have an opposite strangeness. Thus, Λ0, Σ+, Σ-,Σ0 have S = + 1 while K0 and K- have S = -1.

The law of strangeness conservation is applicable only in strong interaction; it is not applied in weak interaction observed during radioactive decay processes.

## Particles and Antiparticles - Interaction and Laws of Conservation Revision Questions

1. Which of the following reactions is possible to occur due to the conservation of baryon charge?

1. p + vμ → e- + νπ
2. v + p → n + e+
3. e- + n + γ → e+ + π- + K-
4. p + π+ → e- + K+

2. In which of the following reactions the lepton charge is conserved?

1. μ- + e-ve + νμ
2. π- → γ + γ
3. π+ → μ+ + νμ
4. μ- → e+ + νe + νμ

3. In which of the following reactions all four laws of conservation (of electric, baryon, lepton charge and strangeness) are applied?

1. p + π- → Λ0 + K0
2. p + π- → Σ+ + K-
3. p + π- → p + K-
4. μ- → e- + νe + νμ