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# Case Study: Quarks and other Sub-Nucleon Particles

This module was created to better your understanding of quarks and other sub-nucleon particles. Both of these topics fall into the study of particle physics, which is the study of elementary particles that are too small to study directly.

### Introduction

Particle physics is the study of the basic nature of time, space, energy, force and matter. Particle physics mainly deals with elementary particles. The standard model of physics attempts to explain all forces and particles that exist in our universe. These elementary particles that exist in this standard model are too small to study, because they are much smaller than molecules, atoms, protons and neutrons. Scientists are able to study these elementary particles by using particle accelerators. These accelerators collide particles with high energy due to high speeds (almost the speed of light). The data is then analyzed to obtain the results that are all put together to form the standard model.

### Contents

Particle physics follows what is known as the Standard Model. This model includes the most elementary particles, which can combined to form composite particles. All known matter consist of fundamental particles, fermions and bosons, which are not known to have any substructure. Fermions are the most basic building blocks of the universe. The list of fermions contains six quarks and six leptons. The six quarks are: up (u), down (d), charm (c), strange (s), top (t), and bottom (b). The six leptons are: electron (e-), electron neutrino (νe), muon (μ), muon neutrino (νμ), tauon (τ), and tauon neutrino (ντ). Quarks and leptons are categorized together, forming six families and three generations. The generations are labeled to show differences in mass of the particles, organized so that the higher the generation, the higher the mass (i.e. third generation particles have greater mass than the first and second generation). Most atoms in the universe are made up of first generation particles. The other particles are only seen in extremely high energy conditions. All 12 fermions have antiparticles, which are identical in characteristics and mass to their corresponding fermion, but have an opposite electric charge. Bosons are what allow these fermions to interact with each other from a distance. Bosons are the carrier particles of all the forces that exist.

### Quarks

The six different types of quarks are known as flavors. These flavors combine in certain patterns to form many common particles. Each quark has an electrical charge and a spin. The u, c, and t quarks all have charges of +2/3 whereas the d, s, and b quarks all have -1/3 charges. Quarks are classified as spin-1/2 particles, meaning that their spin is either positive or negative 1/2. The heavier quarks (generation II and III) are unstable, therefor they rapidly become u and d quarks through the process of particle decay. Particle decay is the transformation from higher to lower mass states, either by breaking into more particles or by taking the form of energy. This gives us that u and d quarks are the most common in the universe, and are also the most stable.

Categories of Quarks

 Generation I Generation II Generation III Charge +2/3 Up quark (u) Charm quark (c) Top quark (t) -1/3 Down quark (d) Strange quark (s) Bottom quark (b)

Quarks possess what is known as color charge, which include three colors: red, blue, and green. The attraction and repulsion of these color charges are known as strong interactions (see strong nuclear force). Quarks change their color charges as they interact with other quarks. Strong interaction is carried out by a force carrying particle known as a gluon (see gluon), which is a type of massless vector gauge boson (see bosons). Quarks are never observed by themselves due to this strong interaction (see hadrons). Quarks are the only fundamental particles that experience all four fundamental forces.

#### Antiquarks

Categories of Antiquarks

 Generation I Generation II Generation III Charge -2/3 Up antiquark (u) Charm antiquark (c) Top antiquark (t) +1/3 Down antiquark (d) Strange antiquark (s) Bottom antiquark (b)

For every quark there is an antiquark, denoted with a bar above the symbol. Each antiquark is identical to its corresponding quark in all characteristics, including its mass and spin, except for charge which is of opposite sign. Antiquarks possess color charges as well, and these colors are antired, antiblue, and antigreen.

### Leptons

Categories of Leptons

 Charge Generation I Generation II Generation III -1 Electron (e-) Muon (μ−) Tau (τ−) 0 Electron neutrino (νe) Muon neutrino (νμ) Tau neutrino (ντ)

Leptons are spin-1/2 particles, and can spin in one of two directions: up or down. Electrons, muons, and tauons have a -1 electromagnetic charge whereas the neutrino's all have no charge. While electrons, muons, and tauons all have noticeable masses, neutrinos are almost massless (and are very hard to find). The masses of each lepton increase as generation increases. The heavier leptons (generation II and III) are not found in ordinary matter, because they decay very rapidly into lighter, more stable leptons.  Leptons, unlike quarks, are solitary, and are found alone.

Hadrons are particles that are composed of either two or three quarks and/or antiquarks and are held together by the strong strong nuclear force. Despite being formed by quarks that have fractions as charges, hadrons always have integer charges due to the sum of the fractions. The color charge of hadrons sums up to zero, which results in hadrons being colorless or "white". This is because the quarks each have their specific color charge, and when they interact with one another, the color charges cancel each other out leaving the hadron colorless. The most stable hadrons are protons and neutrons. Hadrons are classified as being either a meson or a baryon.

Fig. 1: Pion, formed from an up and an antidown quark.Fig. 2: Neutron, formed from an up and two down quarks.Fig. 3: Proton, formed from a down and two up quarks. (Figure 1-3 courtesy of Arpad Horvath, used with permission from Wikipedia Commons.)

#### Baryons

Baryons consist of three quarks. All baryons have antiparticles known as antibaryons in which each quark is replaced with its corresponding antiquark. The most common types of baryons are protons and neutrons, which make up most of the matter you see around. Protons are made up of two up quarks (+2/3 charge) with one down quark (-1/3), giving the proton a total net charge of +1 (4/3 - 1/3 = 1). Neutrons,on the other hand, are made up of two down quarks with one up quark, giving a total net charge of 0, or neutral (-2/3 + 2/3 = 0).

Fig. 4: Heavy hydrogen, containing one proton, one neutron, and one electron (Original work, courtesy of Michael Norton).

#### Mesons

Mesons are comprised of one quark and one antiquark. The most common mesons are pions (π-, π0, π+) and kaons (K-, K0, K+). Pions are composed of either an up quark with a down antiquark, a down quark with an up antiquark, a down quark with a down antiquark, or an up quark with a up antiquark. Kaons are composed of one strange quark paired with either an up or down quark.

### Fundamental Forces

There are four fundamental forces, which are each responsible for how particles interact with one another and all of the forces that we see around us. Any force you can think of is due to one of these fundamental forces.

• Electromagnetic force: The electromagnetic force is the force between any two charged particles. This force causes similarly-charged particles to attract, and oppositely-charged particles to repel, such as protons and electrons attraction in an atom. This force is why objects don't pass through other objects, since the atoms in the objects do not want to be shoved around when repelled by the other object. This force is also what holds atoms and molecules together. The electrons of one atom can be attracted to the protons of a completely separate atom, causing both of the atoms to bind together. This force acts on quarks, charged leptons, W, and W+.
• Weak nuclear force: The weak nuclear force mediates decay. Weak forces allow for the decay of the more massive quarks, leptons, and neutrinos into the lighter more stable forms. The smallest quarks, leptons, and neutrinos cannot decay any further. The weak force is responsible for radioactive decay and fusion. This force acts on quarks and leptons.
• Strong nuclear force: The strong nuclear force holds quarks together in hadrons (see hadrons) such as protons and neutrons. A strange thing about the strong force is that it actually gets stronger as the quarks get further apart. We are used to forces getting weaker as the two objects get further apart, just like how magnets attract less as they are separated, so it is strange for us to discover that the strong force gets STONGER as the quarks separate. In fact, if the quarks are separated enough, the energy of the force can convert directly into new quarks rather than increasing more in strength! This force acts on quarks and gluons.
• Gravitational force: The gravitational force is proportional to the particle's mass and determines the motion of the planets and galaxy. Gravity is the one fundamental force that physicists cannot yet explain. Luckily, gravity is so weak when compared to the other forces that it can generally be ignored. This force acts on all particles, including bosons.

### Bosons

There are four confirmed bosons, which are force carrier particles for the fundamental forces. Bosons allow particles to interact with other particles, without ever touching. Think of magnets: even when not touching the magnets interact, and can repel or attract one another. Gravity is another good example for bosons: an apple falls to the ground even with nothing between them.

Bosons have integer spin, which is different than the half-integer spins of fermions. All particles fill the space around them with countless numbers of bosons, which exist only briefly and are then replaced. If one or more of these bosons come into contact with the same type of boson but of a different parent particle, they can exchange. This exchanging of bosons is how particles interact, and therefor causes a force on each particle.

#### Photons

Photons (γ) are the force carriers for the electromagnetic force. Photons can have different levels of energy which all together form the electromagnetic spectrum. Photons travel at the speed of light (c), which is about 3×108 meters per second. This boson is massless, allowing for it to have an infinite range of interaction. The photon interacts with quarks, charged leptons, W, and W+.

#### W Boson

W bosons (W, W+) are force carriers for the weak nuclear force, are electrically charged, and are very massive (almost a hundred times heavier than a proton). Since they are so massive, they are limited to a small range of interaction. The emission of this boson can either raise or lower the electric charge of the parent particle, due to the W boson being electrically charged. This boson interacts with quarks and leptons.

#### Z Boson

Z bosons (Z) are also force carriers for the weak nuclear force, are neutral, and are very massive (almost a hundred times heavier than a proton). Since they are so massive, they are limited to a small range of interaction. With no electric charge, the emission of a Z boson does not alter the electric charge of the parent particle. This boson interacts with quarks and leptons.

#### Gluons

Gluons (g) are the force carriers for the strong nuclear force. They carry a color charge just like quarks do. When two or three quarks are close to each other, they exchange gluons forming a strong color force field which binds the quarks together. When a quark absorbs or emits a gluon, the color charge of the quark changes to a new color charge depending on the color charge of the gluon. In hadrons, the colors of the quarks are constantly changing, but always in a way so that the hadron remains color-neutral. This boson interacts with both quarks and bosons.

#### Theoretical Bosons

There are several theorized bosons to help describe other events and relationships that occur in the universe. These bosons have not yet been discovered, but are still predicted to exist.

##### Higgs Boson

The Higgs boson (H0) is predicted to give mass to all massive particles. This boson is predicted to be extremely massive itself, and attempts are being made to discover it using the LHC (see particle accelerators). It is theorized that when particles interact with the Higgs boson, they obtain mass, and that when particles ignore the Higgs boson, they are massless.

##### Graviton

The graviton (G) is predicted to be the force carrier for the gravitational force. The force carrier for the gravitational force has not yet been found, yet is predicted to exist, and will help with the explanations of gravity. The graviton is predicted to interact with all fundamental particles.

### Particle Accelerators

It use to be the belief that protons, neutrons, and electrons were the smallest particles in the universe until the invention of the particle accelerator. Particle accelerators were first invented in the 1930s, and have since transformed into some of the most impressive and groundbreaking machines in the world. Today's most powerful particle accelerator is the Large Hadron Collider (LHC). This is a 27 km circular tunnel in Europe that shoots particles up to more than 99.999999% the speed of light. How do these machines apply to particle physics and elementary particles? The tunnel uses superconducting magnets and huge amounts of energy (as high as 1 trillion electronvolts) to send particles racing around the circular track. They often send electrons in one direction and either hydrogen nuclei, hadrons, or entire atoms in the opposite direction until they collide with each other. These collisions occur inside detectors that are placed at intervals in the tunnel.

Fig. 5: Particle accelerator's detector showing a proton colliding with an antiproton (Courtesy of Famargar, used with permission from Wikipedia Commons.)

The elaborate and often spectacular collisions are what scientists use to determine that quarks and other particles smaller than electrons, protons, and neutrons exist. The different color patterns and schemes of the collisions allow scientist to determine spin, charge, and momentum of the particles in the collision.

### References

1. Hurtado, K., Romero, C., and Salinas, Solano. Introduction to Elementary Particle Physics. Google Docs. 2005 pg 1-7.
2. Smith, Timothy P. Hidden Worlds: Hunting for Quarks in Ordinary Matter. Princeton University Press, 2005. Print.
3. Harris, Randy. Modern Physics Second Edition. Pearson Addison Wesley, 2008. Print.
4. Petrucci, Ralph H, et al. General Chemistry Custom Edition for CHEM 2. Pearson Learning Solutions, 2011. Print.

### Problems

Problem 1

Name all of the six leptons.

Problem 2

Name all of the six quarks.

Problem 3

Which two quarks are the lightest, most stable, and most common in the universe?

Problem 4

What are the two most common types of mesons?

Problem 5

How many, and what types of quarks are protons made up of?

Problem 6

(True/False) Particle accelerators send all projectiles in the same direction through the tunnel.

Problem 7

Which is not one of the colors in color charges: A) green B) orange C) red D) blue

Problem 8

What hadron is composed of two down quarks, and one up quark?

Problem 9

Which fundamental force is carried by the photon: A) gravitational B) electromagnetic C) weak nuclear force D) strong nuclear force

Problem 10

Which fundamental force is responsible for planetary orbits?

Problem 11

Why can't quarks be alone?

Problem 12

Name two theoretical bosons, and what they are responsible for?

Problem 13

Is it predicted that the Higgs boson interacts with photons?

Problem 14

What fundamental force is responsible for the attraction and repulsion of magnets?

Problem 15

What fundamental force is responsible for the decay of generation II and III particles into generation I particles?

Problem 16

If a new particle is discovered to have an integer spin, would it be categorized as a fermion or boson?

Problem 17

What could be the color charge of the two quarks in a meson for it to remain color neutral?

Problem 18

What could be the color charge of the three quarks in a baryon for it to remain color neutral?

1. Electron (e-), electron neutrino (ve), muon (m-), muon neutrino (vm), tauon (T-), and tauon neutrino (vT).
2. Up (u), down (d), charm (c), strange (s), top (t), and bottom (b).
3. The up and the down quark.
4. Pions and kaons.
5. Two up quarks and one down quark.
6. False, they send projectiles both directions through the tunnel.
7. B) orange
8. The neutron, with a net charge of 0, is composed of two down quarks and one up quark.
9. B) electromagnetic
10. Planets orbit the sun due to the gravitational force.
11. Quarks are never alone because the color force field increases in strength as distance is increased. If they are separated far apart enough, the energy of the color force field may actually convert to new quarks.
12. The graviton and Higgs boson are both undiscovered. The graviton should be responsible for the gravitational force. The Higgs boson should be responsible for the mass of massive objects.
13. No, because photons are massless, they most not interact with the Higgs boson.
14. The electromagnetic force causes magnets to interact.
15. The weak nuclear force causes unstable particles to decay into more stable particles.
16. Since the particle has an integer spin, it would be categorized as a boson. This new particle could even be the graviton or Higgs boson!
17. The possible combinations of color charges are green-antigreen, red-antired, and blue-antiblue.
18. The only possible combination of color charges is green, red, and blue. This is because for quarks to interact, they must have different color charges, and since there are only three color charges, each of the three quarks must be one of the three different colors.

### Contributors

• Ben Havemann (UCD), Michael Norton (UCD)