Physics Lournal

Particle Physics (CERN Lectures)

1. Introduction to Particle Physics

The purpose of these lectures is to consider the fundamental question of science: What are the fundamental building blocks of the universe, from which everything is constructed?.

In the 20th century, a remarkable amount of progress towards the answer to this question was made: everything could be described in terms of particle interactions, which were due to forces, packaged up unto the The Standard Model.

The Structure of the Atom

Before atoms, or nuclei or elementary particles, science made sense of chemistry, with the understanding starting with the work of John Dalton, and the law of multiple proportions, which states the quantities used for combining elements should be integer quantities.

This presentation become more robust due to Mendelev's development of the structure of the periodic table, placing the elements in order of mass, grouped together by their known properties.

The table had gaps in it, which he found to be elements that were not discovered as of yet.

The importance of the periodic table in physics is that it gives hints about what may lie under it, suggesting a structure of the atom, with the atomic number telling us where the atom belongs in the table, and the atomic weight telling us the mass of the atom.

A concrete step in this direction was made by J.J Thomson, with his discovery of the Electron.

After this, was a 35 year period of work, a large portion of which was done by Rutherford, as well as some of his contemporaries, made it clear that the atom had a nucleus, which was in some way, orbited, by the electrons, with the nucleus being comprised of neutrons and protons.

The atomic number counts the number of protons in the nucleus, and the atomic weight counts the number of neutrons and protons.

Electrons carry negative charge, and the protons carry positive charge, and the magnitude of the charge of the proton, is exactly that of the electron.

The nucleus is tiny in size compared to the entirety of the atom, which has a size of $\approx 10^{-10}m$ , while nuclei are roughly $10^{-15}m$ , though the nuclei contains most of the mass of the atom, because the electron is the lightest constituent of the atom:

$m_{\text{electron}} \approx 9.1 \times 10^{-31}kg$ .

The proton and neutron are $\footnotesize \approx 2000$ times larger:

$m_{\text{proton}} \approx 1837 \times m_{\text{electron}}$ .

$m_{\text{neutron}} \approx 1839 \times m_{\text{electron}}$ .

This presents a much simpler situation at first, with the entirety of the periodic table being reduced to three particles, however it was soon discovered that there are anti-particles, and much more after that.

The Structure of the Structure

The history of the understanding of the structure of matter is rich, and varied, but around 1932, there was a very simple picture: the electron as fundamental, and the proton and neutron are composite.

Generally speaking, the Neutron and Proton are composed of Quarks, of two different varieties, the Up Quark, and the Down Quark.

Protons are built of two up quarks and a down quark, and the neutron is the exact opposite, and these quarks have fractional charge that leads to the integer charge of composite particles.

There's also the neutrino, which rarely interacts with other particles, having a very low mass, and no electric charge.

What's peculiar about this is that, these particles seem to have been copied twice over by nature: there are two copies of the electron, the muon and tau, with 207 and 3483 electron masses respectively.

Additionally, there are two extra neutrinos, and four additional quarks.

These are referred to as the generations of matter, each containing an electron like particle, two quarks, and a neutrino, leaving us with 12 matter particles.

Forces

All of these particles interact via a number of forces, known as the Four Fundamental Forces, though arguably there are five, if you consider the interactions with the Higgs boson.

Gravity was the first force to be discovered, but ironically, may be the one we understand least, and to date, is best explained by General Relativity.

Electromagnetism is familiar because it can be observed at the classical scale, and is the source of chemical properties of elements.

The Strong force has no classical counterpart, and binds quarks together to form protons and neutrons, and binds protons and neutrons together to form atomic nuclei.

The Weak force primarily accounts for particles decaying into other particles, via the ejection (or creation) of other particles.

Technically, at the fundamental level, electromagnetism is more accurately described as a combination of hypercharge and the weak force.

See: Electroweak Unification.

The Higgs force has no classical analogue, but it plays an extremely important role, in that it gives the elementary particles their mass.

1.1 Quantum Fields

Particle physics is technically not about particles, but rather about fields.

Mathematically, these fields are functions $E(x,t), B(x, t)$ , which can have different values at different points

in space ( $x_i$ ) and different points in time ( $t_i$ ).

This concept becomes more intriguing with the introduction of quantum mechanics, which tells us that some properties of reality can't take on continuous values, only discrete ones.

The combination of fields and quantum implies that the waves that comprise light are not continuous (like waves on the beach), consisting of parcels of energy, known as photons.

This also holds for every other particle: every force has a field, and the ripples of the field are particles.

The electromagnetic force is associated with the photon, denoted by $\gamma$ .

The Strong force is associated with the Yang-Mills field, for which the particles are gluons.

The Weak force is also associated with a Yang-Mills field, and gives us the W & Z Bosons.

The Higgs force, is associated with the Higgs field, and the particle associated is the Higgs Boson.

The Gravitational force is unique in that the associated field is actually spacetime, and while the ripples (gravitational waves) have been observed, the hypothesized associated particle, the graviton, has not.

Implications of Quantum Fields

1.2 Natural Units

Particle Physics (CERN Lectures)

Particle Physics (CERN Lectures)

1. Introduction to Particle Physics

The purpose of these lectures is to consider the fundamental question of science: What are the fundamental building blocks of the universe, from which everything is constructed?.

In the 20th century, a remarkable amount of progress towards the answer to this question was made: everything could be described in terms of particle interactions, which were due to forces, packaged up unto the The Standard Model.

The Structure of the Atom

Before atoms, or nuclei or elementary particles, science made sense of chemistry, with the understanding starting with the work of John Dalton, and the law of multiple proportions, which states the quantities used for combining elements should be integer quantities.

This presentation become more robust due to Mendelev's development of the structure of the periodic table, placing the elements in order of mass, grouped together by their known properties.

The table had gaps in it, which he found to be elements that were not discovered as of yet.

The importance of the periodic table in physics is that it gives hints about what may lie under it, suggesting a structure of the atom, with the atomic number telling us where the atom belongs in the table, and the atomic weight telling us the mass of the atom.

A concrete step in this direction was made by J.J Thomson, with his discovery of the Electron.

After this, was a 35 year period of work, a large portion of which was done by Rutherford, as well as some of his contemporaries, made it clear that the atom had a nucleus, which was in some way, orbited, by the electrons, with the nucleus being comprised of neutrons and protons.

The atomic number counts the number of protons in the nucleus, and the atomic weight counts the number of neutrons and protons.

Electrons carry negative charge, and the protons carry positive charge, and the magnitude of the charge of the proton, is exactly that of the electron.

The nucleus is tiny in size compared to the entirety of the atom, which has a size of ≈10−10m\approx 10^{-10}m≈10−10m, while nuclei are roughly 10−15m10^{-15}m10−15m, though the nuclei contains most of the mass of the atom, because the electron is the lightest constituent of the atom:

melectron≈9.1×10−31kgm_{\text{electron}} \approx 9.1 \times 10^{-31}kgmelectron​≈9.1×10−31kg.

The proton and neutron are ≈2000 \footnotesize \approx 2000 ≈2000 times larger:

mproton≈1837×melectronm_{\text{proton}} \approx 1837 \times m_{\text{electron}}mproton​≈1837×melectron​.

mneutron≈1839×melectronm_{\text{neutron}} \approx 1839 \times m_{\text{electron}}mneutron​≈1839×melectron​.

This presents a much simpler situation at first, with the entirety of the periodic table being reduced to three particles, however it was soon discovered that there are anti-particles, and much more after that.

The Structure of the Structure

The history of the understanding of the structure of matter is rich, and varied, but around 1932, there was a very simple picture: the electron as fundamental, and the proton and neutron are composite.

Generally speaking, the Neutron and Proton are composed of Quarks, of two different varieties, the Up Quark, and the Down Quark.

Protons are built of two up quarks and a down quark, and the neutron is the exact opposite, and these quarks have fractional charge that leads to the integer charge of composite particles.

There's also the neutrino, which rarely interacts with other particles, having a very low mass, and no electric charge.

What's peculiar about this is that, these particles seem to have been copied twice over by nature: there are two copies of the electron, the muon and tau, with 207 and 3483 electron masses respectively.

Additionally, there are two extra neutrinos, and four additional quarks.

These are referred to as the generations of matter, each containing an electron like particle, two quarks, and a neutrino, leaving us with 12 matter particles.

Forces

All of these particles interact via a number of forces, known as the Four Fundamental Forces, though arguably there are five, if you consider the interactions with the Higgs boson.

Gravity was the first force to be discovered, but ironically, may be the one we understand least, and to date, is best explained by General Relativity.

Electromagnetism is familiar because it can be observed at the classical scale, and is the source of chemical properties of elements.

The Strong force has no classical counterpart, and binds quarks together to form protons and neutrons, and binds protons and neutrons together to form atomic nuclei.

The Weak force primarily accounts for particles decaying into other particles, via the ejection (or creation) of other particles.

Technically, at the fundamental level, electromagnetism is more accurately described as a combination of hypercharge and the weak force.

See: Electroweak Unification.

The Higgs force has no classical analogue, but it plays an extremely important role, in that it gives the elementary particles their mass.

1.1 Quantum Fields

Particle physics is technically not about particles, but rather about fields.

The most familiar fields the electric and magnetic, which are related to the electromagnetic force, and can be thought of as containing vectors, one for every point in space (and time).

Mathematically, these fields are functions E(x,t),B(x,t)E(x,t), B(x, t)E(x,t),B(x,t), which can have different values at different points

This concept becomes more intriguing with the introduction of quantum mechanics, which tells us that some properties of reality can't take on continuous values, only discrete ones.

The combination of fields and quantum implies that the waves that comprise light are not continuous (like waves on the beach), consisting of parcels of energy, known as photons.

This also holds for every other particle: every force has a field, and the ripples of the field are particles.

The electromagnetic force is associated with the photon, denoted by γ\gammaγ.

The Strong force is associated with the Yang-Mills field, for which the particles are gluons.

The Weak force is also associated with a Yang-Mills field, and gives us the W & Z Bosons.

The Higgs force, is associated with the Higgs field, and the particle associated is the Higgs Boson.

The Gravitational force is unique in that the associated field is actually spacetime, and while the ripples (gravitational waves) have been observed, the hypothesized associated particle, the graviton, has not.

Implications of Quantum Fields

1.2 Natural Units

The nucleus is tiny in size compared to the entirety of the atom, which has a size of $\approx 10^{-10}m$ , while nuclei are roughly $10^{-15}m$ , though the nuclei contains most of the mass of the atom, because the electron is the lightest constituent of the atom:

$m_{\text{electron}} \approx 9.1 \times 10^{-31}kg$ .

The proton and neutron are $\footnotesize \approx 2000$ times larger:

$m_{\text{proton}} \approx 1837 \times m_{\text{electron}}$ .

$m_{\text{neutron}} \approx 1839 \times m_{\text{electron}}$ .

Mathematically, these fields are functions $E(x,t), B(x, t)$ , which can have different values at different points

The electromagnetic force is associated with the photon, denoted by $\gamma$ .