# Physics Tutorial: Classification of Elementary Particles. Quarks and Charm

In this Physics tutorial, you will learn:

• How many types of interactions are there? Which are they?
• What are the main features of various types of interaction?
• How the elementary particles are classified?
• What are quarks? How many types of quarks are there?
• What is the elementary charge of each type of quarks? What about their spin, baryon number, strangeness, etc.?
• How many generations of quarks are there? Which quarks do belong to each generation?
• What are quark antiparticles? What are their corresponding charges?
• What are quark mediators? How do we express them?
• What is charm?
• What is the standard model? What are its main features?
• Why symmetry is so important in standard model?
• What scientists are trying to achieve in respect to various types of interactions? What are the missing steps in this regard?

## Introduction

So far, we have briefly mentioned many elementary particles to illustrate a number of physical phenomena related with them. This may create confusion, as it is very difficult to remember all names, properties and numbers related to the specific type of charge contained in an elementary particle.

Scientists have classified elementary particles in groups in order to have an easier understanding of them. Such classification is made based on the types of interaction elementary particles experience during their lifetime. In this tutorial, we will try to clarify the reasons of such approach and the ease derived from the classification mentioned above when dealing with elementary particles. In addition, a number of new elementary particles and properties of already known ones are provided and explained.

## Types of Interaction

As discussed in the previous articles, the last 80-90 years, especially the second half of 20th century were very prolific in the discovery of new elementary particles. So far, four basic types of interaction were known:

1. Strong interaction. This is an interaction experienced by all elementary particles except leptons, photons and gravitons (elementary particles still not identified experimentally to this date that are thought to be responsible for the gravitational attraction). The nuclear forces acting between nucleons are explained relying on the concept and existence of strong interaction.
2. Electromagnetic interaction. This is an interaction experienced by all electrically charged elementary particles. All biological and chemical reactions take place due to the existence of such an interaction. Electromagnetic interaction determines the matter structure outside the nucleus. In the macroscopic level, electromagnetic effects are evident when photons are generated and absorbed.
3. Weak interaction. It is present in all types of beta decay, in many elementary particles decay processes, as well as in all processes involving neutrino interaction with matter. All particles are affected by weak interaction except graviton. This type of interaction is the most relevant for neutrino. Weak interaction is encountered during the fission processes of many unstable particles (muons in electrons, pions in mesons, Σ-hyperons in protons and so on).
4. Gravitational interaction. This is an interaction experienced by all particles without exception, but since it is very weak, it is often neglected when dealing with elementary particles. Gravitational interaction is very small even when compared with electromagnetic interaction, as discussed in Section 14. You can easily prove that EM repulsion between two protons in an atomic nucleus is about 1036 times greater than gravitational attraction between them (you can find the ratio k · q1 · q2/G · m1 · m2 and obtain the above approximate value). Gravitational interaction is considerable only in massive objects such as celestial bodies.

The table below summarizes some principal data regarding the four fundamental interactions. ## Classification of Elementary Particles

Based on the type of interaction they experience, elementary particles are classified in three major groups:

1. Photons (quants) γ, which are the carriers of EM interaction;
2. Leptons, a group composed by muons, electrons, the two types of neutrino and their corresponding antiparticles. All these elementary particles experience the weak interaction during their lifetime; and
3. Hadrons ("hadros" from Greek means big and strong). All particles that experience strong interaction such as protons, neutrons, hyperons and their corresponding antiparticles, mesons with or without strangeness as well as a number of resonances (elementary particles with a very short lifespan) are included in hadrons group. The two major subgroups of hadrons are mesons and baryons.

The following tables shows a more structured and complete information on the two most populated groups of elementary particles: leptons and hadrons, as the other group (photons) are well explained already.

### Table of leptons   ### Quarks

In the above tables of hadrons, there is a column (the last one) named "Quark composition." It seems a bit strange, as we have not explained the meaning of "quark" yet. However, since all properties of elementary particles given in the other columns are known, it was included in the tables. We will refer to these tables when discussing about quarks in the current paragraph.

Leptons have the possibility to group in three heavy particles and three neutrinos, each of them having their own antiparticles. On the other hand, the hadrons family cannot represent the fundamental particles of matter, as there exist many other particles that do not belong to this family. However, the main reason why hadrons are not considered as the building blocks of matter is because they (hadrons) are not simple but composite particles instead, where each component has a spin of 1/2. Such components of leptons are known as quarks. If we recap what we said earlier on quarks, it is clear that:

"A quark is one of the fundamental particles in physics. Quarks join to form hadrons, such as protons and neutrons, which are components of the nuclei of atoms. Quarks interact between them mainly through the strong force. The antiparticle of a quark is the antiquark. Quarks and antiquarks are the only two fundamental particles that interact through all four fundamental forces of physics: gravitation, electromagnetism, and the strong and weak interactions."

Quarks exhibit the confinement property, i.e. a specific quark cannot exist separately but only in pair with another quark. A baryon is composed by three quarks (qqq), while a meson is composed by a quark-antiquark pair (qq). Given this, it is evident that a quark has an electric charge equal to 1/3 or 2/3 of the charge of electron, which was previously thought to be the smallest unit of electric charge. Likewise, quarks have a non-whole baryon number.

As for the spin, since each individual quark has a spin of 1/2, two opposite quarks can be combined to give a zero spin. When three quarks are combined, their total spin may be 1/2 or 3/2 based on the presence of antiquarks in the system.

The original theory of quarks included three types of quarks: up (u), down (d) and strange (s) (hence the three letters appearing in the last column of hadrons table of the previous paragraph). However, now the concept of six flavors of quarks is widely accepted. According to this concept, there are six flavors of quarks: up (u), down (d), strange (s), charm (), bottom (B), and top (T). The flavor of the quark determines its properties. For example, quarks with a charge of + (2/3)e are called up-type quarks, and those with a charge of -(1/3)e are called down-type.

There are three generations of quarks, based on pairs of weak positive/negative, weak isospin. The first generation includes the up and down quarks, the second-generation includes strange, and charm quarks, and the third generation includes the top and bottom quarks.

All quarks have a baryon number (B = 1/3) and a lepton number (L = 0). The flavor determines certain other unique properties, described in individual descriptions.

The up and down quarks include protons and neutrons present in the nucleus of ordinary matter. They are the lightest and most stable. The heavier quarks are produced in high-energy collisions and rapidly decay into up and down quarks. Thus, for example, a proton is composed of two up quarks and a down quark. A neutron is composed of one up quark and two down quarks.

The numbers that determine the main properties of quarks are summarized in the table below. Remarks!

1. We will discuss charm (C) - an important property of quarks - in the next paragraphs.
2. Do not confuse the baryon number B with bottomness B (this last one represents one of quark's direction of orientation); they represent completely different things despite having the same symbol.

The corresponding antiquarks u,d and s have opposite values to u, s and d for baryon charge, electric charge and strangeness. The elementary particles composed by these three quarks are: protons, neutrons, pions, kaons and especially hyperons. For example, protons are composed by three quarks, uud, as explained earlier. Thus, based on the above table, the electric charge number is

q/e = 2qu + qd
= 2 ∙ 2/3 + (- 1/3)
= 4/3 - 1/3
= 3/3
= 1

This means the electric charge of proton is 1q (as expected). As for the baryon charge (number) of proton, we have:

Bp = 2Bu + Bd
= 2 ∙ 1/3 + 1/3
= 2/3 + 1/3
= 3/3
= 1

This is also a known fact indicated in the table of baryons.

#### Example 1

Calculate the electric, baryon and strangeness numbers of K+ meson, antiproton and π- meson if the corresponding quark compositions are:

Antiproton p = u u d
K+ meson = us
π- meson = u d

Check the results with the values given in the hadrons tables.

#### Solution 1

From the values given in the quarks table, we have:

##### For antiproton:
p ̅= u u d
q/e (p) = 2 ∙ q/e (u) + q/e (d)
= 2 ∙ (-2/3) + [-( - 1/3)]
= - 4/3 + 1/3
= - 3/3
= -1
B(p) = 2B(u) + B(d)
= 2 ∙ (- 1/3) + (- 1/3)
= -3/3
= -1
S(p) = 2S(u) + S(d)
= 2 ∙ 0 + 0
= 0
##### For K+ meson:
K+ = us
q/e (K+ ) = q/e (u) + q/e (s)
= 2/3 + [- (- 1/3)]
= 3/3
= + 1
B(K+ ) = B(u) + B(s)
= 1/3 + (- 1/3)
= 0
S(K+ ) = S(u) + S(s)
= 0 + [-(-1)]
= + 1
##### For >π- meson:
π- = ud
q/e-) = q/e (u-) + q/e (d)
= -2/3 + (- 1/3)
= - 3/3
= -1
B(π-) = B(u-) + B(d)
= -1/3 + 1/3
= 0
S(π-) = S(u-) + S(d)
= 0 + 0
= 0

You can have a check at the baryons table to find out that all the above values correspond to those provided in the table.

The figure below illustrates the quark composition of four hadrons: proton (p), neutron (n), positive pion (π+) and positive kaon (K+). #### Quark Mediators

Since quarks are charged particles, the question that arises here is: "What is the factor that holds them together?" Experiments show that quarks and antiquarks interact with each other by exchanging virtual particles called gluons (from "glue"). They are particles that have the spin equal to 1 and behave in a similar way to photons (through which the electromagnetic interaction is realized) or pions (which are the elementary particles in-charge for the strong interaction in Yukawa theory).

Since quarks have the spin 1/2, they belong to the fermions class (fermion is a subatomic particle, such as a nucleon, which has half-integral spin and follows the statistical description given by Fermi and Dirac). Fermions are subject to the exclusivity principle, i.e. two fermions cannot have more than one quark of the same type. To have a better understanding of quark types, scientists have classified them in "colours". They have proposed three colors to identify various types of quarks: red, green and blue. The exclusivity principle is applied for each color separately. Thus, a baryon composed by three quarks of different colors is colorless in itself as based on the theory of colors in optics, when red, green and blue are combined they give the white light. Each gluon is associated with one color and one anti-color. During the process of absorption or emission of a gluon by a quark, the color is conserved. The process of gluons exchange occurs in such a way that there is always a quark of each color in every individual baryon. However, the color of any specific quark changes continuously. The following figures clarifies this point.

The first figure below shows a pion containing a blue quark and an anti-blue antiquark. In the second figure, the blue quark emits a blue-anti-red gluon, transforming in this way into a red quark. In the third figure, the gluon is absorbed by the anti-blue antiquark, which is transformed into an anti-red antiquark. The pion is already composed by a red quark - antired antiquark pair. The actual quantum state of a pion is a superposition of red-antired, blue-antiblue and green-antigreen pairs. The gluon exchange connects two quarts in a pion, which are always "colored". Let's suppose that initially, a pion is composed by a blue quark and an anti-blue antiquark. The blue quark can emit a virtual bue-antired gluon, turning into a red quark. The gluon at this moment is absorbed by the anti-blue antiquark which gives an anti-red antiquark as shown in the above figures. The color is conserved in every emission and absorption; however, a blue-antiblue pair is transformed into red-antired one. Hence, we assume a pion as a superposition of three quantum states: blue-antiblue, red-antired and green-antigreen. The same process is observed in mesons a as well.

## Charm

Nowadays, the theory of strong interactions is known as quantum chromodynamics (chromo = colors). It is considered as the key to understand strong interactions. Prior to tau particles discovery, only four leptons were known. By analyzing the quarks behavior during various decay processes, made scientists think that there exists another quark still undiscovered at that time. They called it charm, C, which means "fascinating". It has the following values for each type of charge: q = 2/3, B = 1/3, S = 0 and C = + 1.

The existence of charm was confirmed experimentally in 1974, when a heavy meson of mass 3100 MeV/c2 was detected. Nowadays, there are 6 types of quarks known. The following table summarizes all properties of each type of quark. ### Example 2

The Λ0 elementary particle is composed by a u-quark, a d-quark and s-one. What is its electric charge, baryon number, strangeness and charm?

### Solution 2

The composition of this elementary particle is uds. The values required represent the arithmetic sum of each individual quark. Thus, referring to the above table, we obtain the following results.

#### for electric charge:

q/e0) = q/e (u) + q/e (d) + q/e (s)
= 2/3 + (- 1/3) + (- 1/3)
= 0

#### For baryon charge, we have:

B(Λ0) = B(u) + B(d) + B(s)
= 1/3 + 1/3 + 1/3
= 1

#### For strangeness, we have:

S(Λ0) = S(u) + S(d) + S(s)
= 0 + 0 + (-1)
= -1

#### Finally, for charm, we have:

C(Λ0) = C(u) + C(d) + C(s)
= 0 + 0 + 0
= 0

## Main Features of Standard Model

What is standard model?

Nowadays, the physics of elementary particles is a distinct branch of modern physics, despite initially it has been a sub-branch of nuclear physics. It is clear that the term "elementary particles" now is outdated as those particles once considered as elementary in the sense of inseparability resulted as composed by two or three smaller ones. Perhaps, even smaller particles will be discovered in the future and so on. Therefore, the actual frame of elementary particles is temporary. It is known as the "standard model" of structure of matter. This model includes three main families of elementary particles:

• Six leptons not related to the strong interaction;
• Particles that are mediators of various interactions.

We have seen so far gluons as mediators of strong interaction between quarks and photons as mediators of electromagnetic interaction between charged particles. Both gluons and photons are massless and have a boson spin equal to 1.

The other two types of interaction are also mediated by particles. The W+ , W- and Z0 weak bosons are responsible for weak interaction. They are massless bosons having a spin equal to 1.

Actually, there are indications that gravitational interaction is mediated by a boson of spin 2 named graviton (as explained earlier). This elementary particle is difficult to be detected experimentally because it is very weak.

## Symmetry

Symmetry is a very important property of elementary particles that has helped a lot in the progress made in this field of science in the sense that particles not discovered yet have been predicted just by looking the symmetry of the corresponding schemes. One of such schemes involves the eight bosons (8-vertices symmetry) having the value of baryon spin 1/2. They are: protons and neutrons, the family of single-strangeness particles (Λ0, Σ+ , Σ0 and Σ-) and that of double-strangeness particles (Ξ0 and Ξ-). For each particle, the values of electric charge q and strangeness S are shown. The first figure below shows the values of Q and S for half-spin baryons, giving thus the 8-particles symmetric model. The other figure shows the corresponding quarks composing these half-spin baryons. Thus, the quark composition of Λ0 and Σ0 is the same; Σ0 represents an excited state of Λ0 and it can split by emitting gamma radiation (photons).  Another symmetry used to describe how elementary particles are related to each other is the one shown in two following figures, where the values of electric charge q and strangeness S for 9 mesons that have a zero spin are given applying again the same symmetry as before. In this scheme, each particle is in the opposite vertex to its corresponding antiparticle while the three particles at centre of the figure are antiparticles of themselves. The next figure shows the quark composition of each particle involved.  ## Unification of Interactions

The list of fundamental interaction has experienced many changes during various stages of science development. Prior to Newton's work, people didn't have the minimum idea about the weak and strong interactions existence. He was the first who realized that in essence, terrestrial and celestial gravitation are the same thing. Likewise, Maxwell unified the electric and magnetic interaction between charged particle by introducing the idea of electromagnetic interaction.

Scientists have always sought to merge all types of interactions in a single theory known as the theory of universal interaction. The first concrete steps in this regard are made by Einstein, who spent much of his time trying to unify the fields theory, in which gravitational and electromagnetic fields would be included. He was partially successful in his attempts.

Later on (in 1967) a group of scientists proposed the idea of unification of weak and electromagnetic interaction. According to this idea, Z0 particles and W- and W+ bosons (including their corresponding masses as well) are considered as mediators of such interaction. More specifically, this theory supports the idea that the difference in mass between photons (that have zero mass) and weak bosons makes the weak and electromagnetic interaction unaffected by low energy states but very sensible by high energy ones (1 TeV). This theory was confirmed experimentally in 1983.

Likewise, many attempts are made in trying to unify the electro-weak interactions with the strong ones. If confirmed experimentally this unification would be the last stage of the general theory of unification, which will be one of the most important discoveries in science. The scheme below shows the path towards the general theory of unification where the already linked interactions are connected through bold arrows while those still to be confirmed are connected through dashed lines. ## Summary

There are four types of interaction occurring in the universe:

1. Strong interaction. This is an interaction experienced by all elementary particles except leptons, photons and gravitons.
2. Electromagnetic interaction. This is an interaction experienced by all electrically charged elementary particles.
3. Weak interaction. It is present in all types of beta decay, in many elementary particles decay processes, as well as in all processes involving neutrino interaction with matter.
4. Gravitational interaction. This is an interaction experienced by all particles without exception, often neglected when dealing with elementary particles, as it is very weak at this level.

Based on the type of interaction they experience, elementary particles are classified in three major groups:

1. Photons (quants) γ, which are the carriers of EM interaction;
2. Leptons, a group composed by muons, electrons, the two types of neutrino and their corresponding antiparticles. All these elementary particles experience the weak interaction during their lifetime; and
3. Hadrons, responsible for the strong interaction. All particles that experience strong interaction such as protons, neutrons, hyperons and their corresponding antiparticles, mesons with or without strangeness as well as a number of resonances (elementary particles with a very short lifespan) are included in hadrons group. The two major subgroups of hadrons are mesons and baryons.

A quark is one of the fundamental particles in physics. Quarks join to form hadrons, such as protons and neutrons, which are components of the nuclei of atoms. They interact between them mainly through the strong force. Quarks exhibit the confinement property, i.e. a specific quark cannot exist separately but only in pair with another quark. A quark has an electric charge equal to 1/3 or 2/3 of the charge of electron, which was previously thought to be the smallest unit of electric charge. Likewise, quarks have a non-whole baryon number.

There are three generations of quarks, based on pairs of weak positive/negative, weak isospin. The first generation includes the up and down quarks, the second-generation includes strange, and charm quarks, and the third generation includes the top and bottom quarks.

Experiments show that quarks and antiquarks interact with each other by exchanging virtual particles called gluons. They are particles that have the spin equal to 1 and behave in a similar way to photons.

Since quarks have the spin 1/2, they belong to the fermions class that are subject to the exclusivity principle. To have a better understanding of quark types, scientists have classified them in "colours". They have proposed three colors to identify various types of quarks: red, green and blue. The exclusivity principle is applied for each color separately.

By analyzing the quarks behavior during various decay processes, made scientists think that there must exists another quark. They called it charm, C, which means "fascinating". It has the following values for each type of charge: q = 2/3, B = 1/3, S = 0 and C = +1.

The actual frame of elementary particles is temporary as there are many mysteries of micro-world still undisclosed. The actual framework of elementary particles is known as the "standard model" of structure of matter. This model includes three main families of elementary particles:

• Six leptons not related to the strong interaction;
• Particles that are mediators of various interactions.

Symmetry is a very important property of elementary particles that has helped a lot in the progress made in this field of science in the sense that particles not discovered yet have been predicted just by looking the symmetry of the corresponding schemes. The 8-vertices symmetry is often used to describe the structure of elementary particles.

Scientists have always sought to merge all types of interactions in a single theory known as the theory of universal interaction. Despite many attempts made in this direction, this is still a dream.

## Classification of Elementary Particles. Quarks and Charm Revision Questions

1. What are the quarks of negative pion based on the table of quarks shown earlier in this guide if its electric charge is -1 and baryon charge is zero?

1. u and d
2. u and d
3. u, d and s
4. u, s and s

2. Based on the laws of conservation, find the missing elementary particle in the reaction below. Use the tables for info about specific particles.

p + p → Λ0 + K+ + ?
1. P
2. n
3. K-
4. π+

3. The quark composition of a certain elementary particle is uss. What is its strangeness?

1. +1
2. 0
3. -1
4. -2