Particle Physics

CERN Lectures

David Tong
Department of Applied Mathematics and Theoretical Physics,
Centre for Mathematical Sciences,
Wilberforce Road,
Cambridge, CB3 OBA, UK

http://www.damtp.cam.ac.uk/user/tong/particlephysics.html
d.tong@damtp.cam.ac.uk
Recommended Books and Resources

There are a number of textbooks and semi-popular books that hit roughly the right
level. First the semi-popular:

• Tini Veltman, “Facts and Mysteries in Elementary Particle Physics”

A straightforward book describing the essentials of the particle physics with some his-
torical anecdotes thrown in for colour. Veltman won the Nobel prize with Gerard ’t
Hooft for demonstrating the renormalisability of the Standard Model.

• Abraham Pais, “Inward Bound”

A spectacularly detailed book, covering discoveries in particle physics throughout the

20th century by a scientist who had a ringside seat for many of the key developments.
Pais was no slouch as a physicist, providing important classification schemes for parti-
cles, naming both “baryons” and “leptons” and, with Gell-Mann, the first to understand
the mixing of neutral kaons. On the flip side, he also coined the wildly inappropriately
modest name “The Standard Model”. (And he didn’t even capitalise it.)

If you want more mathematical meat, then there are a few books that require a
knowledge of quantum mechanics but fall short of using the full machinery of quantum
field theory. Two good ones are:

• Halzen and Martin, “Quarks and Leptons”

• David Griffiths, “Introduction to Elementary Particles”

Contents
1 Introduction 3
1.1 Quantum Fields 11
1.2 Natural Units 15

A Interlude: The Road to Discovery 20

A.1 Ray Physics 20
A.2 The Electron 23
A.3 The Proton 25
A.4 The Neutron 27

2 A First Look at Quantum Fields 30

2.1 Matter Fields and Force Fields 30
2.1.1 Spin 31
2.1.2 The Dirac Equation 32
2.1.3 Anti-Matter 33
2.1.4 Massless Particles 37
2.2 Quantum Electrodynamics 38
2.2.1 Feynman Diagrams 41
2.2.2 What is a Feynman Diagram Really? 44
2.2.3 New Particles From Old 47
2.3 Renormalisation 48
2.3.1 The Long, Confusing History of Renormalisation 51

B Interlude: Looking to the Sky 55

B.1 The Positron 56
B.2 Expecting a Meson 59
B.3 The Muon and the Pion 60
B.4 The Beginning of the Deluge 63

3 The Strong Force 65

3.1 Yang-Mills Theory 65
3.1.1 Gluons and Asymptotic Freedom 67
3.1.2 The Mass Gap 71
3.2 Quarks 72
3.2.1 Colour 75

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 3.2.2 A First Look at Mesons and Baryons 75
3.3 Baryons 77
3.3.1 Protons and Neutrons 77
3.3.2 Delta Baryons 79
3.3.3 Strangeness 80
3.3.4 The Eightfold Way 82
3.4 Mesons 84
3.4.1 Pions 84
3.4.2 The Eightfold Way Again 86

C Interlude: The Rise of the Machine 90

C.1 The Cyclotron 90
C.2 The Synchrotron 96
C.3 Quarks 101

4 The Weak Force 111

4.1 The Structure of the Standard Model 112
4.1.1 Parity Violation 112
4.1.2 A Weak Left-Hander 114
4.1.3 A Perfect Jigsaw 118
4.2 The Higgs Field 121
4.2.1 The Higgs Potential 122
4.2.2 W and Z Bosons 127
4.2.3 Weak Decays 129
4.3 Flavours of Fermions 136
4.3.1 Yukawa Interactions 136
4.3.2 Symmetry Breaking 138
4.3.3 Quark Mixing 141
4.3.4 CP Violation and Time Reversal 146
4.3.5 Conservation Laws 149
4.4 Neutrinos 154
4.4.1 Neutrino Masses 155
4.4.2 Neutrino Oscillations 161

D Interlude: Big Science for Weak Things 167

D.1 The Neutrino 168
D.2 Not P and Not CP Either 172
D.3 The Bosons of the Weak Force 176

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 D.4 Neutrino Oscillations 182

5 What We Don’t Know 188

5.1 Beyond the Standard Model 190
5.1.1 Unification 191
5.1.2 The Higgs Potential 197
5.1.3 A Bit of Flavour and Strong CP 205
5.2 Gravity 209
5.2.1 Quantum Gravity 212
5.3 Cosmology 217
5.3.1 The Cosmological Constant 218
5.3.2 Dark Matter 223
5.3.3 Baryogenesis 227
5.3.4 Primordial Fluctuations 228

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 Acknowledgements

Every summer, CERN plays host to a cohort of university students from around the
world. The students come from a range of backgrounds, from theoretical and experi-
mental physics, to computing, engineering and mathematics. They spend the summer
working on some of the CERN experiments, while taking a number of crash courses
designed to get them up to speed with the CERN mission.

These lecture notes form the introduction to the CERN course. They cover the ba-
sics of particle physics and are designed to be accessible to students with any scientific
background. This means that, despite the advanced topics, the notes require signif-
icantly less mathematical sophistication than my other lecture notes. Sadly there is
a price to be paid, and this comes in the form of facts. Lots and lots of facts. But
particle physics is a subject where it helps to know what you’re getting yourself into
before you meet the somewhat daunting mathematics. These lectures should hopefully
give you a flavour of what awaits in more detailed courses.

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1 Introduction
The purpose of these lectures is to address one of the oldest questions in science: what
are we made of? What are the fundamental building blocks of the universe from which
you, me, and everything else are constructed?

In the twentieth century, progress in addressing this question was nothing short of
spectacular. By the time the dust had settled, we were left with a remarkably simple
picture: every experiment that we’ve ever performed can be explained in terms of a
collection of particles interacting through a handful of forces. The theory which ties
all of this together is the pinnacle of 350 years of scientific endeavour. It is, by any
measure, the most successful scientific theory of all time. Yet we give it a rubbish
name: it is called the Standard Model.

These lectures have two, intertwined narratives. The main thread describes the
contents and structure of the Standard Model. The language in which the Standard
Model is written is known as quantum field theory, and much of our initial focus will be
on describing this framework, and the way it forces upon us certain inescapable facts
about the universe. As we proceed, the emphasis will be on the key theoretical ideas
that underpin the Standard Model and more detailed descriptions of the particles and
the forces that make up our world.

Many of the ideas that we will meet are abstract and counterintuitive and they
took physicists many decades to understand. It is striking that, at nearly every step,
what ultimately lead physicists in the right direction was experiment. Sometimes these
experiments simply confirmed that theorists were on the right path, but more often
they came as a surprise, forcing physicists in entirely new directions.

The second thread of these lectures is to describe these experimental advances, and
attempt to connect them to the more theoretical ideas. With this goal in mind, each
chapter ends with an accompanying “Interlude” in which we take a more historical tour
through the subject, describing some of the key experimental results, along with some
of the confusions that plagued the physicists of the time.

Finally, it is clear that the Standard Model is not the last word, and we will see
what questions it fails to answer. In last Section we raise some of the outstanding open
problems and speculate a little on what lies beyond.

In the remainder of this extended introduction, we will give a whirlwind tour of the
Standard Model, painting the big picture by omitting many many details. As these

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lectures progress, we will fill in the gaps. Much of the theory sits on an excellent footing,
in the sense that we now know that some aspects of the laws of physics could not be
any di↵erent: many details are forced upon us by mathematical consistency alone. In
contrast, other parts of the theory remain mysterious and it is unclear why the world
appears one way, rather than another.

The Structure of the Atom

Before our forefathers understood atoms, or nuclei, or elementary particles, they un-
derstood chemistry. And this is where our story starts.

Our modern, scientific understanding of the structure of matter begins the the
chemist John Dalton and his “law of multiple proportions”. This is the observation
that, when mixing elements together to form di↵erent compounds, you should do so
in integer amounts. So, for example, you can combine carbon and oxygen to form one
type of gas, but it you want to make a di↵erent type of gas then you need exactly
double the amount of oxygen.

That’s surprising. It’s not, for example, what happens when you bake. If you’ve
discovered the perfect amount of flour to get a bagel, then doubling it does not give
sourdough. That’s not the way things work. Dalton understood the importance of his
observation which he interpreted, correctly, as evidence for the old ideas of Leucippus
and Democritus who argued that matter is made of indivisible objects called atoms.

These days, the idea of atoms is sewn into the names that we give to the gases. Add
carbon and oxygen in equal measure and you get carbon monoxide (CO). Double the
oxygen and you get carbon dioxide (CO2 ). But there’s no such thing as COp2 because
p
you can’t have 2 oxygen atoms attached to each carbon atom.

A fuller picture came with Mendelev’s arrangement of the elements in the pattern
known as the periodic table. In 1867, he placed the elements in (roughly) order of their
mass, grouped together based on their observed properties. Mendelev realised that the
gaps in his table were opportunities, rather than flaws: they were elements that were
yet to be discovered. In this way, he predicted the existence of germanium, gallium
and scandium. It would not be the last time that a theorist was able to predict the
existence of a new, seemingly fundamental, particle.

From the perspective of a chemist, the periodic table is important because it places
elements in groups with similar behaviour. Those elements on the left of the table go fizz
when you put them in water. Those on the right don’t. However, from the perspective
of fundamental physics, the importance of the periodic table can be found in the clues

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Figure 1. The periodic table of elements. (Image from Wikipedia.) We can now do better.

it gives us for what lies beneath. By Mendelev’s time, it had long been understood that
elements are made of atoms. The name atom was optimistically derived from the Greek
“atomos”, meaning “indivisible”. The order in the periodic table suggests a structure
to the atoms. The elements are labelled by two numbers. The atomic number Z is an
integer and tells where the atom sits in the table. The atomic weight A tells us the
mass of the atom and, for the first few elements in the table, is very close to an integer.
We now know that both of these numbers have their origin in the fact that atoms are
very much divisible.

Concrete progress came in 1897 when JJ Thomson discovered the particle that we
now call the electron. He announced the discovery to a stunned lecture room at the
Royal Institution in London. Thomson later recalled that one of the distinguished
scientists in the audience told him that he thought the whole thing was a hoax.

It took another 35 years to unravel the full structure of the atom, with much of the
work done by Ernest Rutherford and his colleagues. By the time the dust had settled,
it was clear that each atom consists of a nucleus, surrounded by a somewhat blurry
cloud of electrons. The nucleus itself is comprised of two further particles, the proton
and neutron. The atomic number Z counts the number of protons in the nucleus; the
atomic weight A counts (roughly) the combined number of protons and neutrons.

The electrons carry electric charge. By convention, the charge is taken to be negative,
an annoying choice that you can blame on Benjamin Franklin, one of the founding

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fathers of the US. The protons carry positive charge. The neutrons are, as their name
suggests, neutral. Remarkably, but importantly, the magnitude of the charge of the
proton is exactly the same as the electron; they di↵er only in sign. Atoms contain an
equal number of electrons and protons and so are themselves neutral.

The nucleus sits at the heart of the atom, but is tiny in comparison. Atoms have
a typical size of 10 10 m, while the nuclei have a typical size of 10 15 to 10 14 m.
Rutherford himself used the analogy of a fly in the centre of a cathedral. Despite its
small size, the nucleus contains nearly all the mass of the atom. This is because the
protons and neutrons are much heavier than the electron. We will learn more about
the properties of particles later, but for now we’ll just mention that the mass of the
electron is
31
melectron ⇡ 9.1 ⇥ 10 kg

(The kilogram is a useful unit when weighing humans. Less so for elementary particles.
We’ll meet a better unit shortly.) Both the proton and neutron are roughly 2000 times
heavier. Or, more accurately,

mproton ⇡ 1837 melectron

mneutron ⇡ 1839 melectron

The fact that the masses of the proton and neutron are so close remains something of a
mystery. As we will later see, it is closely related to the fact that two smaller particles
called quarks have almost negligible masses but this, in turn, is not something that we
can explain from more fundamental arguments. Nonetheless, the approximate equality
mproton ⇡ mneutron is important and is the reason that the atomic weights A are so
close to integers for the light elements. For now, these numbers simply tell us that the
electrons contribute less than 0.1% of the mass of an atom.

The story above paints a much simpler picture of the structure of matter than that
proposed by Mendelev. At the fundamental level, the complicated periodic table can
be replaced by something significantly simpler. It would appear that we need just three
particles to explain the elements. They are:

Electron Proton Neutron

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Figure 2. The proton, shown on the left, contains two up quarks and a down quark. The
neutron, shown on the right, contains two down and an up.

Sadly physicists had less than 100 days to enjoy this simple picture! The neutron was
the last of the three particles to be discovered. That happened in May 1932. In August
of the same year, anti-matter was discovered and subsequent discoveries then came
thick and fast. We now know that the sub-atomic world contains many riches beyond
the three obvious particles that can be found in atoms.

The Structure of the Structure of the Atom

The history of how we understood the structure of matter is long, complicated and
confusing and will be told in part as these lectures progress. But, at first blush, the
end result seems to be not much more complicated than that of the rosy picture that
scientists had in early 1932. For all we can tell, the electron remains as a fundamen-
tal particle. In contrast, neither the proton nor the neutron are fundamental. Each
contains smaller particles known as quarks. A cartoon version (we’ll do better later)
says that the proton and neutron each consist of three quarks that, in turn, come in
two di↵erent varieties. They are called the up quark and the down quark. The names
are not particularly evocative: there is nothing “up” nor “down” about either of the
quarks.

The proton contains two up quarks and a down quark, while the neutron contains
two down quarks and an up. Both quarks have fractional electric charge. In units in
which the electron has charge 1, the up quark has charge + 23 and the down quark
charge 13 . This then gives the familiar charges of the proton ( 23 + 23 13 = +1) and
the neutron (- 13 13 + 23 = 0).

In addition, there is a further, neutral particle called the neutrino. This is not one of
the building blocks from which we’re made but, as we shall see, has an important role
to play in the universe. The neutrino carries no electric charge and is much lighter than
all the other particles. It is usually introduced with the epithet “elusive”: it barely

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interacts and can travel through a lightyear of lead with only a 50% chance of hitting
anything.

This, then, leaves us with our new periodic table, a world with just four particles:

One might have thought this was a good place to stop. However, at this stage, some-
thing strange happens. For reasons that we don’t understand, Nature chose to take
this pattern of four particles and repeat it twice over. The total number of particles of
this type that we know about in the Universe isn’t 4, but 12.

In addition to the electron, there are two further particles. They behave like the
electron in every possible way. For example, they have the same electric charge and, as
we will see later, the same interactions with other forces. The only way in which they
di↵er from the electron is that they’re heavier. They are called the muon and the tau
(pronounced to rhyme with “now”). They have masses

mmuon ⇡ 207 melectron

mtau ⇡ 3483 melectron

Similarly, there are two extra neutrinos and four extra quarks. The neutrinos inherit
their name from the corresponding electron-like particle: we talk of “electron neutrinos”
and “muon neutrinos” and “tau neutrinos”. The quarks in the second group are called
strange and charm. There was a brief time when physicists toyed with the idea of
naming the third group of quarks beauty and truth. The latter was subsequently rejected
out of a well-placed sense of embarrassment, but the names that remain in their place,
bottom and top, are astonishingly dull1 . This, then, is the final pattern of particles that
we find ourselves with:
1
Nearly everyone now refers to the b quark as bottom. One exception is LHCb, an important
experiment at CERN devoted to the study of b quarks. They prefer the older name, presumably
because they would rather be LHC-beauty than LHC-bottom. The obvious suggestion that they
embrace both names and rebrand themselves LHCbb has gone sadly unheeded.

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The numbers in the table are the masses of the particles, written as multiples of the
electron mass. (Hence the electron itself is assigned mass 1.) The masses of the
neutrinos are known to be very small but, otherwise are only constrained within a
window and not yet established individually.

Each horizontal line of this diagram is called a generation. Hence, each generation
consists of an electron-like particle, two quarks, and a neutrino. The statement that
each generation behaves the same means that, among other things, the electric charges
of all electron-like particles in the first column are 1 (in appropriate units); the electric
charges of all quarks in the second column are 13 and all those in the third column
+ 23 . All neutrinos are electrically neutral.

We understand aspects of this horizontal pattern very well. In particular, various

mathematical consistency conditions tell us that the particles must come in a collective
of four particles, and their properties are largely fixed. In particular, we understand
why the particles have the electric charges that they do: this is forced upon us by the
mathematics and they simply can’t be anything else. Moreover if, one day, we were
to find a fourth species of electron-like particle, then we can be sure that there are
also two further quarks and a neutrino to discover as well. We’ll describe this more in
Section 4.

We don’t, however, understand the observed pattern of masses. More importantly,

we don’t understand the vertical direction in the pattern at all. We don’t understand
why there are 3 generations in the world and not, say, 17. Nonetheless, we know from
both particle physics and from cosmological observations that there are no more than 3

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light neutrino species. If there is an undiscovered fourth generation then the neutrino
must be much much heavier (by a factor of about 1010 !) than the neutrinos in the
existing generations. This is highly suggestive that the story stops at three.

The 12 particles listed above are all the “matter particles” that we have so-far dis-
covered in the universe. Each has some fairly intricate properties that we will learn as
these lectures progress. In particular, each particle has a corresponding anti-particle,
and both the particles and anti-particles decompose further into “left-handed” and
“right-handed” pieces. We will describe all this in Section 2.

Forces
All the particles that we described above interact through a handful of forces. It’s
usually said that there are four fundamental forces at play in the universe. In fact, by
any logical count, we should say that there are five forces, with the interaction of the
Higgs boson providing the fifth.

The traditional four forces of Nature are:

• Gravity: This was the first force to be discovered and, in many ways, the one
we understand least. The e↵ects of gravity are very familiar: it’s the reason why
apples fall from trees and tides wash in and out. It’s the reason why planets
orbit stars, and stars form galaxies, and the reason why these are all dragged
inexorably apart by the expansion of the universe. Our best theory of gravity
was given to us by Einstein: it is the theory of General Relativity.

• Electromagnetism: Like gravity, this force is familiar because it manifests itself

in the macroscopic world, where it is harnessed for much of modern technology.
On the atomic level, it is the electromagnetic force, acting between the electrons
in an atom, that give rise to the chemical properties of the elements.

• Strong Nuclear Force: This force has no counterpart in classical physics. It is

responsible for binding quarks together inside protons and neutrons and, subse-
quently, for binding protons and neutrons together as nuclei.

• The Weak Nuclear Force: Another force that manifests itself only on very small
scales. Its primary role is to allow certain particles to decay into other particles.
For example, beta radiation, in which a neutron decays into a proton, electron
and anti-neutrino occurs because of the weak force.

The story above contains a little bit of a lie. At the fundamental level (meaning
at the shortest distance scales), the force of electromagnetism should be replaced by

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something called hypercharge. It’s not dissimilar to electromagnetism, but it di↵ers
in details. What we observe as electromagnetism is some mix of hypercharge and the
weak force.

Finally, the “fifth force” is:

• The Higgs Force: Again, a force which has no classical analog. Its role, however,
is rather dramatic: it allows all the elementary particles described in the table
above to get a mass.

Each of these five forces will be described in considerable detail as the lectures
progress. Section 2 describes the matter particles and their interaction with electro-
magnetism; Section 3 describes the strong force; and Section 4 describes the weak force
and the Higgs boson. Finally, we will turn to gravity in Section 5.

1.1 Quantum Fields

Ironically, the theory of particle physics is not a theory of particles. It’s a theory of
fields. A field is a fluid-like object which is spread throughout all of space. A field can
take a di↵erent value at every point in space, and that value can change with time.

The most familiar examples are the electric and magnetic field which are associated
to the electromagnetic force. These comprise of a pair of vectors, which exist at every
point in the universe. Mathematically, the electric and magnetic field are functions
E(x, t) and B(x, t), which can take di↵erent values at di↵erent points x in space and
points t in time. Like all fluids, the electromagnetic field can ripple. These ripples are
what we call light waves.

Things get more interesting when we introduce quantum mechanics into the mix.
In the 1920s, physicists understood that, on the smallest distance scales, the universe
doesn’t follow the common sense laws that Newton gave us. Instead, it’s much more
mysterious and counter-intuitive, and follows the rules of quantum mechanics. One of
the key consequences of quantum mechanics is that energy isn’t something smooth and
continuous. Instead, energy can only be parcelled in discrete lumps. That’s what the
word “quantum” means: discrete, or lumpy.

The real fun happens when we try to combine the ideas of quantum mechanics with
fields. One implication is that the electromagnetic waves that make up light are not
continuous. Instead light is made up of particles called photons. The photons are
ripples of the electromagnetic field tied into little parcels of energy due to quantum
mechanics.

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Figure 3. This is not what physicists mean by a field. It’s what a farmer means by a field.
Or a normal person.

The surprise is that the paradigm above holds for all other particles too. First, each
of the forces described above has a field associated to it. And, when quantum mechanics
is taken into account, ripples of the field become particles. The names of the particles
associated to each of the forces are:

• Electromagnetism: As described above, the particle is the photon. In particle

physics, photons are denoted by the greek letter (gamma). This comes originally
from high-energy photons known as “gamma rays”, but is now used to describe
photons of any energy.

• Strong Nuclear Force: The field associated to this force is called the Yang-Mills
field. The corresponding particles are gluons.

• Weak Nuclear Force: The field is another variant of the Yang-Mills type. The
corresponding particles are the W and Z bosons.

• The Higgs Force: The associated particle is called, unsurprisingly, the Higgs
boson. It was discovered at CERN in 2012, the last of the Standard Model
particles to be found experimentally.

• Gravity: The force of gravity is rather special. Einstein’s theory of general rel-
ativity teaches us that the gravitational field is actually space and time itself.
Ripples of space and time are called gravitational waves and were first observed
by the LIGO detector in 2015. The associated quantum particles, known as gravi-
tons, have not been observed experimentally. Given the weakness of gravitational
interactions, it seems unlikely that this situation will change any time soon.

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 So each force is associated to a field and an associated quantum particle. But, so
too, are the matter particles. For example, spread throughout the room you’re sitting
in, and in fact throughout the entire universe, there exists something called the electron
field. The ripples in this fluid get tied into little knots, little bundles of energy by the
rules of quantum mechanics. And those bundles of energy are the particles that we call
electrons. Every electron is a ripple of the same underlying field, like waves are ripples
of the same underlying ocean.

There is also a muon field, and a tau field, together with six di↵erent kinds of quark
fields and three kinds of neutrino fields. The Standard Model of particle physics is a
theory describing how 12 matter fields interact with 5 fields of force. If one field — say
the electron field – starts to move and sway, then it causes the gravitational field and
the electromagnetic field to move. These, in turn kickstart the quark fields, and so on.
All of these fields are engaged in an intricate, harmonious dance, swaying backwards
and forwards, to a music that we call the laws of physics.

This can be contrasted with our view of classical physics. There we have two very
di↵erent objects: particles and fields. At times, they make fairly awkward bedfellows.
But there is a beautiful unification in the quantum world: everything is field. The
particles are emergent objects.

The Implications of Quantum Fields

The world of quantum fields can, at times, be difficult to get our heads around. It is
often easier to resort to the language of particles and, for the most part, this is what we
will do in these lectures. Nonetheless, there are times when the particle picture breaks
down and it is only when we think in terms of fields that things make sense. Here we
describe a number of implications of the field theoretic picture. We’ll see many more
as the lectures progress.

Implication 1: First, and most importantly, field theories allow us to write laws
of physics consistent with locality. If you shake an electron, it doesn’t immediately
a↵ect a second electron sitting elsewhere. Instead the shaking electron produces a
perturbation in the neighbouring electromagnetic field. This then propagates outwards,
until it reaches the second electron. In this manner, there is no “action-at-a-distance”,
and causality is ingrained in the very structure of field theory.

Implication 2: The second consequence of quantum fields is the following: all

particles of a given type are the same.

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 For example, two electrons are identical in every way, regardless of where they came
from and what they’ve been through. The same is true of every other fundamental
particle. Suppose, for example, that we capture a proton from a cosmic ray which we
identify as coming from a supernova lying 8 billion lightyears away. We compare this
proton with one freshly minted in a particle accelerator here on Earth. And the two are
exactly the same! How is this possible? Why aren’t there errors in proton production?
How can two objects, manufactured so far apart in space and time, be identical in all
respects? The answer is that there’s a sea of proton “stu↵” that fills the universe. This
is the proton field or, if you look closely enough, the quark field. When we make a
proton we dip our hand into this sea and mould a particle. It’s not surprising that
protons forged in di↵erent parts of the universe are identical: they’re made of the same
stu↵.

Implication 3: The field perspective allows us to simply interpret situations where

the number of particles changes. For example, beta decay is a process in which the
neutron decays,

n ! p + e + ⌫¯e

The decay products are a proton p, and electron e and an electron neutrino ⌫¯e . (The
bar on the ⌫¯e tell us that it’s actually an anti-neutrino; we’ll describe anti-matter in
Section 2.) In terms of the underlying quarks, the down quark decays into an up quark

d ! u + e + ⌫¯e

From a particle perspective, this is somewhat confusing. You might be tempted to

view the decay above by thinking that a proton, electron and anti-neutrino are sitting
inside the neutron, perhaps bound together by some mysterious force and just waiting
to get out. (Or, equivalently, that the down quark is made of an up quark, electron and
anti-neutrino.) But that’s not the right way to think about the neutron (or the down
quark.) Indeed, we’ve stated above that the down quark is a fundamental constituent
of matter, and that would be difficult to believe if it contained other objects.

Happily, these confusions evaporate when we think in terms of fields. The particle
that we call the down quark is an ripple of the down quark field. But there’s no
reason to think that this ripple can last forever. Instead, it can decay, but only at
the cost of exciting three other fields: those of the up quark, electron and neutrino.
The reason why these three particular fields get excited, and no others, is due to the
detailed interactions of the various fields. These rules will be described as these lectures
progress.

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Figure 4. The vacuum of space is an interesting and complicated place. This picture is
taken from the QCD simulation of Derek Leinweber

Implication 4: There is one last idea that will be useful to have in the back of
your mind: the existence of quantum fields means that empty space, also known as
the vacuum, is not a dull place. It is filled with quantum fields which, even when left
alone, are not necessarily calm. An example is shown in Figure 4, depicting a computer
simulation of empty space. What’s shown is a typical configuration of the gluon field in
the vacuum. The true vacuum is, in fact, much more complicated. It isn’t a single field
configuration but something more murky: a quantum superposition of infinitely many
di↵erent field configurations, each appearing with some probability. In quantum field
theory, the vacuum of space is an interesting place. It froths with quantum uncertainty.

The take-home message for these lectures is that the vacuum of space is not some
inert, boring substance. The bubbling fields breath life into the vacuum and mean that
it is able to respond to things happening within it. This phenomenon, as we shall see,
lies at the heart of some of the more subtle e↵ects of quantum fields.

1.2 Natural Units

Before we get going, we should introduce the units that we use to quantitatively describe
the sub-atomic world. Usually in physics, we introduce di↵erent units for length, time
and mass. For example, the SI units are meters, seconds and kilograms respectively.
However, at the fundamental level these concepts are not as di↵erent as they first
appear and the laws of physics provide a way to translate between them.

– 15 –
 For example, there is a speed limit in place in the universe. No particle can travel
faster than
1
c = 299792458 ms ⇡ 3 ⇥ 108 ms 1
(1.1)

All particles with mass are obliged to travel slower than this speed, while all massless
particles are obliged to travel at exactly this speed. The most familiar massless particle
is the photon and for this reason c is referred to as the speed of light.

The speed of light allows us to translate freely between units of length and units of
time. Given a length scale L, there is a natural time scale T = L/c, which is the time
it takes light to cross the distance L.

In fact, the existence of a constant speed in the universe is hinting at something

deeper: the concepts of space and time are not as distinct as we first thought. To put
this in perspective, here’s an analogy. I might decide that I’m going to measure all
horizontal distances in centimeters, and all vertical distances in inches. I then proudly
reveal a new fundamental constant of nature C which translates between the two,
1
C ⇡ 0.394 Inches cm

This is clearly a dumb thing to do. If I have a ruler marked in cm to measure horizontal
distances, then I can always rotate it and use it to measure vertical distances in cm
as well. The rotational symmetry in the world means that there is no fundamental
di↵erence between distances in the horizontal and vertical directions.

But exactly the same story holds for the speed of light. The theory of special rela-
tivity means tells us that there is a symmetry between space and time, albeit one that
only becomes apparent when you travel fast. If you move close to the speed of light
you experience strange e↵ects like time dilation and length contraction, which can be
explained by a rotation of time into space and vice versa. What this means is that, at
the fundamental level, we should measure time and space using the same units. If we
choose to measure time in seconds, then we should measure length in light-seconds, the
distance that light travels in a second. With this choice, the speed of light is simply

c=1

A corollary of this is that mass is now measured in the same units as energy. This is
because Einstein’s famous formula E = mc2 becomes simply E = m. In these lectures,
we will specify the masses of elementary particles in units of energy. If, for some reason,
you want to put get the mass in, say, kilograms, then you simply need to reinstate the
factor of the speed of light in m = E/c2 and use the value (1.1).

– 16 –
 A similar story arises when we consider quantum mechanics. The fundamental con-
stant in quantum mechanics is Planck’s constant,

~ = 1.054571817 ⇥ 10 34
Js

It has units of energy ⇥ time. What this constant is really telling is us that, at the
fundamental level there is a close connection between energy and time. A process with
energy E will typically take place in a time T = ~/E. In this way, we can translate
between units of energy and units of time, and these concepts are not as distinct as our
ancestors believed. To highlight this, we choose units so that

~=1

The choice c = ~ = 1 are referred to as natural units. It means that there’s only one
dimensionful quantity left, which we usually take to be energy. Any measurement —
whether it’s of length, time or mass — can be expressed in terms of energy.

A Sense of Scale
The SI unit of energy is a Joule and is not particularly appropriate for the sub-atomic
world. Instead, we use the electronvolt (eV) which is the energy an electron picks up
when accelerated across 1 volt. This is
19
1 eV ⇡ 1.6 ⇥ 10 J

The electronvolt is the energy scale appropriate for atomic physics. For example, the
energy that binds an electron to a proton to form a hydrogen atom is E ⇡ 13.6 eV.
For elementary particles, we will need a somewhat larger unit of energy. We typically
use MeV = 106 eV or GeV = 109 eV. The LHC, our best current collider, runs at an
energy scale measured in TeV = 1012 eV.

The masses of the 12 matter particles cover a range from eV to GeV. They are:

– 17 –
The entries for neutrinos are upper bounds on the mass. Meanwhile, the masses of the
5 force-carrying particles are

For each of these particles, there is an associated length scale. We get this by by
transforming energy E into a length using the fundamental constants of Nature c and
~,
~c
= (1.2)
E
This is known as the Compton wavelength. Roughly speaking, it can be viewed as
the size of the particle. For example, for the electron the Compton wavelength is
12
e ⇡ 2 ⇥ 10 m. Perhaps somewhat surprisingly, the heavier a particle is, the smaller
its Compton wavelength.

The Biggest and the Smallest

There are two further length scales that we should mention before delving into details
of the subatomic world. One is associated to the strength of the gravitational force.
Newton’s constant is given by

GN ⇡ 6.67 ⇥ 10 11
m3 kg 1 s 2

– 18 –
In natural units, Newton’s constant has dimensions of [Energy] 2 . Putting back the
factors of ~ and c, we can derive an energy scale known as the Planck mass
r
~c
Mpl = ⇡ 2 ⇥ 1018 GeV
8⇡G
(The factor of 8⇡ is conventional, and is sometimes dropped.) This is an enormous
energy scale, fifteen orders of magnitude larger than the scales that appear in the
Standard Model. The corresponding length scale is the Planck length
r
8⇡~G
Lpl = ⇡ 8 ⇥ 10 35 m
c3
This, in turn, is a tiny length scale, 15 orders of magnitude smaller than the scale
that we have explored at our best particle colliders. The Planck scale is where both
quantum mechanics and gravity both become important. It seems likely that space
and time cease to make sense at these scales, although it’s not clear exactly what this
means.

On the other end of the spectrum, the largest size that we can talk about is the
entire observable universe,

Luniverse ⇡ 9 ⇥ 1026 m

The corresponding energy scale is

33
H ⇡ 2 ⇥ 10 eV

This energy scale is closely related to the so-called “Hubble constant” that measures
how fast the universe is expanding, albeit written in the unusual units of electronvolts.
Clearly, it’s a tiny energy scale. A particle with the mass of H would have the same
size as the entire universe.

This, then, is the playground of physics. The goal of physics is to understand every-
thing that can happen at lengths in the range
34
10 m < L < 1026

or, equivalently, at energies in the range

33
10 eV < E < 1027 eV

It turns out that there is quite a lot of interesting things in this window! And, under-
lying many of them, is the Standard Model.

– 19 –
A Interlude: The Road to Discovery
Throughout these lectures, our focus will be on explaining the key ideas and concepts
that underlie the subatomic world. This means that we will describe our current un-
derstanding viewed through the lens of the Standard Model. Yet this theory took many
decades to build, years in which physicists were mostly bewildered and confused. It’s
important to ask: how did we arrive at this point?

The answer to this question is almost entirely: experiment. While there were many
groundbreaking theoretical observations, at each step the important progress was only
made in response to a novel experimental discovery. After each section of these lectures,
we will have a short interlude in which we describe this experimental progress. This
will also provide an opportunity to present a more historical approach to the subject
of particle physics. The hope is that these interludes will serve to ground some of the
ideas that we meet in the main thread, and place them in more concrete context.

In this first interlude, we explain the beginnings of particle physics. We describe the
discoveries that resulted in the comforting and familiar picture of matter as made of
just three particles: the electron, proton and neutron.

A.1 Ray Physics

Before particle physics was the study of fields, it was the study of rays. By the end of
the 1800s, several kinds of “rays” had been found, each seemingly exhibiting di↵erent
properties. It took several decades to distill the properties of these rays (do they
undergo di↵raction? can they be bent by electric or magnetic fields?) and, ultimately,
to understand their particle constituents.

Cathode Rays
Take a glass tube, and remove most of the air. If you drop a large voltage across the
tube, a faint glow can be seen at one end, a result of rays emitted by the cathode
(the negatively charged electrode) hitting the glass wall. In many ways the discovery of
these cathode rays, first observed in 1869 by the German physicists Hittorf and Plücker,
marks the beginning of modern day particle physics.

A number of properties of cathode rays were soon established, including the fact that
they travel in straight lines, as revealed by the shadow cast by objects placed in their
path, but their trajectory can be deflected by both electric and magnetic fields. We
now know that cathode rays are beams of accelerated electrons.

– 20 –
 With hindsight, these early discharge tubes can be viewed as the world’s first particle
accelerators. The electrons were accelerated to energies of around 105 eV. In contrast,
in the last electron-positron accelerator at CERN, known as LEP, electrons were ac-
celerated to energies of around 2 ⇥ 1011 eV. Its successor, the LHC, accelerates protons
to energies of 6 ⇥ 1012 eV. Evidently, the increase of energy by 7 orders of magnitude
took 150 years of hard work. There are reasons to believe that the next 7 orders of
magnitude will be even more challenging.

X-Rays
One recurring theme of particle physics is how one discovery paves the way for the next.
The first example occurred in November 1895, when Wilhelm Röntgen was playing with
cathode rays. He covered the glass tube with thin black cardboard and noticed that,
when the tube was turned on, a paper screen painted with a chemical called barium
platinocyanide would give a faint green glow, even when placed up to a meter away
from the apparatus. He concluded that the tube was emitting some invisible rays,
which he dubbed X-rays.

Röntgen’s subsequent investigations showed that X-rays

were not the same as the cathode rays from which they
originated since they travelled much further in air. He also
realised that X-rays could be used to develop photographic
plates, and his first paper includes the astonishing photo-
graph of his wife’s hand shown to the right. His wife’s
perfectly reasonable response: “I have seen my death”.

Röntgen’s paper resulted in enormous excitement, both

among other scientists and the general public. Rather like
Einstein in later years, everyone wanted a piece of Röntgen.
However, it appears that he was less than impressed with
the whole show and worked hard to stay out of the lime-
light. A sole newspaper interview from this time reveals a
Dirac-like level of brevity:
Interviewer: What did you think?
Röntgen: I did not think; I investigated.
Interviewer: What is it?
Röntgen: I don’t know.
The nature of X-rays remained mysterious for a long time. The suggestion that they
may be short wavelength electromagnetic waves was not generally accepted since no one

– 21 –
succeeded in observing X-ray di↵raction. This changed in 1912, when Max Laue (later
von Laue) realised that the crystal lattice of solids had the right separation needed to
observe di↵raction of X-rays, opening up the entire field of X-ray crystallography.

Uranic Rays
Among the many people to be inspired by Röntgen’s discovery was a French physicist
named Henri Becquerel. For some years, he had held a fascination with phosphorescent
materials and decided to explore the connection to X-rays. Ironically, in the end his
discovery had nothing to do with X-rays.

Uranium salts had long been known to have phosphorescent properties. Becquerel’s
experiment involved exposing uranium to sunlight for several hours. With the uranium
suitably excited, he observed that it emitted rays which, rather like X-rays, created
silhouetted images on photographic plates wrapped in thick, black paper.

Becquerel’s breakthrough came because of the weather.

The final days of February 1896 were dark and overcast in
Paris. With no sunlight available, Becquerel stored his ex-
periment in the drawer of his desk and got on with other
things, like a spot of shopping. By March 1st the sky re-
mained cloudy and, perhaps bored, perhaps inspired, Bec-
querel decided to develop the photographic plate anyway,
expecting to find nothing. Instead, to his astonishment,
there appeared the clear image of copper cross that had
been placed between the plate and the uranium source. Becquerel’s photograph is
shown to the right.

Becquerel’s desk drawer discovery showed that all his careful preparation, exposing
uranium to sunlight, had nothing to do with the uranic rays that it emitted. This was,
to say the least, disconcerting. If the rays were emitted without any prompting from
an external energy source like the Sun then where did their energy come from? It was
tempting to think that the whole thing violated the conservation of energy.

↵, and Rays
Soon after Becquerel’s breakthrough, three further radioactive elements – thorium,
polonium and radium – were discovered by Marie Curie (née Sklodowska) and her
husband Pierre. The next step was to try to characterise the rays that were emitted.
This was done by one of the early heroes of particle physics: Ernest Rutherford.

– 22 –
 Rutherford was the first to realise that uranium emitted not one, but two di↵erent
types of radiation. He called these ↵-rays and -rays:
• ↵-rays: Alpha radiation is easily absorbed. Indeed, we now know that all ↵-rays
would have been absorbed by the black paper wrapping the photographic plate
in Becquerel’s original experiment and so were not detected. Over a period of 13
years, from 1895 to 1908, it slowly became clear that ↵ particles are four times
heavier than hydrogen, with charge +2. In other words, they are what we now
know to be the nucleus of a helium atom.

• -rays: Beta radiation is more penetrating. In time, it was identified with a

stream of electrons. This will be described below.
Later, Villard discovered that radium emitted yet a di↵erent kind of radiation, one
that he naturally called. . .
• -rays: Another, very penetrating form of radiation. This was later found to be
highly energetic electromagnetic waves.
Around the turn of the century, the situation was rather confusing. There were
cathode rays and x-rays and ↵ and and rays. not to mention a number of false
discoveries that were purely illusory. Getting to the heart of these phenomena would,
ultimately, require an understanding of electromagnetism and the strong and weak
nuclear forces.

A.2 The Electron

Cathode rays were the first to be discovered and, subsequently, the first to be under-
stood in terms of a constituent particle. This particle is, of course, the electron.

The claim that rays are composed of particles means that their properties can be
understood using Newtonian mechanics in which the particles are endowed with a mass
m and electric charge e. In 1985, Hendrik Lorentz wrote down the equation of motion
for such a particle moving in the presence of an electric field E and magnetic field B.
A particle with velocity v will experience an acceleration a given by
ma = e(E + v ⇥ B) (A.1)
The first goal was therefore to measure the deflection of the cathode rays due to elec-
tric and magnetic fields. This measurement was performed by J.J. Thomson in 1897.
Two other physicists, Wiechert and Kaufmann made similar measurements using only
magnetic fields around the same time. However, as you can see from the equation of
motion, the deflection of the rays cannot tell us about m and e individually: it only
tells us about the ratio e/m.

– 23 –
 Fortuitously, the same ratio e/m had arisen in an entirely di↵erent context the year
before. This came from the discovery that the atomic spectral lines can be split in
the presence of a magnetic field, a phenomenon known as the Zeeman e↵ect. Lorentz
himself analysed this e↵ect using the equation (A.1) and, happily, the value of e/m that
was needed to explain the observed splitting was close to that later found in cathode
rays.

But the ratio e/m for cathode rays came with a surprise: it was significantly larger
than the value for other known ions. (Thomson’s measurement of e/m gave a value
that was 770 times larger than that of a hydrogen ion – the particle that would later
be rebranded as a proton. We now know that the correct value of the ratio is around
1836.) But the question remained: is this this because the electric charge e of the
particle is very big, or because the mass m is very small. To resolve this issue, one had
to find a way to measure either e or m individually.

The prevailing viewpoint at the time was the right one: that the mass of the particle
was unusually small. Indeed, there was already some indication of how small it had
to be, since the electric charge on a hydrogen ion had been estimated to reasonable
accuracy. This in itself was no mean feat. It was fairly straightforward to measure the
electric charge on, say, a mole of ions. The difficulty is in figuring out how many atoms
are in a mole. Or, in other words, in figuring out Avogadro’s number N ⇡ 6⇥1023 . (See
the final question on this Statistical Mechanics Example Sheet if you want to challenge
yourself.) A number of ingenious ways to determine N were proposed, resulting in a
ballpark figure for e, the minimum unit of electric charge carried by what we now call
the proton. One of the best estimates (out by a factor of 20 or so) was proposed by the
Irish physicist Stoney, who also coined the name electron, for this “atom of electricity”.

A more direct measurement of the electric charge was first achieved by J.J. Thomson,
and this is the reason that he, rather than Wiechert or Kau↵man, is primarily remem-
bered as the discover of the electron. He didn’t study cathode rays, but he turned
instead to the photoelectric e↵ect. This occurs when UV light is shone on a material,
causing electrons to be emitted. Thomson measured the ratio e/m of these emitted
particles and found that it agreed with his earlier measurements of cathode rays. But
this time he could go further, employing a preliminary version of a detector known as
the cloud chamber. This chamber contains supersaturated vapour which condenses into
little droplets, or clouds, as a ray passes through and ionises the atoms. In this way,
the path of the emitted object can be tracked.

– 24 –
 In 1899, with his new cloud chamber toy in hand, Thomson was able to determine the
number of negatively charged ions that formed due to photoelectric emission simply by
counting the droplets along the path. He was also able to determine the overall electric
charge by observing how the the fall of the droplets under gravity was a↵ected by an
electric field. In this way, he measured the charge on each individual droplet, getting
within 30% of the electric charge that we know today. This was the first time that the
cloud chamber gave rise to a major breakthrough in physics. It would not be the last.

A more precise measurement, employing a similar technique but using oil droplets,
rather than a cloud chamber, was performed in 1909 by Millikan and Fletcher. They
again balanced gravitational and electric forces, but were able to observe individ-
ual droplets, deducing that the charge was always quantised in units of 1.6 ⇥ 10 19
Coulombs. Their measurement was within less that 1% of the modern value. Fa-
mously, Millikan struck a dubious bargain with his student Fletcher and the resulting
paper was published under Millikan’s name alone. No doubt he felt bad as he collected
his Nobel prize ten years later.

A.3 The Proton

The discovery of the proton went hand in hand with the discovery of the nucleus itself.
The key experiment is one of the most famous in physics. Working in Manchester in
1909, Hans Geiger and his undergraduate assistant Ernest Marsden were firing alpha
particles at thin sheets of metal and measuring how they bounced o↵. One day Ruther-
ford entered the room and, according to Marsden, suggested “see if you can get some
e↵ect of ↵-particles directly reflected”.

The results were startling and entirely unexpected. About 1 alpha particle in 8000
was reflected back in the direction from which it came. In later years, Rutherford
recounted his surprise in a well known quote:

“It was quite the most incredible event that has ever happened to me in my
life. It was almost as incredible as if you fired a 15-inch shell at a piece of
tissue paper and it came back and hit you.”

But what did it mean?

The prevailing theories for the structure of the atom could not account for these
experiments. Of course, physicists knew that atoms contained electrons, and there was
acceptance that there had to be a compensating positive charge, but theories of the
structure of the atom – whether based on plum puddings, planetary systems, or vortices
– were put forward with little evidence.

– 25 –
 The Gieger-Marsden experiment held the key. That it was Rutherford himself who
understood its consequences is, in some ways, rather surprising. Rutherford was not
known to hold much love for theoretical physics. He is reported to have said of relativity,
“Oh, that stu↵. We never bother with that in our work.” and he was never a strong
proponent of Bohr’s founding work on quantum theory. My favourite Rutherford quote,
capturing both his attitude to theorists, and his personality, is

“How can a fellow sit down at a table and calculate something that would
take me – me – six months to measure in a laboratory?”

Nonetheless, when needed, Rutherford showed himself to be no mean theorist. In

1911, he postulated that each atom contains a heavy, almost point-like object at the
centre, carrying positive charge Q. He computed that an ↵-particle, repelled by the
electrostatic Coulomb force, would be deflected by an angle ✓ with probability

Q2 q 2
(✓) = (A.2)
4m2 v 2 sin4 (✓/2)

Here q, m and v are the charge, mass and velocity of the ↵-particle. This formula is
now known as the Rutherford cross-section. You can find a derivation in the lecture
notes on Dynamics and Relativity. The formula agrees with the experimental data
with impressive accuracy.

As with many great discoveries in science, there was no small amount of luck involved.
On the experimental side, the alpha particles used in the experiment were fast enough
to blast through the electrons of the atom without care, but slow enough to be deflected
from the nucleus before they experienced the strong nuclear force. On the theoretical
side, Rutherford deduced his formula using Newtonian classical mechanics. But the
correct calculation of the cross-section requires quantum mechanics and in nearly all
cases this di↵ers from the classical result. The Coulomb force law turns out to be
special – it is the one force where classical and quantum results for scattering agree!
(You can learn more about this in the scattering theory section of the lectures on Topics
in Quantum Mechanics.)

With Rutherford’s explanation of the nucleus, there was still work to be done. At
the time, all elements were labelled by their atomic weight A which, at least for light
elements, was close to an integer. Listing all the elements in order then gives two
numbers, the weight A and their place in the list Z. The first few are shown in Table
1.

– 26 –
 H He Li Be B C N O
Z 1 2 3 4 5 6 7 8
A 1 4 7 9 11 12 14 16

Table 1. The first few elements

But the question remained: what is the physical meaning of Z? In particular, if

you’re just given the list of known elements, how do you know you’ve got them all? For
example, it might be tempting to think that A is really telling us the rightful place in
the list, with two missing elements with A = 2 and 3 that are just waiting to be found.

The suggestion that Z should be equated with the positive electric charge of the
nucleus did not have an auspicious start. It was first made by van den Broek, a Dutch
real estate lawyer who was pushing some new and improved 3d version of Mendelev’s
periodic table. His accounting of the elements never took o↵, but his suggestion that Z
measures the electric charge was rapidly accepted. Moreover, Rutherford’s scattering
formula (A.2) gives a clear way to measure the charge Q of the nucleus. These, and
other experiments, ultimately led to the complete periodic table that we know and love
today2 .

From here it was a short step to the idea that the hydrogen nucleus – originally called
the H-particle – was a building block of all nuclei. The issue was finally put to rest
some years later when Rutherford demonstrated that H-particles were emitted by other
nuclei – specifically nitrogen – when bombarded by ↵-particles. The name “proton”
was coined by Rutherford at this time.

A.4 The Neutron

In 1911, the nucleus was discovered. By 1920, there was no doubt about the existence
of the proton. But it took until 1932 for the other constituent of the nucleus, the
neutron, to be found.
2
A physicist called Henry Moseley deserves special credit here. When Mendelev originally proposed
his periodic table he found gaps, allowing him to successfully predict the existence of three new
elements. Moseley, using X-ray techniques to determine the atomic number Z, successfully predicted
seven more!
Moseley, like many physicists of that time, was drafted into the Great War. Geiger and Marsden,
for example, found themselves both posted to the Western front, but on opposite sides! Both survived.
Moseley was not so lucky, and the man widely recognised as England’s most promising young physicist
was killed in the battle of Gallipoli by a bullet in the head. He was 27 years old.

– 27 –
 In the decade between the discoveries of the proton and neutron, physics changed
beyond anyone’s wildest imagination. Quantum mechanics was formulated and the
basics of quantum field theory were laid down. These ideas provide the foundation for
nearly everything that we discuss in these lectures – both experimental and theoretical.
Yet the discovery of the neutron owed only little to these new developments. The
neutron took so long to find simply because it’s hard to see. For this reason, the neutron
still carries an air of that pre-quantum world, less exotic than, say, anti-matter whose
origin story is so closely tied to developments in quantum theory. Yet, astonishingly,
there was less than a 100 days between the discovery of the two particles!

You might wonder why physicists didn’t stay up at night, puzzled by the di↵erence
between the atomic number Z and the mass A of the nucleus. It’s because they had a
very convincing explanation. They thought that the nucleus must consist of A protons
with A Z electrons to cancel the charge. Moreover, there was an extremely good reason
to think that the nucleus contained electrons. This was beta decay. The electrons
emitted in beta decay are far more energetic than the orbiting electrons in the atom,
and this meant that they had to have their origin in the nucleus. But if electrons were
being emitted from the nucleus, then obviously they must have been there all along.
That’s simply common sense. Of course, we now know that common sense isn’t always
the best guide when it comes to the sub-atomic world.

If you knew where to look, the advent of quantum mechanics did make it increasingly
difficult to believe in electrons in the nucleus. Trapped inside a cell the size of a nucleus,
the Heisenberg uncertainty relation means that the electron necessarily has energy
greater than 40 MeV, significantly larger than nuclear binding energies and making
it untenable that the electron could remain in place. Further troubles came with the
discovery of spin. (We describe spin in more detail in Section 2.1.) If both the proton
and electron have spin 1/2 then, regardless of whether spins add or subtract, a nucleus
with A protons and A Z electrons should have integer spin when Z is even and half-
integer spin when Z is odd. But that’s not what’s seen. Nitrogen, for example, has
Z = 7 but appeared to have integer spin. Opinions di↵ered on what to make of this.
So ingrained was the idea that the nucleus contains protons and electrons that Fermi
and Rasetti even wrote a paper suggesting that the mismatch should cast doubt on the
idea of spin.

Still, when the breakthrough came it owed essentially nothing to new-fangled quan-
tum ideas and everything experiment. The first hint that something new was afoot
came in 1930 in Berlin. Walther Bothe and Herbert Becker took alpha rays from a
polonium source and directed them on beryllium. They found that the beryllium gen-

– 28 –
erated a new radiation of great penetrating power which they concluded, incorrectly,
must be gamma rays. Over the next couple of years the experiment was repeated and
improved, notably by Iréne Curie who was sitting on the world’s most powerful source
of polonium, a gift from her mother. Together with her husband Fréderic Joliot (by
that time both doubled-barrelled Curie-Joliot’s), they directed this beam of supposed
gamma rays at parafin, and found that it could eject protons at huge velocities. But
still they stuck with the gamma ray interpretation.

The Curie-Joliot experiment was the watershed moment. Their interpretation was
not, it’s fair to say, universally embraced. Apparently the Italian physicist Ettore
Majorana responded to the news with the exclamation

“What fools! They have discovered the neutral proton, and they do not
recognise it!”

In Cambridge, Rutherford and James Chadwick, his second-in-command, held similar

sentiments. There was too much amiss for the radiation to be gamma rays. Less than
three weeks later, Chadwick discovered the neutron.

In fairness, Chadwick had been searching for something like a neutron for over a
decade. He didn’t originally envisage a new elementary particle, but instead a closely
knit bound state of a proton and electron, much smaller than a hydrogen atom so that
it could fit inside the nucleus. That meant he was well prepared when the Curie-Joliot
result came in. His short paper studies the penetrating power of the radiation. The
Bothe-Becker-Curie-Joliot interpretation was that the original alpha rays react as
9 13
Be + ↵ ! C+

But the properties of the carbon nucleus were known well enough to be put an upper
bound on the energy of the emitted gamma ray. Whatever was coming out of this
reaction was much more powerful. Chadwick found the correct conclusion: he was
seeing something entirely new
9 12
Be + ↵ ! C +n

Chadwick had found the neutron.

– 29 –