Download Notes/All Physics IB/Fundimental Particles

03
Perimeter
Explorations
Beyond the Atom:
Remodelling Particle Physics
T E A C H E R ’ S
G U I D E
Contents
3
Opening Information
Introduction to Particle Physics
Curriculum Links
Suggested Ways to Use this Resource
Teacher Tips
7
Particle Physics in a Nutshell
A one-page summary of the video’s contents
8
Student Activities
These activities can be used individually or in combination
with others. The material can be adapted to a variety of
classroom levels and courses. Student activity sheets are
included on the DVD-ROM in an editable electronic format so
you can adapt them to your classroom.
8
Activity 1: Video Summary
A set of discussion questions that review the content of the
video.
10
Activity 2: Scattering Experiment
Students use balloons, marbles, and a wine glass
to explore Rutherford’s scattering experiment.
12
Activity 3: Bubble Chamber Detective
Students use conservation of charge and momentum to
analyze two historic images from CERN and Brookhaven.
Requires a prior knowledge of moving charges in a magnetic
field.
16
Activity 4: Taming the Particle Zoo
Students sort particle zoo cards and use the patterns
they find to explore an early quark model.
18
Activity 5: Finding the Top Quark
Students use conservation of momentum and energy
to analyze data from Fermilab’s D-Zero detector.
21
Video Chapter Summaries
This section provides additional background information on
the content of the video, as well as further topics to extend
the video. Questions are anticipated and clear, concise, and
accurate information is provided.
32
Activity Solutions
37
Closing Information
Who are the people in the video?
Appendix A: Particle Zoo Cards
Appendix B: Particle Physics Equations and Constants
Credits
1
Beyond the Atom: Remodelling Particle Physics
Perimeter Institute
PERIMETER EXPLORATIONS
PERIMETER INSTITUTE
This series of in-class educational resources is designed
to help teachers explain a range of important topics in
physics. Perimeter Explorations is the product of extensive
collaboration between international researchers, Perimeter
Institute’s outreach staff and science educators. Each
module has been designed with both, expert and less
experienced teachers in mind, and thoroughly classroom
tested.
Perimeter Institute for Theoretical Physics is an independent,
non-profit, research institute whose mission is to make
breakthroughs in our understanding of our universe and the
forces that govern it. Such breakthroughs drive advances
across the sciences and the development of transformative
new technologies. Located in Waterloo, Ontario, Canada,
Perimeter also provides a wide array of research training and
educational outreach activities to nurture scientific talent
and share the importance of discovery and innovation with
students, teachers, and the general public. In partnership
with the Governments of Canada and Ontario, Perimeter
is a successful example of public-private collaboration in
scientific research, training, and outreach.
2
Beyond the Atom: Remodelling Particle Physics
Introduction
What is everything made of? Humans have asked this
question for thousands of years and are still actively searching for the answer today. Ernest Rutherford began a new
chapter in this pursuit over a century ago when he fired
alpha particles at gold foil, uncovering the atomic nucleus.
The Large Hadron Collider (LHC) at CERN is the latest effort to probe deeper into nature. The LHC smashes protons
together at the unprecedented energy levels of 14 TeV (1 TeV
is the amount of energy an electron gains when accelerated
through a potential difference of 1 000 000 000 000 V). Our
current model of matter is the Standard Model and while it
is extremely good at describing how matter behaves at low
energies it is expected to fail at energies higher than a few
TeV. The LHC has been designed to push the limits of the
Standard Model—discoveries are going to be made.
The Standard Model states that all matter is made of fundamental particles called quarks and leptons. There are
six quarks and six leptons arranged in three families, or
generations. In reality, the answer to the question “What is
everything made of?” is found in the first generation. The
atoms and molecules of our everyday world are all made of
up quarks, down quarks and electrons. The other generations are needed to explain the structure of particles created
in high-energy physics labs, cosmic rays or various exotic
astronomical objects.
The Standard Model also states that matter interacts through
bosons—force-mediating particles exchanged between similar particles of matter. For example, when two charged particles interact, they will exchange photons, which will either
cause the charged particles to be attracted or repelled. There
are bosons for each of the atomic forces: the photon for
the electromagnetic force, the gluon for the strong nuclear
force, and the W and Z bosons for the weak nuclear force.
Each of these bosons has been observed and the theories
describing these forces are very well developed. Any new
model will have to surpass one of the strongest theories ever
constructed.
mechanism, the universe is saturated with a field called the
Higgs field that interacts with some particles more than
others. Any attempt to accelerate these particles is met by a
resistance called inertia. The LHC is testing for the existence
of this field by putting so much energy into a small space
that the Higgs field will produce a Higgs boson. If the Higgs
boson exists, it will be created during collisions in the LHC.
The challenge for researchers will be to detect the Higgs
boson if it is created. One of the basic concepts in particle
physics is that if there is enough energy to create a set of
particles (via E = mc2), then the particles will be created
(within the constraints of other parameters). At the energy
level of the LHC, every particle in the Standard Model will
be created in the collisions. The number of Higgs bosons
produced is expected to be very small, however, so the LHC
has been designed to produce over 600 million collisions per
second. Even with this enormous collision rate, the production rate of Higgs events is expected to be one every few
hours—that is a lot of data to sift through to find a single
event! After two and a half years of operation the LHC announced the discovery of a new boson consistent with the
Higgs model. Further analysis will reveal whether this boson
is the Higgs or something else.
Particle physics and the LHC may represent the epitome of
advanced physics but many of the fundamental concepts
involved are accessible to a high school physics audience.
In this Perimeter Institute Exploration, students review how
electric and magnetic fields, conservation of momentum,
and special relativity led to the development of the Standard Model. The video features state-of-the-art animations,
researcher interviews, and narration to introduce students
to the Higgs mechanism and other concepts being explored
at the LHC. Through the video and accompanying activities students will see that the physics they are studying in
high school is is at the centre of the largest particle physics
experiment ever.
You may notice the absence of gravity from the previous
list of forces. The Standard Model does not include gravity, although some theorists have proposed the existence of
a graviton as a mediating particle. Another feature missing
from earlier versions of the Standard Model is an explanation
for mass—not the mass of atoms (that is largely explained
using E = mc2), but the mass of fundamental particles. In the
Standard Model, fundamental particles would be massless
—if not for the Higgs mechanism. According to the Higgs
Section of the LHC's 27km long tunnel
3
Beyond the Atom: Remodelling Particle Physics
Curriculum
Links
Topic
Connection to
Particle Physics
Relevant
Materials
Nature of Science
Scientists use models to explain complex phenomena. These models are often
based on patterns and make testable predictions. Experiments are designed to
test models.
Activity 2: Scattering Experiment
Activity 4: Taming the Particle Zoo
Video: Chapter 1, 3 and 5
Models of Matter
Experiments have refined our models of matter from Dalton to Thomson to
Rutherford. Increasing energies have allowed scientists to probe deeper into matter, leading to the Standard Model.
Activity 1: Video Summary
Activity 2: Scattering Experiment
Activity 4: Taming the Particle Zoo
Video: Chapter 1, 3 and 4
Rutherford Scattering
Rutherford used alpha particles to probe the structure of matter. He concluded
that the positive charge and almost all the mass were concentrated in a very small
volume.
Activity 1: Video Summary
Activity 2: Scattering Experiment
Video: Chapter 1
Fields
Forces act at a distance through fields. Electromagnetic fields are used to accelerate
and guide beams of charged particles. Magnetic fields are used in particle detectors
to identify the charges and momenta of particles.
Activity 3: Bubble Chamber Detective
Activity 5: Finding the Top Quark
Video: Chapter 1 and 2
Standard Model
The Standard Model of matter uses six quarks, six leptons, and four bosons to
give a complete description of matter and forces. The Large Hadron Collider is
testing the Standard Model.
Activity 1: Video Summary
Activity 4: Taming the Particle Zoo
Activity 5: Finding the Top Quark
Video: Chapter 3 and 4
Energy-Mass
Equivalence
Particle accelerators put enough energy into a small volume that matter is produced, according to E = mc2.
Activity 1: Video Summary
Activity 5: Finding the Top Quark
Video: Chapter 2, 3 and 4
Conservation Laws
Particle collisions obey the laws of conservation of energy, of momentum, and
of charge.
Activity 3: Bubble Chamber Detective
Activity 5: Finding the Top Quark
Video: Chapter 2, 3 and 4
4
Beyond the Atom: Remodelling Particle Physics
Suggested Ways to
Use this Resource
This resource has been developed by a team of experienced
educators in collaboration with Perimeter Institute researchers and outreach staff. The resource consists of a 30-minute
video, five classroom activities and background material. The
activities can be adapted to a variety of classroom levels and
courses.
The activity sheets are available in editable form on the DVDROM.
Intermediate Level Science (1+ Lesson)
Most intermediate Science courses include models of the
atom and the Periodic Table. This resource will supplement
these lessons and show students how the process of science that led to the Periodic Table is still ongoing.
Activity 2: Scattering Experiment (30 minutes) introduces
students to Rutherford’s gold foil experiment.
Video (30 minutes) can be paused at several points to encourage interactive discussions.
Activity 1: Video Summary (15 minutes) can be used as a
discussion tool or as a homework assignment.
Activity 4: Taming the Particle Zoo can be used as an extension activity when studying the Periodic Table.
Senior Level Physics (2 Lessons)
This resource can be used in several places in the senior
Physics curriculum. Particle physics is a fantastic application of conservation of energy and momentum, electric and
magnetic fields, and special relativity. The activities allow students to gain a deeper appreciation for the Standard Model
as well as experiencing the process of science involved in
developing models.
First Class:
Activity 4: Taming the Particle Zoo (30 minutes) uses patterns to predict the omega-minus particle. This activity can
be adapted to use only spin-3/2 cards to predict the omegaminus particle.
Activity 3: Bubble Chamber Detective (45 minutes) guides
students through the analysis of two bubble chamber images, including the image that resulted in the discovery of
the omega-minus particle.
Second Class:
Video (30 minutes) can be paused at several points to encourage interactive discussions.
Activity 5: Finding the Top Quark (45 minutes) shows how
conservation laws and energy-mass equivalence are used to
analyze data from a particle detector.
Teacher Tips
The 30-minute video has been divided into scenes based on
curriculum topics. The video can be viewed in one continuous showing or in parts, according to your preferences.
Activity 2: Scattering Experiment
This activity is appropriate for an intermediate level class that
is studying the model of the atom or for a senior level class
that is studying fields. Students will explore Rutherford’s scatThe following suggestions are the product of many workshops tering experiment using several approaches: physical models,
role playing, and scale diagrams.
with experienced teachers and their students. We are confident that these activities will challenge and inspire your students to discover the amazing world of particle physics. Each In the first activity, students need to put as large a charge as
activity can be used individually or in combination with others. possible on the balloons. The charge on the suspended balloon must cover the entire surface or the balloon will simply
rotate instead of swing. A longer thread will produce a bigger
Activity 1: Video Summary
This question sheet has been designed to encourage student deflection.
dialogue. Students can work independently, in pairs, or participate in a larger group discussion.
5
Beyond the Atom: Remodelling Particle Physics
Teacher Tips
continued
In the second activity, a little bit of modeling clay is needed to
create a smooth lip for the ball to roll up. The launching ramp
should be kept at least 15 cm from the glass in order to make
it challenging. An effective track can be fashioned from shelving support cut into 25 cm lengths. Encourage students to
test a variety of scenarios (e.g., what happens when you miss
the glass altogether?).
These two activities can be supplemented with a computer
simulation such as: http://phet.colorado.edu/en/simulation/
rutherford-scattering
Activity 3: Bubble Chamber Detective
The photograph in Figure 1, a tutorial, and more examples can
be found at the CERN High School Teacher program website: http://teachers.web.cern.ch/teachers/archiv/HST2005/
bubble_chambers/BCwebsite/index.html.
This activity gives students who are familiar with conservation laws and charged particles moving in a magnetic field
the chance to apply that knowledge. Conservation of charge
is used to identify whether an event is a collision or a decay.
Conservation of momentum is used to infer the trajectory of
neutral, and therefore unseen particles. These unseen particules are vital to the discovery of the omega-minus particle in
Part 2.
Activity 4: Taming the Particle Zoo
Remove the eta-prime (η′), omega-minus (Ω–), and Nobel Prize
cards before giving the cards to the students.
An intermediate Science class can do Part 1 as a modelling
activity. Allow enough time for the students to attempt several
sorting methods before steering them in the right direction
(group the particles by spin). Once the particles are separated
by spin, they can be organized by charge and strangeness to
produce patterns. Part 1 can be simplified by only using the
spin-3/2 cards to predict the existence of the omega-minus
particle. The first group to use the pattern to give a correct
description of the omega-minus particle can be awarded the
Nobel Prize. Students in a senior class can go on to complete
Part 2, which uses the quark model to explain the pattern in
the particles. Students are encouraged to look for problems
raised by the quark model and to suggest solutions. Note: The
solution that works for the mesons does not work for the baryons. The explanation for this involves a superposition of states
and is probably too advanced for a high school class.
6
Activity 5: Finding the Top Quark
Students in a senior level class will use conservation of momentum and energy to determine the mass of the top quark.
Role playing helps students picture this three-dimensional
collision more clearly and reinforces that it does not involve
large objects breaking apart into smaller pieces. Starting with
a Think-Pair-Share activity before moving on to the enactment
will help students conceptualize the collision.
The numerical analysis starts with inferring the momentum of
the undetected neutrino by finding the total momentum of the
detected particles and asserting that total momentum should
be zero. Once the momentum of the neutrino is determined,
the total energy of the collision can be calculated by adding
the magnitudes of the momentum vectors together (do not
forget the neutrino). The total energy comes from the mass of
the top-antitop pair according to E = mc2.
The Higgs simulation gives students the chance to get a feel
for the statistical nature of the data analysis used in modern
detectors. Students will find that a cutoff of around 50 GeV
seems to give good results.
The simulation will not let you use Auto events until you have
done three by hand. If you want students to get a better feel
for the experiment, do not mention Auto events. Scientists
wait until they accumulate enough data to generate a significance of 5 before announcing a discovery. Even with the
Auto function on, students will find that it takes a long time to
achieve a significant result.
Beyond the Atom: Remodelling Particle Physics
Particle Physics
in a Nutshell
• All matter is made out of atoms. Atoms are organized into the
Periodic Table.
• More exploration leads to more particles, requiring more
quarks. The current model has six quarks (and six antiquarks),
six leptons (and six antileptons), and four bosons.
• Rutherford scattering reveals the internal structure of atoms.
• Charged particles interact through fields. Fields convert the kinetic energy of moving particles into potential energy. In particle
collisions, more kinetic energy means a closer approach, which
means more detail.
• Focusing a lot of energy into a small volume can create new
particles (E = mc2). When matter is created out of energy, we
also create antimatter.
• Technological improvements lead to increases in energy and
rapid discovery of many new particles. The lack of an organizing structure leads to the “particle zoo”.
• Patterns found in the particle zoo points to deeper structure—
quarks. Quarks are fundamental particles that have fractional
charge (e.g., ⅓ or ⅔) and new characteristics such as strangeness and colour.
• The quark model introduces a new force to hold quarks
together—the strong force. The strong force acts on colour
charge and gets stronger as distance increases.
ATLAS simulated Higgs event
Bubble chamber image
• The mass of the proton is mostly due to the binding energy of
the quarks that make it up, not to the mass of the quarks. Why
do quarks even have mass? This question leads to the Higgs
field.
• Particles interact with the Higgs field, which impedes acceleration, giving inertia (mass). Massless particles like the photon do
not couple to the Higgs field.
• Every field has a boson associated with it. The Higgs boson is
like a ripple in the Higgs field. The Large Hadron Collider (LHC)
will operate at high enough energy levels to generate Higgs
bosons.
• The LHC will produce over 600 million collisions per second.
Researchers expect to produce one Higgs event every three
hours (talk about a needle in a haystack!).
• Four large detectors at the LHC will study the collisions for
many different things: the Higgs boson, dark matter, quark-gluon plasma, matter-antimatter asymmetry, and supersymmetry.
The Compact Muon Solenoid (CMS) detector at CERN
7
Beyond the Atom: Remodelling Particle Physics
Activity 1
Video Summary
NAME :
1. The model of the atom has changed over the past 150 years as new evidence has been found. Draw labelled diagrams for a
helium atom using each of these models.
Dalton’s model of indivisible
balls of matter
Thomson’s model using
electrons in a positive mass
Rutherford’s model using
electrons and nuclei
2. Rutherford fired alpha particles at gold foil and was surprised by the results.
He developed the nuclear model of the atom because
(a) most of the alpha particles went through
(b) most of the alpha particles bounced back
(c) a few of the alpha particles went through
(d) a few of the alpha particles bounced back
Explain your choice and make a labelled diagram of Rutherford’s experiment.
3. The Large Hadron Collider (LHC) accelerates particles to unprecedented energy levels.
Higher-energy particles are used at the LHC because they can
(a) get closer to each other and probe smaller distances
(b) create massive particles from the energy
(c) both of the above
Explain your choice.
4. The most famous physics equation is Einstein’s E = mc2.
(a) Explain what each letter in the equation represents, and what the equation means.
(b) Draw a picture of what happens when an electron and a positron are created in a bubble chamber.
Where does the mass of the electron and positron come from?
5. Science was much simpler 80 years ago. Everything appeared to be made of just electron, protons, and neutrons.
Then physicists probed deeper into matter and detected new particles.
(a) Why was the discovery of new particles a problem?
(b) How was it solved?
8
| Activity 1
Beyond the Atom: Remodelling Particle Physics
6. The electromagnetic force pulls opposite charges together and pushes like charges apart. The strong
force is different from the electromagnetic force in that the strong force is only attractive and it has
(a) three types of charge and gets weaker with distance
(b) three types of charge and gets stronger with distance
(c) two types of charge and gets weaker with distance
(d) two types of charge and gets stronger with distance
7. The Standard Model describes what is needed to make matter and the forces that hold it together.
(a) Fill in the table for the Standard Model.
1st
Generation
2nd
Generation
3rd
Generation
Bosons
Quarks
Leptons
(b) What is special about the first column?
(c) How are the next two columns different from the first?
(d) How is the last column different from the other three?
(e) Compare the periodic table of chemistry and the Standard Model of physics.
8. What particle in the Standard Model is the LHC designed to find? Why is it important?
9. What else might the LHC find? Make a list of all the possibilities mentioned.
Activity 1 | 9
Beyond the Atom: Remodelling Particle Physics
Activity 2
Scattering Experiment
NAME :
Over one hundred years ago, J.J. Thomson showed that all atoms contained smaller negatively charged particles called
electrons. This implied that most of the mass and all of the positive charge in the atom had to be made of something else.
Physicist Ernest Rutherford explored the distribution of positive charge within the atom by directing alpha particles at a thin
gold foil. Most of them went through, but about 1 in every 8000 was repelled backwards.
1. The positively charged alpha particles were repelled by the positive charge of the gold atoms.
We can model this repulsion with two charged balloons. Hang one balloon from a thread.
Use the other balloon to see how far away from vertical you can repel the first balloon.
The balloons cannot touch.
Predict and Explain: What should you do to get the greatest deflection?
Observe and Explain: What conditions give the greatest deflection?
Extend and Explain: How is the balloon activity similar to Rutherford’s experiment?
How is it different? How could you change the activity to make it more similar?
2. In this activity, you will use a ball, a wine glass and a metal track to model how
alpha particles are scattered by the gold foil. The ball represents the alpha
particles and the wine glass stem represents the nucleus of the gold atom.
The track is used to launch the ball at the glass (see figure at right). Spread
a bit of modeling clay around the edge of the base of the glass to make a
smooth ramp for the ball to roll up. Position the track 15 cm away from the
glass. Place the ball at the top of the track and let go.
Predict and Explain: What should you do to get the ball to roll up onto the
base and roll straight back down, without bouncing off the stem?
10 | Activity 2
15 cm
Beyond the Atom: Remodelling Particle Physics
Observe and Explain: What happens to the ball if it is not aimed directly at the stem?
Extend and Explain: How is the wine glass activity similar to Rutherford’s experiment?
How is it different? How could you change the activity to make it more similar?
3. The alpha particles in Rutherford’s experiment had similar speeds and trajectories and yet they were scattered by different
amounts. Most travelled straight through the gold without any deflection, some slowed down and were slightly deflected
and a few stopped and were repelled back. Get into groups of four or five. Plan and perform a skit explaining these results.
You may use props and sound but no words. What are the key ideas that you need to communicate?
4. Rutherford calculated that the alpha particles got to within 2.7 x 10-14 m of the centre of the gold nucleus. Later experiments have shown that the radius of the gold nucleus is 0.75 x 10-14 m.
(a) Let a centimetre represent 10-14 m. Draw a scale model of the nucleus and the path of an alpha particle that makes a
head-on approach and gets as close as possible.
(b) Alpha particles that approach the nucleus off to one side are deflected as they go by. Add the path of one of these
particles to your scale model. Will it get as close to the nucleus as one that approaches head-on?
(c) The gold atoms are separated by 10-10 m. Where would the next gold nucleus be in your diagram?
Activity 2 | 11
Beyond the Atom: Remodelling Particle Physics
Activity 3
Bubble Chamber Detective
NAME :
Physicists discovered dozens of different ‘elementary’ particles using bubble chambers. Bubble chambers are large vessels
of super heated liquids (usually hydrogen) in a uniform magnetic field. Identical charged particles are injected into the chamber where they collide inelastically with protons in the liquid to form new particles which may or may not decay. The following
principles will allow you to analyze the events photographed in a bubble chamber:
Charge is always conserved.
• Only moving charged particles leave a trail. Neutral and stationary particles do not leave trails.
• The charged particles have a charge of either +1e or -1e, where e = 1.6 x 10-19 C
• Charge is determined by the direction the particle curves in a magnetic field.
Momentum is always conserved.
• The magnetic field bends the path of charged particles.
• The radius of a curved trail is proportional to particle’s momentum.
Changes in the trails are evidence of an interaction
• A particle can collide with the protons in the liquid hydrogen to form new particles, or
• A particle can decay into new particles.
The radius of a curved trail is
proportional to momentum
Part 1: CERN’s Two Metre Hydrogen Bubble Chamber
Figure 1 is a photograph showing seven kaons entering a bubble chamber filled with liquid hydrogen. Kaons are unstable
subatomic particles that can be produced in large quantities, making them useful in bubble chamber experiments.There is a
uniform magnetic field directed into the page. Answer each question and provide a brief written justification for your answer.
1. The kaon trails are curving slightly to the right. What is the charge of the kaons?
(a) –1
(b) +1
(c) 0
(d) not enough information
2. At point P the single trail of a kaon branches into two trails. What is the charge of the particle on the right?
(a) –1
(b) +1
(c) 0
(d) not enough information
3. Compare the total charge going into point P with the total charge going out. The single charged kaon
(a) has decayed into two oppositely charged particles.
(b) has decayed into two identically charged particles.
(c) has interacted with a proton and produced two oppositely charged particles.
(d) has interacted with a proton and produced two identically charged particles.
4. Compare the tracks going into point P with the tracks going out. What can you infer?
(a) A charged particle has been produced that moves up and to the left.
(b) A charged particle has been produced that moves up and to the right.
(c) A neutral particle has been produced that moves up and to the left.
(d) A neutral particle has been produced that moves up and to the right.
5. There is a kink in the track at point T. The particle making the track has
(a) interacted with a neutral particle.
(b) interacted with a positively charged particle.
(c) decayed into a positively charged particle and a neutral particle.
(d) decayed into a negatively charged particle and a neutral particle.
12 | Activity 3
Beyond the Atom: Remodelling Particle Physics
6. There is a very slight kink in the track at point R where the curvature increases. The particle making the track has
a) interacted with a neutral particle.
b) interacted with a positively charged particle.
c) decayed into a positively charged particle and a neutral particle.
d) decayed into a negatively charged particle and a neutral particle.
7. The two charged particles that appear at point S pass by each other at point U. Draw a straight line from this intersection to point S, where the particles were created from a neutral particle. This line gives the direction of the original neutral
particle. Extend the line back down the page. Where did the neutral particle originate?
a) at point P
b) at point Q
c) at point R
d) not enough information
8. Two new particles appear at point Q. What can we infer about the event happening at point Q?
a) A stationary charged particle has decayed into two new particles.
b) A stationary neutral particle has decayed into two new particles.
c) A charged particle moving up and to the left has decayed into two new particles.
d) A neutral particle moving up and to the left has decayed into two new particles.
9. Extend the curved trails from point Q to find their intersection point by tracing the existing curve onto another piece of
paper and using this to extend the path. Where did the neutral particle that decayed to form these particles originate?
a) at point P
b) at point Q
c) at point R
d) not enough information
10. Put it all together and give a complete description of the events that happen in this photograph.
Part 2: Brookhaven National Laboratory’s Bubble Chamber
Figure 2 is an historic photograph. It provided the first evidence for the omega-minus particle which had been predicted two
years earlier by Murray Gell-Mann. Negative kaons enter at the bottom. A uniform magnetic field is directed into the page.
The essential trails have been darkened.
1. Identify the charges of the particles interacting at point V.
2. Identify the charges of the particles interacting at point W.
3. Two oppositely charged particles have been created from a neutral particle at point Y. The curves have been extended until
they intersect. Draw a line to show where the neutral particle originated.
4. Oppositely charged particles have been produced from neutral particles at points X and Z. Find the origin of these neutral
particles by extending the line that bisects the ‘vee’ formed by the charged particles. These lines should intersect with the
line you drew in question 3 at a single point. What can you infer from this? Refer back to Question 2 in your explanation.
5. Reconstruct the interactions by labeling the visible and invisible particle trails on Figure 2. Begin at point V where a kaon (K–)
–
collides with a proton to produce the omega-minus (Ω ), a neutral kaon (K0) and a positive kaon (K+). The omega decays
0
at point W into a neutral xion (Ξ ) and a negative pion (π–). The xion then decays into a neutral lambda (Λ0) and a neutral
pion (π0). The neutral pion decayed almost immediately into two photons (γ) which decay at points X and V into electronpositron (e–, e+) pairs. The lambda decays at point Y into a proton and a negative pion.
6. Dusan Radojicic was the researcher who first analyzed this photograph in 1964. Imagine that it is three in the morning
when he realizes that he has evidence for the omega-minus particle predicted by Gell-Mann in 1962. He wants to phone
his boss with the news right away but his analysis is based on four invisible trails. What would you do? How would you
explain your analysis over the phone?
Activity 3 | 13
Beyond the Atom: Remodelling Particle Physics
U
T
S
R
Q
P
Figure 1 Photograph of CERN bubble chamber. Arrows indicate kaons moving up the page. There is a
constant magnetic field into the page.
14 | Activity 3
Beyond the Atom: Remodelling Particle Physics
Z
Y
X
W
V
Figure 2 Photograph from Brookhaven National Laboratory. Negative kaons enter from the bottom of the image.
There is a constant magnetic field directed into the page.
Activity 3 | 15
Beyond the Atom: Remodelling Particle Physics
Activity 4
Taming the Particle Zoo
NAME :
We have come a long way from Dalton and the indivisible atom. First, Thomson found the electron, Rutherford discovered the
proton, and in 1932 Chadwick found the neutron. Then, the list expanded over the next 30 years to include over 90 different
particles. Particle physics in the 50s and 60s was much like chemistry in the 1880s: a tremendous amount of data but no
widely accepted theory to provide an organizing structure.
In this activity we will examine some of these particles, identify a pattern, and explore a theory that will help us tame the particle zoo, just as Mendeleev did for the elements when he built the first Periodic Table.
Part 1: Finding Patterns
1. Take a deck of particle cards and inspect the information on the cards. [Note: S is a new property called “strangeness”.]
2. Sort the particles into three distinct groups based on information on the cards. Which characteristic is the best choice for this?
Why?
3. Take one of the three groups. Organize its particles into rows and columns based on two of the other characteristics. Repeat for
the other two groups.
4. Two of the groups should have eight members and look similar. The third group should look different and have nine members.
Describe the geometric patterns that emerge from your arrangement of the cards. Patterns are often a clue to deeper structure.
5. Inspect the larger group. The pattern seems incomplete. You can complete the pattern by adding one more particle to the group.
On a blank card, write down the characteristics (mass, spin, Q, S) you expect the missing piece will have. Show this prediction to
your teacher.
Murray Gell-Mann won the Nobel Prize in 1969 for his theory explaining all of the known particles and predicting the omegaminus particle. Gell-Mann arranged the known particles into groups, much as you did in Part 1 of this activity. His theory
was motivated by the geometric patterns that he found. He recognized that these patterns pointed to a deeper structure
within matter. Just as the patterns in the Periodic Table can be explained using protons and electrons to build atoms, GellMann’s patterns suggested that the particles were made of smaller, more fundamental, particles which he called quarks.
Each quark has a characteristic charge and strangeness. It also has a “mirror image” antiquark with the opposite charge and
strangeness.
Quark Characteristics
Flavour
up (u)
Charge
Strangeness
down (d)
0
strange (s)
0
-1
antiup ( u )
antidown ( d )
antistrange ( s )
0
1
0
All of the known particles can be constructed by arranging quarks according to a simple set of rules:
• Baryons are made of three quarks. (Antibaryons are made of three antiquarks)
• Mesons are made of one quark and one antiquark.
• Quarks have fractional charge and combine to produce integer charge (e.g., +
- = +1).
• Quarks have two distinct spin states: (½ or –½). When we combine quarks, the spins either add
or subtract, just like the charges do to produce either spin-0, spin-½, or spin- particles.
16 | Activity 4
Beyond the Atom: Remodelling Particle Physics
Part 2: Understanding Patterns
1. Mesons are a combination of one quark and one antiquark. The table below has all of the possible combinations of u, d,
and s quarks and antiquarks. Determine the combined Q and S values for each combination. Then, match these values
with the mesons in the spin-0 group that you built in Part 1.
Spin-0 Mesons
qq
uu
ud
Q
+1
S
0
us
du
dd
ds
su
sd
ss
Particle
Symbol
What problems do you see in your results? How could you resolve them?
2. Baryons are a combination of three quarks. The table below has all of the possible combinations of u, d, and s quarks.
Determine the combined Q and S values for each combination. Then, match these values with the baryons in the spingroup and the spin-½ group that you built in Part 1.
Baryons
qqq
uuu
uud
Q
+1
S
0
udd
ddd
uus
uds
dds
uss
dss
sss
Spin-3/2
Baryons
Spin-1/2
Baryons
p
What problems do you see in your results? How could you resolve them?
Activity 4 | 17
Beyond the Atom: Remodelling Particle Physics
Activity 5
Finding the Top Quark
NAME :
In 1995, Fermilab discovered evidence for the sixth and final quark of the Standard Model. This was done by accelerating
and colliding protons and antiprotons together to form a top quark and an antitop quark. The energy of the protons was converted into the mass of the quarks via E = mc2. The two quarks cannot be detected directly because they decay immediately
into other particles. In this activity, you will use the mometum and energy of the decay particles to determine the mass of the
original pair.
Part 1: Top Quark
1. Protons and antiprotons were accelerated to equal and opposite speeds of over
99% of the speed of light. When they collided, as shown in Figure 1, the following
interactions occurred:
•
•
•
•
They annihilated and produced a top-antitop pair with almost no momentum.
This quark pair decayed almost immediately into lighter particles with lots of
momentum which moved approximately at right angles to the original proton beams.
Three of these particles continued to decay into other particles, producing four
“jets” that were measured in the inner sections of the detector.
The fourth particle decayed into a muon that was detected in the
outer part of the detector and a neutrino that was not detected.
Figure 1 A Top Antitop Quark Event
Model these interactions with beach balls, tennis balls, and marbles. Be sure that
momentum is conserved at each step.
from the D-Zero Detector at Fermilab
2. Figure 2 shows an event display from one of these collisions. Draw the horizontal and vertical components for each of the
five labelled momentum vectors. Measure the length of each vector and each component. Record these lengths in the
table below (the first one has been done as an example). Add the numbers in each direction and then convert these lengths
to momentum units, using the scale: 1 mm = 1 GeV/c.
Magnitude
(mm)
95.5
Horizontal
(mm)
-94
Vertical
(mm)
-14
Total
(mm)
Total
(GeV/c)
3. The momentum vectors do not add up to zero. Conservation of momentum demands that the initial and final momenta must be
equal. D-Zero detects most particles, but neutrinos slip through unobserved. Use conservation of momentum to determine the
momentum of the missing neutrino. Draw this momentum on the event display.
4. The equation E = mc2 is for a particle at rest. The full equation is E2 = (pc)2 + (mc2)2, where p is the relativistic momentum
of the particle. The top and antitop quarks decay and produce jets of high-momentum particles. The momenta of these
particles is so large that we can ignore the (mc2)2 term here and the equation can be simplified to E = pc. This means that a
small particle with 95.5 GeV/c of momentum has 95.5 GeV of energy. Find the total energy of all of the particles, including
the neutrino, by adding their energies. (Remember that energy is added as a scalar, not a vector.)
18 | Activity 5
Beyond the Atom: Remodelling Particle Physics
5. The energy released by the collision of the proton and antiproton is just enough to produce a top-antitop pair that is at rest
in this particular, carefully-chosen event. The momentum of the top-antitop pair is extremely small compared to their
rest-mass energy. The first term in E2 = (pc)2 + (mc2)2 vanishes and the equation simplifies to E = mc2. Use this to find the
mass of a top quark.
6. In order to find the top quark, Fermilab collided a proton and an antiproton together at very high speeds. You have a friend
who studies biology. Your friend thinks that this is a rather sloppy way to dissect protons to see what is inside them.
Explain to your friend how this collision is not like a dissection. Be sure to refer to the masses of protons (0.938 GeV) and
top quarks (172 GeV).
Part 2: Higgs Particle Simulation
In 2010 the LHC began colliding protons at the unprecedented energy of 7 TeV. This ambitious project was designed to detect the only particle in the standard model that had not yet been found—the Higgs particle. Based on previous experiments,
it was expected to have a mass of between 115 and 185 GeV. Fermilab had hoped to discover it, but reached the limits of its
energy without finding the elusive particle. The LHC is now the only accelerator with enough energy to produce the Higgs.
If the Higgs is found at the lower end of possible energies, it will most likely be detected through a decay into two photons.
Lancaster University in England has a simulation that lets you look at data to find evidence for a Higgs particle. Your job is to
find collisions that produce two photons, measure their energies, and use the energies and the angle between them to determine the mass of the particle that formed them. There are a lot of other interactions taking place, so there is a lot of noise in
the data. You need to look at many examples for your results to be statistically significant.
1. Go to http://www.lppp.lancs.ac.uk/higgs/higgs.html. Go to Measurement and scroll to the bottom of the page. Press Fire.
You should see an image similar to the top quark data in Figure 2 Look for two towers that do not have any lines leading
to them. That is the signature of two photons. You will probably not find them at first. Go to Options and select an energy
cutoff of 20 GeV, then press Fire. Try other energy cut-offs. What energy cut-off lets you find photon events most rapidly?
What happens when the energy cut-off is too high or too low?
2. Find an event with two photon towers. To calculate the mass of the particle that created the two photons, select Measure
energies and click on the two photon towers. Then select Measure angle and click on the angle. Finally, select Calculate
mass. The mass will be displayed on a histogram on the bottom left. To confirm the detection of a Higgs particle you need
to get a lot of events. Your challenge is to collect as many events as possible in 10 minutes and to develop the largest
significance value. How many did you find? Click on the Fit button in the bottom right when it is red. What was the significance of your findings? You are aiming for a significance greater than 5.
Activity 5 | 19
Beyond the Atom: Remodelling Particle Physics
54.8 GeV
c
17.0 GeV
c
95.5 GeV
c
.
.
.
.
.
.
.
.
.
.
.
.
.
.
..
.
.
.
.
.
..
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
. .
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
. .
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
..
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
..
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
..
. .
.
.
.
.
. .
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
..
.
. .
.
.
. .
. .
.
.
.
.
.
.
.
.
.
.
.
.
.
. .
.
.
.
.
. .
.
.
.
.
.
.
.
61.2 GeV
c
muon
muon
+y
+x
65.9 GeV
c
Figure 2 D-Zero Detector at Fermi National Accelerator Laboratory
20 | Activity 5
Beyond the Atom: Remodelling Particle Physics
Video Chapter 1
Models
This chapter of the video:
• introduces the Large Hadron Collider (LHC) and particle
physics
• reviews how scientific models are developed
• describes Rutherford's gold foil experiment
Introduction
Science is a process of learning about our universe through
observation and explanation. We build models to explain our
observations and then test these models using logic and experiment. Experiments are designed to test specific predictions made by the models and to provide new observations
that the models must explain. Models that fail to predict or
explain observations are modified or discarded. As observations improve, so do the models.
Particle physics is the study of the elementary building
blocks of the universe and the forces through which they
interact. Its origins go back to ancient times when philosophers considered what would happen if an object were cut
into smaller and smaller pieces. Some felt that matter could
be continuously divided into smaller and smaller pieces forever. Others concluded the logical answer was that eventually one would reach a point where the object could no longer
be divided—our word atom comes from the Greek word
for “uncuttable.” This idea stood untested for almost two
thousand years, until developments in chemistry and physics
allowed scientists to probe deeper into matter.
One of the earliest developments was electrolysis: the
process of applying an electric
potential across a solution to
separate the constituent parts.
As researchers developed this
tool, they modified their experiments to pull gases apart.
This led to the development of
the cathode ray tube (CRT). In
a CRT, even when an electric
potential is applied across
a vacuum, something is still
observed moving from one
end of the tube to another: a
flow of electrons. In a sense,
the CRT acts like a very sharp
knife, allowing scientists to
“cut the uncuttable.”
Figure 1 Early cathode ray tube.
The discovery of the electron by J. J. Thomson in 1897
showed that atoms were made of even smaller parts. This
raised the question: What is the structure of the atom?
Thomson knew that atoms were electrically neutral and that
electrons were negatively charged. He imagined the atom
looking like a “raisin bun,” with the “bun” being a positive
substance that held the tiny negatively charged electrons or
“raisins” in place. It was this model that Ernest Rutherford
set out to examine.
Figure 2 Ernest Rutherford set up an experiment to test the "rasin bun" model
of the atom.
Rutherford’s scattering experiment overthrew the raisin bun
model and demonstrated that the positively charged part
of the atom must be concentrated into a very small volume
at the centre of the atom—the nucleus. The significance
of Rutherford’s discovery does not stop at the knowledge
gained in the experiment. The technique that Rutherford
used was revolutionary. Instead of pulling atoms apart by
applying an electric potential across them, he probed the
atom by firing particles at it—a technique that is still proving
useful today.
Figure 3 The "raisin bun" model fails to explain the observations
21
Beyond the Atom: Remodelling Particle Physics
Rutherford’s Model and Fields
Electrically charged objects exert forces over a distance—a
seemingly mysterious phenomenon. Somehow, the objects
are able to reach out through space and affect each other
without touching (as the students observe in the Scattering
Experiment). This behaviour can be explained using fields.
An electric field is a region of space surrounding charged objects in which other charged objects feel a force. Since fields
exert forces, they are capable of doing work and transferring
energy.
[
[
“It was as though you had fired a 15-inch shell at a piece of
tissue paper and it had bounced straight back and hit you.”
– Ernest Rutherford
surrounding the target flashed whenever struck by an alpha
particle. Rutherford and his students observed the individual
flashes through low-power microscopes. Eventually they
accumulated enough data to determine that 1 out of every
8000 alpha particles was being deflected straight back. This
was a huge surprise and a puzzle that took Rutherford over a
year to solve.
Rutherford knew that the strength of the electric field surrounding the gold nucleus decreases with distance. Alpha
particles that travel straight through the gold must be far
from any nuclei. Particles that are deflected slightly must
have been closer to a nucleus and experienced a small force.
Particles that bounce back must have traveled directly at a
nucleus, slowed down, stopped and then reversed direction.
The strength of the field depends on the charge distribution
of the object producing the field. In the raisin bun model, the
atom was a lump of positive matter with little negative bits
suspended in it. Rutherford knew that the field generated
by such a dilute positive charge would barely disturb the
trajectory of an alpha particle passing through the atom. To
test this idea he fired positively charged alpha particles at a
thin gold foil. He chose gold foil as his target because it can
be made very thin, giving clean results. A scintillating screen
Figure 4 Flashes of light are produced when an alpha particle hits the screen.
22
Beyond the Atom: Remodelling Particle Physics
Video Chapter 2
Fields and E=mc2
This chapter of the video:
• reviews how energy is transferred in fields
• explains how E= mc2 leads to particle production
• describes how particles are detected in bubble chambers
The kinetic energy of the particle is stored up by the field
as potential energy and then transformed back into kinetic
energy as the alpha particle moves away. The initial energy
of the alpha particle determines how close it gets to the gold
nucleus, as the equation below shows. Rutherford’s original
experiment shows that the minimum separation distance
between the alpha particles and the gold nucleus was
2.7 × 10–14 m, which is about 10 000 times smaller than the
atom. This is not the actual radius of the nucleus, just the
distance of closest approach for the particles that collided
with the nucleus head-on.
collider. Conservation of energy dictates that the total energy
before a collision must equal the total energy after a collision,
but it does not say how that energy is distributed between
rest-mass energy and momentum. The particles produced
in a collision are constrained by various conservation laws
(charge, spin, etc) but within those parameters, anything that
can happen, will happen with a certain probability. Due to
quantum randomness, we cannot predict what particles will
be produced in any one collision. We can, however, predict
the probability of a given result. As long as the initial collision has enough energy to produce the total rest mass of a
certain set of particles, then it will produce those particles
some of the time.
Figure 1 Equations for distance of closest approach
In order to get closer to the nucleus, the alpha particle must
start with more kinetic energy. To increase the kinetic energy
of particles, we accelerate them. The increased energy allows them to penetrate into more intense regions of the electric field, giving researchers a more precise description of the
nucleus. As the energy of the particles increases, we reach
a point where there is so much energy in such a small region
of space that new particles appear. In order to understand
where these new particles come from, we must examine the
nature of energy and mass.
Energy-Mass Equivalence
One result of Einstein’s special theory of relativity is the
unification of energy and mass. Einstein showed that energy
and mass are equivalent and interchangeable. This can be
seen in the general form of the relativistic energy-momentum
expression E2 = (E_o )2 + (pc)2, where E is the total energy, E_o
is the rest mass energy (E_o = mc2, where m is the rest mass
and c is the speed of light), and p is the relativistic momentum (p = γmv, where γ is the relativistic factor due to the
velocity v). For objects that are at rest (p = 0), this expression
simplifies to the more familiar E = mc2.
Figure 2 Particles created in a detector seem to appear out of nowhere.
Note that the rest mass of a particle does
not change when it is accelerated—even
to relativistic speeds. As energy is added
to the system the first term in the energymomentum expression will not change,
so at relativistic speeds the contribution
of rest mass to the total energy becomes
negligible and the expression simplifies to
E = pc. It is sometimes said that as objects
approach the speed of light they get
heavier and heavier, but that is misleading.
As objects approach the speed of light they
get harder to accelerate, which is the same
effect as would occur due to an increase in
mass, but does not actually mean that there
is a change in the rest mass of the particle.
Particle physicists
usually refer to E_0
as "rest energy" and
rarely use the term
"rest mass". There
is no need to qualify
mass because there
is only one mass and
it does not change.
We use the term
"rest-mass energy"
to reflect common
pedagogical usage.
The relativistic energy-momentum expression encapsulates
the fundamental physics behind the creation of particles in a
23
Beyond the Atom: Remodelling Particle Physics
Consider the collision that produced the top quark at Fermilab in the United States, a discovery announced in 1995
(students analyze these results in the Activity 5: Finding the
Top Quark). A proton and antiproton each having rest mass
energy of 0.938 GeV were accelerated to energies of 900
GeV before colliding with a total energy of 1.8 TeV. With so
much energy available there were many possible combinations of rest mass energy and momentum in the products of
the collision. The combination that researchers were looking for was a spray of particles whose total momentum and
energy pointed to a large rest mass. This rest mass was that
of a top quark–antitop quark pair. The energy needed to
produce this pair came from the momentum of the proton
and antiproton. Notice how the analysis moves fluidly from
momentum to energy to mass without really differentiating
between them. Researchers are not being sloppy in their
treatment of units—they are making use of deep connections
between these three quantities.
Figure 3 A Top Antitop Quark Event from the D-Zero Dectector at Fermilab
Antimatter
One of the more exotic results from particle physics is the
discovery and production of antimatter. British physicist Paul
Dirac predicted the existence of a positively charged version
of the electron while deriving a relativistic version of the
Schrodinger wave equation for electrons. The equation had
two possible solutions: one solution was the electron, the
other was a particle with the same mass as an electron but
opposite charge—the positron. This new antimatter particle
was discovered within four years of Dirac’s prediction and
antimatter has played a major role in particle physics ever
since.
24
Antiparticles are fundamental particles that have the same
mass as their counterparts but opposite properties (such as
charge, colour, and strangeness). Thus, the positron is the
antiparticle of the electron. When particles and antiparticles
meet, they can annihilate, releasing all of their rest mass energy as other particles according to E = mc2. Science-fiction
writers have long admired antimatter and routinely invoke it
as a source of energy or as a weapon. In reality, however, it
can be very difficult to produce. One of the largest producers
of antimatter is CERN and they estimate that it would take
100 billion years and over 1000 trillion dollars to produce
even a single gram of antiprotons. Antimatter does, however,
have many applications in medicine. For example, positrons
are used routinely in hospitals for positron electron topography (PET) scans.
Figure 4 A PET scan of a brain
Beyond the Atom: Remodelling Particle Physics
Video Chapter 3
Particle Zoo and Standard Model
This chapter of the video:
• describes how scientists found patterns in the particle zoo
that gave it order
• introduces quarks and the strong nuclear force
• gives an overview of the Standard Model
The Eightfold Way
The first half of the 20th century was a very productive time
for particle physics. At the beginning of the century, the electron was the only subatomic particle that had been discovered. By the mid 1960s, there were dozens of subatomic particles, but no underlying theory to explain this “particle zoo.”
The particles were grouped by behaviour into two categories:
leptons and hadrons. Hadrons were further divided into mesons and baryons. Murray Gell-Mann won the Nobel Prize
in 1969 for his “contributions and discoveries concerning the
classification of elementary particles and their interactions”.
What Gell-Mann and several of his contemporaries did was
to organize the known hadrons by their spin, charge, and
strangeness (just as students do in the Activity 4: Taming the
Particle Zoo). The pattern that emerged revealed a special
symmetry among mesons and baryons, which Gell-Mann
coined the “Eightfold Way”.
success of the model in predicting the existence of the
omega-minus particle was further bolstered by the ability
of the model to adapt to the discovery of new particles by
incorporating three more quarks.
Figure 2 Quarks bring order to the particle zoo.
The Standard Model
The early quark model brought order to the hadrons in the
particle zoo of the early 1960s, but as technology improved
the number of particles increased. The quark model grew to
four, then five, and finally six flavours of quarks organized
into three generations. According to the Standard Model
of particle physics, these six quarks (and their antiquark
counterparts) produce all the observed hadrons: mesons are
quark-antiquark pairs, baryons are quark triplets.
Quark
Figure 1 The Eightfold way brought order to the particle zoo.
Two things were apparent to Gell-Mann: first, one of the
groups was missing a particle (the omega-minus), whose
existence he was able to successfully predict; second, the
basic structure of the patterns seemed to be built out of
triangles. This pointed to the existence of three fundamental
particles: the up, down, and strange quarks. Thus, the quark
model was Gell-Mann’s explanation for the Eightfold Way
symmetry he had observed.
One of the compelling aspects of the Eightfold Way and the
quark model behind it was the way they revealed order within
the particle zoo via a simple set of rules. Two requirements
of a scientific model are that it makes testable predictions
and that it can accommodate new observations. The quark
model has proven to be very robust in this regard. The early
First
generation
Second
generation
Third
generation
Flavour
Down
Up
Strange
Charm
Bottom
Top
Symbol
d
u
s
c
b
t
Charge (e)
Notice that quarks have fractional charges. In nature we do
not find free particles with fractional charge; the smallest
charge we find is the elementary charge e. The only quark
combinations allowed in the Standard Model produce particles with an integer charge.
Quarks are spin-½ particles, which means they have two
distinct spin states (up and down). The Pauli Exclusion
Principle says that two identical particles of this type cannot
occupy the same state. There are particles, like the delta-
25
Beyond the Atom: Remodelling Particle Physics
plus-plus, that have three apparently identical quarks in them
which seems to violate the Pauli Exclusion Principle, so an
additional quantum property, colour charge, was added
to the quark model to further distinguish one quark from
another. Quarks can have one of three “colours”: red, blue,
and green. Of course, quarks do not actually have colour
in the conventional sense; colour is used here to describe
a property of quarks with three variations that combine to
produce a neutral result, just as actual primary colours do.
Colour charge is not observed in baryons and mesons, so
quarks must combine in a way that produces only colourneutral particles. In baryons, this is accomplished by adding
a red quark, a blue quark, and a green quark together to get
a white (colourless) particle. In mesons, this is accomplished
by adding a quark that has colour with an antiquark that has
the corresponding anticolour.
The Standard Model might appear quirky, with its language
of quarks, flavour, colour, strangeness, and spin, but it is described by two very precise mathematical theories: quantum
chromodynamics (QCD) and electroweak theory. These
are two of the most successful and far-reaching theories ever
produced by science. QCD gives a complete description of
how the strong nuclear force works. It sets out the rules that
govern how quarks combine to give hadrons. Electroweak
theory unifies two of the fundamental forces (electromagnetic
and weak nuclear). It describes how electrically charged
particles behave and sets out the rules for the behaviour of
leptons.
Leptons are fundamental particles that do not interact with
the strong force (i.e. they do not have colour). Like quarks,
they come in three generations, with each generation having
a negatively charged particle, such as an electron, and a
neutrino counterpart. Neutrinos are particles that are produced in prodigious numbers during fusion reactions inside
stars. They are incredibly difficult to study because they
interact so weakly with matter. There are many experiments
being conducted around the world to learn more about these
elusive particles.
Lepton
First
generation
Name
electron
Symbol
e
νe
Charge (e)
–1
0
26
electron
neutrino
Second
generation
muon
Third
generation
muon
neutrino
tau
tau
neutrino
μ
νμ
τ
ντ
–1
0
–1
0
The Standard Model is not just about particles. It also gives
a complete description of the strong, weak and electromagnetic forces. In the Standard Model, objects exert forces by
exchanging particles called bosons. Bosons carry information about how strong the force is and whether it is attractive or repulsive. The electromagnetic force is mediated by
photons, (i.e., electrostatic repulsion occurs when photons
are exchanged between two like charges). The strong force
is a short-range force that acts between coloured particles
(i.e., quarks) by exchanging gluons, massless bosons that
carry colour. The weak force is involved in radioactive decay
and is mediated by the W and Z bosons.
Mediator
Electromagnetic
Force
Strong
Force
Weak
Force
Name
photon
gluon
W
Symbol
γ
g
W
Charge (e)
0
0
±1
0
Mass
(MeV/c2)
0
0
81 800
92 600
±
±
Z0
Z0
The final particle in the Standard Model is the Higgs boson.
The Higgs boson was introduced into the Standard Model
to explain why fundamental particles have mass. On July
4, 2012 researchers at CERN announced the discovery of a
Higgs-like particle. Further analysis is needed to confirm if it
is the actual boson predicted by Peter Higgs.
Beyond the Atom: Remodelling Particle Physics
Video Chapter 4
Higgs and the LHC
This chapter of the video:
• uses inertia and mass to introduce the Higgs field
• builds an analogy for the Higgs field
• describes how particles are accelerated at the LHC
• discusses the LHC's detectors and highlights the immense complexity of data analysis at the LHC
The Higgs Mechanism
The Higgs mechanism is a concept that was first introduced
into electroweak theory to solve a serious problem. The
problem was that there was a theory of the weak interactions—a precursor of the Standard Model—that got many
features right, but seemed to predict that all elementary particles were massless. But if they were massless they would
all have to travel at precisely the speed of light, which they
do not. What made this such a serious problem was that the
same feature of the theory that made it successful—a particular symmetry of its equations—was also precisely what
seemed to require particles to be massless.
The technical details of this symmetry use ideas that go
beyond the scope of this resource, but the idea of the Higgs
mechanism can be more simply understood. The idea is that
the universe is permeated by a Higgs field, which breaks the
symmetry that would otherwise make particles massless.
The Higgs field permeates all of space even in the absence
of any particles; it exists everywhere, even in a vacuum.
that couple more strongly are harder to accelerate and so
have more inertial mass. Photons are massless despite
the Higgs field because they do not couple to it at all. Why
some particles couple to the field more strongly than others
is still an open question: the coupling strength for each
particle is an empirically derived parameter (i.e., we start
with observed masses and work backwards to get the coupling strength, rather than predicting the coupling strength
theoretically).
Because the Higgs mechanism determines every particle’s
mass, it plays a vital role in all physical processes. In particular it makes the weak force very short-ranged and this,
in turn, is what makes the weak interactions experienced
by nuclei so weak. Since the weak force is responsible for
all reactions that change protons and neutrons into one
another, it is responsible for the nuclear fusion reaction that
releases energy by converting hydrogen into helium—a
process that requires turning protons into neutrons. Since it
is the strength of this force that controls the rate of nuclear
fusion, the Higgs mechanism is partly responsible for the
reactions that make stars shine. If the Higgs mechanism
were slightly different, stars would either not shine at all or
burn up rapidly. The Higgs mechanism also ultimately determines the fact that the proton is lighter than the neutron,
which is why free neutrons decay into protons (plus other
particles) rather than protons decaying into neutrons. Thus,
the Higgs mechanism is a very important concept, and
finding evidence for or against it will be an important step
forward for science.
In quantum mechanics, every field has a particle associated with it. In the case of the Higgs field, this particle is
the Higgs boson. This boson is like a small ripple in the
Higgs field. If we sufficiently disturb the Higgs field in the
vacuum, we can create a ripple in it– a Higgs boson. This
boson would then decay rapidly into lighter particles, and
it is these lighter particles that the detectors at the Large
Hadron Collider record and analyze.
Figure 1 The Standard Model
Particles experience an energy of interaction with this ambient field, and it is this energy of interaction that we interpret
as their mass (we are able to do this because energy and
mass are interchangeable). Not all particles interact with, or
couple to, the Higgs field with the same strength. Particles
The Large Hadron Collider (LHC)
The Large Hadron Collider or LHC is the world’s largest
particle accelerator—a 27 km-long ring buried 100 m below
the Swiss-French border near Geneva. When running at full
power, it will produce over 600 million collisions per second
at unprecedented energies: 14 TeV for protons, 1150 TeV
for lead ions. The collisions occur at four different locations
on the ring where enormously complicated and sensitive
27
Beyond the Atom: Remodelling Particle Physics
detectors analyze the particles produced by the collisions.
This data is quickly filtered by several layers of computer
analysis to about 100 events of interest per second. These
events are then recorded for further analysis at a rate of
about 700 MB/s. At this rate the LHC creates enough data to
fill a stack of CDs 20 km high every year! Even with this huge
amount of data it is has taken two to three years to accumulate enough data to produce reliable conclusions.
In the LHC’s typical operating mode, two proton beams
circulate in opposite directions. The protons are made by
stripping the electrons from hydrogen. The protons start at
LINAC-2, a linear accelerator that gives them a kinetic energy
of 50 MeV. From LINAC-2 the protons pass through three
accelerating rings: the Proton Synchrotron Booster, Proton
Synchrotron, and Super Proton Synchrotron. At this point
the protons are travelling at a speed of 0.999998c—this is
before they have even entered the LHC! The protons are then
injected into the LHC in two counter-circulating beams, and
for the next 20 minutes they accelerate to their top speed of
0.999999991c.
Each proton beam consists of 2808 bunches that are a few
centimetres long by a millimetre wide and contain about 100
billion protons apiece. As a bunch approaches a collision
point, it gets squeezed into a 16 μm-wide beam by focussing
magnets. It is then deflected by a kicking magnet to collide
with a bunch of protons travelling in the opposite direction.
Figure 2 CERN accelerator complex (simplified)
28
Protons are charged, so they respond to both electric and
magnetic fields. Acceleration is achieved by exerting forces
on the protons with radio waves. As the protons approach
the speed of light they begin to display relativistic effects,
making them increasingly difficult to steer. At the LHC the
protons become so hard to steer that superconducting
magnets with fields in excess of 8 T are used. The magnets
have to be superconducting because it takes such a huge
electric current (11 700 A) to generate this field that it would
be impossible to do so with conventional conductors.
There are four large detectors
attached to the LHC. Each detector records and examines the
collisions in slightly different ways.
The two largest detectors, ATLAS
and CMS, are general-purpose
detectors that are looking for the
all kinds of new physics (including the Higgs boson). Another
detector, ALICE, uses heavy ion
collisions in an effort to study the
behaviour of matter at very high
temperatures and densities. LHCb
is a specialized detector that is
studying rare decays involving the
bottom quark in an effort to test
the Standard Model and to gain
ATLAS:
A Toroidal LHC
ApparatuS
CMS:
Compact Muon
Solenoid
ALICE:
A Large Ion
Collider Experiment
LHCb:
Large Hadron
Collider beauty
Beyond the Atom: Remodelling Particle Physics
insight into the problem of matter-antimatter asymmetry: why
there appears to be so much more matter than antimatter in
the universe.
Each detector has unique features but they are all trying to
do the same basic task—measuring the position, speed,
mass, charge, momentum, and energy of the particles created by collisions. To gather all this information, the detectors are built in layers that measure specific properties of the
particles produced by the collision (except for the neutrinos).
Tracking devices, positioned both near the collision point
and in the outer layers, record the trajectories of charged
particles. Powerful magnetic fields bend the trajectories of
charged particles as they pass through tracking chambers,
revealing the charge and momentum of the particles. As the
charged particles pass through the tracking chamber, electric
signals are sent to a computer for analysis.
Tracking
chamber
Electromagnetic
calorimeter
Hadron
calorimeter
Muon
chamber
photons
e±
muons
π±, p
n
Innermost Layer...
Calorimeters stop the particles and record the amount of
energy deposited. Electromagnetic calorimeters (ECALs)
measure particles like electrons, positrons, and photons.
As these particles pass through an ECAL, they strike the
atoms in the calorimeter and create an avalanche of lowerenergy electrons, positrons, and photons that are detected
by light-sensitive phototubes. Hadronic calorimeters (HCALs)
stop the strongly interacting particles, such as protons, by
having them collide with the atoms in a dense substance like
iron. These collisions rip electrons out of the iron, and these
electrons then radiate photons that in turn produce more
electrons and positrons, in a cascading shower of particles
that can be detected. A typical HCAL will alternate layers of
iron with a less dense substance that will ionize or scintillate
as the particles pass through, allowing the computer to track
them.
Modern detectors produce copious amounts of data for each
collision. Most of this data is filtered out by the computers
in the detector hall. The LHC creates 600 million collisions
every second, so the data analysis challenge is huge. One
of the techniques being developed by CERN to cope with
this challenge is called the Grid. The Grid is a huge global
network of computing centres that share the workload using
new data sharing and analysis techniques. CERN has already
revolutionized the world through the development of the
worldwide web. Who can predict what impact the Grid will
have?
...Outermost Layer
Figure 3 Layers of ATLAS detector
29
Beyond the Atom: Remodelling Particle Physics
Video Chapter 5
Impact of the LHC
0m
1m
2m
3m
4m
5m
6m
7m
Magnetic Field
Directed Out of Page
4T
2T
Silicon
Tracker
ECAL
Electromagnetic
Calorimeter
HCAL - Hadron
Calorimeter
Superconducting
Solenoid
Transverse slice
through CMS
Iron return yoke interspersed
with Muon Chambers
Figure 1 Layers of CMS detector
This chapter of the video:
• reflects on the significance of the LHC
• mentions discoveries the LHC might make
What Else Might the LHC Find?
At peak energy the LHC will be seven times more powerful
than any previous particle accelerator. One goal of the LHC is
to detect the Higgs boson, but at the energy levels the LHC
reaches, there are some other very important phenomena
that it is exploring:
• Dark matter particles – Invisible particles that make up
at least 90% of every galaxy in the universe
• Supersymmetry – A symmetry that predicts the existence of heavier partner particles for every particle in the
Standard Model
• Matter-antimatter asymmetry – Why does the universe
have more matter than antimatter?
• Quark-gluon plasma – An exotic state of matter that may
shed light on the Big Bang
30
Dark Matter Particles
When astronomers look at the night sky, they see stars, planets, gas clouds, and other objects that emit light. Until a few
decades ago, it was thought that these objects made up the
bulk of the universe. However, recent observations, such as
the rotation rates of galaxies, have revealed that light-emitting objects account for just a small fraction of the universe’s
contents. Physicists now think that most of the matter and
energy in the universe is unseen. Ninety percent of the mass
of every galaxy is thought to be made of an invisible substance called dark matter. The leading candidate for this dark
matter is a new type of subatomic particle called a weakly
interacting massive particle (WIMP). Scientists are currently
trying to directly detect WIMPs in a number of experiments.
The LHC could potentially create and detect particles that
would be good candidates for dark matter.
Supersymmetry
Supersymmetry proposes that each particle in the Standard Model has a partner particle with the same charge
but different spin, and possibly with a much higher mass.
Beyond the Atom: Remodelling Particle Physics
For example, the
Particles
electron would
have a supersymmetric partner
called a selectron
that is spinless.
The LHC should
be able to detect
the lowest-energy
supersymmetric
Supersymmetric "shadow" particles
particles—if they
exist. Note that
Figure 2 Schemetic diagram of supersymmetric particles
some of these new
particles could also fit the description for WIMPs and so
supersymmetric theories might also shed light on the origin
of dark matter.
In Summary
The Standard Model provides a very good description of
matter and forces using a small number of fundamental
particles. Scientists are aware of the limitations of this model,
however, and are actively testing it so they can produce a
better model. The Large Hadron Collider represents the latest test of the Standard Model. The LHC operates at such
high energy that it is expected to exceed the limits of the
Standard Model. New discoveries will undoubtedly be made.
Results from the LHC are giving us insight into why particles
have mass, why the universe is made of matter, and even
what the early universe was like. The LHC is moving science
forward to a new deeper understanding of the universe at the
most fundamental level.
Matter-Antimatter Asymmetry
Everything around us—buildings, trees, the Earth, and the
entire solar system—is made of matter, not antimatter. From
the perspective of fundamental physics, this is very puzzling.
Matter and antimatter should have been created in equal
amounts during Big Bang, but detailed observations and
calculations show that there must have been an excess of
matter particles. Why there is more matter than antimatter is
an important open question in science today. The LHCb
detector will provide new insight into this problem by carefully observing reactions involving the b-quark that are slightly
different for matter and antimatter.
Facts and Mysteries in Elementary Particle Physics
by Martinus Veltman (World Scientific, 2003)
Quark-Gluon Plasma
Ordinarily, quarks and gluons are bound inside the nuclei of
atoms. But, in situations with extremely high temperatures
or densities, there can be enough energy for them to be free.
The gluons and quarks then move around freely in a “soup”
called a quark-gluon plasma. According to current Big Bang
theories, the universe went through a quark-gluon plasma
stage before cooling to a point where the quarks and gluons
became confined inside composite particles such as protons
and neutrons. The LHC smashes lead ions together at such
high energies that a quark-gluon plasma should be created.
Physicists can then observe how matter behaved in the earliest stages of the universe.
Further Reading
Understanding the Universe from Quarks to the Cosmos
by Don Lincoln (World Scientific, 2004)
The New Cosmic Onion
by Frank Close (Taylor & Francis, 2007)
Introduction to Elementary Particles
by David Griffiths (Harper & Row, 1987)
The Quantum World: Quantum Physics for Everyone
by Kenneth Ford (Harvard Press, 2004)
Figure 3 A lead-lead collision producing a quark-gluon plasma
31
Beyond the Atom: Remodelling Particle Physics
Activity Solutions
Activity 1: Video Summary
1.
Dalton’s model
of indivisible balls
of matter
Thomson’s model
using electrons in
a positive mass
Rutherford’s model
using electrons
and nuclei
Solid ball of matter
negative electrons
positive substance
positive nucleus
negative electrons
6. (b) has three types of charge and gets stronger with distance. The strong force acts on the colour charge. There
are three colours (red, blue, green). The strong force increases with distance, leading to the strange phenomenon
of quark confinement. Quarks are never found in isolation.
If you try to pull two quarks apart, the force holding them
increases until you add so much energy that a new quark
pair is produced.
7. (a)
2. (d) A few of the alpha particles bounced back. The lump
of positive matter in Thomson’s model was too diffuse to
generate a strong electric field. Rutherford expected the
alpha particles would go right through the foil. When 1 out
of 8000 alpha particles was deflected straight back, he
realized that the positive matter must be concentrated into
a very small space.
3. (c) both get closer to probe smaller distances and create
massive particles from the energy. Higher-energy particles
penetrate deeper into matter, so we get a clearer picture
of what is happening at smaller scales. Higher-energy
particles will also create more massive particles during
collisions.
4. (a) E = energy, m = mass, c = the speed of light. This
equation shows that energy and mass are equivalent and
interchangeable. Mass is a form of energy and energy has
mass.
(b) The mass of the electron-positron pair comes from the
energy of the photon.
Quarks
Leptons
1st
Generation
2nd
Generation
3rd
Generation
Bosons
u
c
t
γ
d
s
b
g
e
μ
τ
Z0
νe
νμ
ντ
W
±
(b) The particles in the first column are fundamental to the
periodic table—the world around us is made of this 1st
generation.
(c) The 2nd and 3rd generations are heavier and are make
exotic particles that are not common to everyday experience.
(d) The bosons are the force mediators. They are involved
in the interactions between matter. The photon and gluon
are massless, while the W and Z bosons are very heavy.
(e) In the periodic table, over 100 elements organized
according to a pattern in the arrangement of the protons,
neutrons, and electrons. In the Standard Model, all the
subatomic particles organized by the arrangement of
quarks and leptons.
8. The one particle that is still being looked for is the Higgs
boson. It is needed to make the Standard Model work at
higher energies, and if detected will give evidence for the
Higgs field which is responsible for giving fundamental
particles mass.
5. (a) The discovery of new particles was a problem because
they were not made of protons and electrons. For example, pions were too big to be electrons but too small to
be protons. There was no model to explain what they were
made of.
(b) The problem required new fundamental particles—quarks.
All known hadron particles can be created using quarks.
32
9. The LHCb experiment is studying the matter-antimatter
asymmetry problem by looking at events involving the bottom quark. The ALICE detector is looking for quark-gluon
plasmas by colliding lead ions together. The LHC might
also find evidence for or against dark matter, supersymmetry, and even extra dimensions.
Beyond the Atom: Remodelling Particle Physics
Activity 2: Scattering Experiment
1. The hanging balloon should be on as long a thread
as possible. This gives maximum deflection for a given
amount of force. The electrostatic force needs to be
made as large as possible. The balloons need to be
rubbed vigorously with fur, hair, or a wool sweater to get as
large a charge as possible. The hanging balloon should
be rubbed all over—not just on one side. If the charge is
just on one side, the hanging balloon will rotate to put this
charge farther away. The balloons need to be brought as
close to each other as possible. The students will probably not predict the difficulty of preventing the hanging
balloon from slipping off to one side or the other.
Similar: The objects have the same electrical charge
and repel each other. The strength of the repulsive force
increases as the separation decreases. The objects are
roughly spherical. It is hard to get a straight-line, head-on
repulsion in both cases.
Different: The gold nucleus is 40 times more massive than
the alpha particle and has about 40 times the charge as
well. The balloons are almost identical. The hanging balloon is like the gold nucleus because it is the target, but it
is like the alpha particle because it was the one that was
deflected. The model involves gravity and tension. The real
experiment does not involve tension and the gravitational
force is negligible.
More similar: Throw the balloon at a balloon that is fixed
in place.
2. The ball should be launched with enough speed to get
on the base, but not to hit the stem. If the balls have too
much energy they will bounce off the stem. The track
needs to be aimed directly at the stem. If it is aimed
slightly to the side, the balls will be deflected.
Similar: The wine glass acts like the gold nucleus by not
moving. The balls are like the alpha particles being fired at
the target. Very few alpha particles bounce straight back.
Different: The force of repulsion is not electrostatic. The
balls could be launched at a variety of speeds.
More similar: Make the ramp a fixed height to produce the
same speed for the balls.
3. Planning the performance requires that students say what
they know and consider how to represent it accurately.
The bulk of the learning takes place during this planning
phase. The performances should show how only the direct
approach will stop the alpha particle completely and send
it straight back. The more the approach differs from this
path, the less it is slowed and the smaller the deflection.
4. (a) The nucleus should have a diameter of 1.5 cm and the
closest approach should be 2.7 cm away from its centre.
(b) The particles off to one side do not get as close. This is
because they don’t stop completely, but begin to deflect
while still moving.
(c) The next nucleus will be 10–10 m (10 000 × 10–14 m) away.
This means that the next nucleus would be 10 000 cm =
100 m or about a residential block away! Most of matter is
empty space. It only appears solid due to the electrostatic
repulsion of the electrons buzzing around in this space.
Activity 3:
Bubble Chamber Detective
Part 1: CERN’s Two Metre Hydrogen Bubble Chamber
1. (a) –1 The kaons curve very slightly to the right. The right
hand (or left hand) rule indicates that they are negative.
2. (b) +1 The particle curves to the left so according to the
right hand (or left hand) rule it must be positive.
3. (c) has interacted with a proton to produce two oppositely
charged particles. Charge is always conserved. A single
negative kaon cannot decay into two charged particles so
(a) and (b) are eliminated. We know that a negative kaon
entered the point and that two charged particles have left
it. The one on the right is positive. The other track doesn’t
curve enough to indicate its charge. However, it must be
negative in order to conserve the kaon’s charge. Where
did the positive charge come from? The kaon must have
interacted with one of the protons in the hydrogen.
4. (c) A neutral particle has been produced that moves up
and to the left. Momentum is always conserved. We see
one track continuing in the original direction and another
track moving up and to the right. There must be another
particle moving somewhat to the left. We can’t see it, so it
must be neutral.
5. (d) Decayed into a negatively charged particle and a neutral particle. Charge is always conserved. The total charge
before and after the event is the same so a decay has occurred. Conservation of momentum infers the existence of
the neutral particle.
33
Beyond the Atom: Remodelling Particle Physics
6. (d) decayed into a negatively charged particle and a neutral
particle. Charge is always conserved. The total charge
before and after the event is the same so a decay has
occurred. Conservation of momentum infers the existence
of the neutral particle. This the same type of event as
question 05 but in this case the neutral particle does not
take away as much momentum so the track only changes
slightly.
7. (c) point R. This is the neutral particle from question 06.
(Note: The negative particle that decays at R is the omegaminus particle. This particle was predicted by Murray GellMann in 1962 and found in 1964 using the next bubble
chamber photograph. The Taming the Particle Zoo activity
has students analyze patterns to make the same prediction
that Gell-Mann did. The second bubble chamber photograph is the one that first detected the omega-minus.)
significant component up the page because of conservation of the original momentum.
3. When you join the intersection points and extend the line,
you find that the neutral particle did not come from the
kink at point W as you might expect. There is not enough
evidence to determine where along this line the particle
was produced.
4. The three lines meet at one point. From this we can infer
that the three neutral particles had the same origin. No
track is visible so we can infer that a neutral particle must
have decayed into three other neutral particles that then
proceeded to decay at points X, Y, and Z.
5.
8. (d) A neutral particle moving up and to the left has decayed into two new particles. Conservation of charge eliminates answers (a) and (c). Momentum is always conserved.
The two particles created at Q have a net momentum
toward the top left. These particles were either produced
by the decay of a neutral particle moving up and to the left
or by the decay of a stationary particle along with a neutral
particle moving down and to the right. This second option
is impossible since the chamber is filled with liquid hydrogen and hydrogen is made of protons and electron which
are stable, so there is nothing that could decay into
three particles.
9. (c) point P. This is the neutral particle from question 04.
10. A negative kaon collides with a proton at point P. This
collision produces three particles: a neutral particle moves
off to the top left where it decays at Q into two oppositely
charged particles, a positive particle that exits the chamber, and a negative particle that decays at R into a negatively charged particle and a neutral particle. The neutral
particle decays into two oppositely charged particles at
S. The negative particle from R moves up and to the right
until it decays into a negative particle and a neutral particle
Part 2: Brookhaven National Laboratory’s Bubble Chamber
1. There is a charged particle moving in almost the same direction as the original kaon. It curves to the left, so it must
be positive. This positive charge indicates that the negatively charged kaon interacted with one of the protons of
liquid hydrogen. The charged particle that branches to the
right must be negative to conserve charge from the kaon.
There must also be a neutral particle going somewhat to
the left to conserve momentum.
2. There is a negative particle going to the right. It must be
negative to conserve charge and because it curves clockwise. There must also be a neutral particle to conserve the
original momentum. Its momentum will ultimately have a
34
6. This question requires that the students clearly explain the
steps of the analysis using the four neutral trails. The full
analysis requires an understanding of what some of the
hundreds of particles are and how they can decay, which
the students can’t be expected to know. This question also
lets the students reflect on science as a human endeavour
with bosses, gambles, and payoffs.
Go to the TeacherGuide folder on the DVD to read an email
from Dusan Radojicic, recounting the night he discovered the
first omega-minus.
Beyond the Atom: Remodelling Particle Physics
Students who recognize this and suggest the possibility
of another particle can be given the eta-prime card–the
missing meson. Second, there are three quark-antiquark
pairs that have the same Q and S values. Students might
suggest that there must be some other property that would
further distinguish the particles. This is partly true: there is
another quantum number called isospin which eliminates
the strange-antistrange solution for π0, but it also demonstrates a very important aspect of quantum mechanics—one particle can be the superposition of two (or more)
different states. The quark content of the π0 can be either
up-antiup or down-antidown which means that if you could
pull a π0 apart, half of the time you would get an up-antiup
pair and half of the time you would have a down-antidown
pair. The η and η’ are a more complicated mixture of upantiup, down-antidown and strange-antistrange quarks.
The difference between η and η’ is very subtle but extremely important to the development of our understanding
of symmetry in the Standard Model.
Activity 4: Taming the Particle Zoo
Part 1: Finding Patterns
2. Students will find that sorting the cards by their spin will
produce three groups of roughly equal size.
3. Organizing these groups by charge and strangeness will
lead to patterns emerging.
4. Two groups (spin-0 and spin-½) will have eight cards in
them arranged in three rows. The top row will contain two
cards, the middle row will contain four cards (two in the
same place) and the bottom row will contain two cards.
The more familiar pattern emerges if the top and bottom
rows are shifted half a card toward the centre by changing
the columns to diagonals.
2.
5. The third group (spin- ) will have nine cards arranged in
three rows. One row will have 4 cards, the next 3, the next
2. From the pattern, it is pretty obvious that the last row
should have 1 card. The more familiar pattern emerges if
the cards are shifted over by changing the columns to diagonals. By inspecting the cards, students should be able
to propose that the missing card will have spin- , Q = –1,
S = –3, mass ≈ 1680 MeV. The omega-minus card can be
given to each group when they give you the description
of the missing particle. A Nobel Prize card is included to
award to the first group to propose this particle (they don’t
have to get the name right, just the description). Murray
Gell-Mann was awarded the Nobel Prize in 1969 for
his model that predicted the existence of the omegaminus.
Part 2: Understanding Patterns
1.
qq
uu
ud
us
du
dd
ds
su
sd
ss
Q
0
+1
+1
-1
0
0
-1
0
0
S
0
0
+1
0
0
+1
-1
-1
0
qqq
uuu
uud
udd
ddd
uus
uds
dds
uss
dss
sss
Q
+2
+1
0
-1
+1
0
-1
0
-1
-1
S
0
0
0
0
-1
-1
-1
-2
-2
-3
p
n
Spin-3/2
Baryons
Spin-1/2
Baryons
Same basic problems: missing particles and more than
one particle in same spot. Instead of pointing to missing
particles (although that is reasonable and students who
suggest that should be congratulated), the empty boxes
are pointing to deeper structural rules. In this activity we
have chosen to only look at the charge and strangeness of
the quarks, but quarks also have spin of ½. When spin-½
quarks are combined they will either produce a symmetric
spin state of or a mixed symmetry spin state of ½. There
are ten quark combinations that will produce a spin of
but only eight that will produce a spin of ½. This has to do
with the total angular momentum of the baryon and the
possible spin configurations that will produce symmetric or
antisymmetric wave functions. There is no way to produce
a spin-½ particle with three similar quarks.
Particle
Symbol
[NOTE: In this activity the students will identify π0 with ss,
which is incorrect but for reasons that are beyond this
simplified activity]
There are two basic problems: First, there are nine combinations and the students have only created an octet.
35
Beyond the Atom: Remodelling Particle Physics
Activity 5: Finding the Top Quark
Part 1: Top Quark
1. Role playing helps students picture this three-dimensional
collision more clearly and reinforces that it does not involve
large objects breaking apart into smaller pieces. Have the
students consider the question first as a Think-Pair-Share
activity. Then give two volunteers two identical small balls
marked + and – for the proton and antiproton. Have them
run toward each other at equal speeds, make the balls
collide and then disappear. Next give eight or so other
students basketballs, ping pong balls, tennis balls, and so
on. Have them hold their particles at the collision point and
then count down to zero. The particles should move off in
all directions so that momentum is conserved in all three
directions. Ask those sitting down if the collision broke any
laws of physics. Ask them if it is possible for the particles
to move just in the horizontal plane. (It is possible, but not
very likely.) Have the participating students demonstrate
this motion. In the example that they are going to look at,
the particles did just happen to emerge with almost all the
momentum in a 2-D plane. This makes the problem much
easier to analyze.
2. Students’ values may differ by ±1 mm, which is not significant. They should notice the fact that it appears that
momentum is not conserved.
Magnitude
(mm)
Horizontal
(mm)
Vertical
(mm)
Total
Total
(mm)
(GeV/c)
22
–35
35 left
–62
1
1 up
95
55
17
61
66
–94
–32
11
58
–15
44
14
20
3. The momentum of the neutrino is equal and opposite to
the net momentum from question 2. Using the given scale
(1 mm = 1 GeV/c) the momentum of the neutrino will be 35
mm long pointing right.
4. The sum of the magnitude of the momentum vectors (plus
the momentum of the neutrino) is equal to the total energy.
The total energy will be around 330 GeV.
5. The total energy of 330 GeV has to be divided by two because a top-antitop pair were created by the collision. This
yields a mass of 165 GeV, which is only 4% different from
the accepted value of 172 GeV.
36
6. The top quark is not a particle that already existed inside
the proton. The top quark’s mass is 180 times greater
than a proton’s mass of 0.938 GeV! When the fast-moving
particles collide, all of their energy—from mass and from
motion—is turned into pure energy. The collision was just a
method to pack a lot of energy into a tiny space.
Part 2: Higgs Particle Simulation
1. Setting a high energy cutoff simplifies the diagram greatly
by removing the lower energy towers. However, if it is set
too high, it may cut off the photons that you are trying to
detect. A value of around 50 GeV seems to give the best
results.
2. A typical result is 29 events with a significance of 1.6, using an energy cutoff of 50 GeV. If you select Auto events,
you can quickly get 71 events with a significance of 2.8.
Many (approximatley two thirds) of the generated events
were discarded because the photon energies were below
the cutoff.
Beyond the Atom: Remodelling Particle Physics
Who are the people in the video?
The status of the contributors below reflect their positions at the time the video was filmed.
BRIAN BATELL
Postdoctoral Researcher,
University of Chicago, Perimeter Institute Batell is a particle
physicist who focuses on theories beyond the Standard Model.
He is particularly interested in
alternative theories of symmetry
breaking and dark matter. He
obtained his PhD from the
University of Minnesota in 2008.
NATALIA TORO
Faculty Member, Perimeter Institute Toro works in particle physics and is interested in physics
beyond the Standard Model.
This includes dark matter, other
new particles, and understanding the hierarchy problem. She
collaborates heavily with experimentalists. Toro obtained her
PhD from Harvard in 2007.
CLIFF BURGESS
Professor, McMaster University
Associate Faculty Member,
Perimeter Institute Burgess is a
physicist with a broad range of
interests including string theory,
cosmology and particle physics. He also has a passionate
interest in outreach. He obtained
his PhD from the University of
Texas.
BRIGITTE VACHON
Canada Research Chair in
Particle Physics. Professor,
McGill University Vachon is an
experimentalist particle physicist involved in CERN's ATLAS
experiment. She works on trying
to understand the nature of
subatomic particles at the scale
of energies created by the LHC.
She obtained her PhD from the
University of Victoria in 2002.
GHAZAL GESHNIZJANI
Postdoctoral Researcher,
Perimeter Institute Geshnizjani
works in the field of cosmology
and focuses on researching the
early universe. She obtained her
PhD from Brown University in
2005.
ANDREAS WARBURTON
Professor, McGill University
Warburton works in experimental particle physicist and is a
member of CERN's ATLAS experiment. One of his research areas is searching for substructure
to quarks. He obtained his PhD
from the University of Toronto in
1998.
PHILIP SCHUSTER
Faculty Member, Perimeter
Institute Schuster is a particle
physicist interested in the nature
of dark matter and the weak
interaction. His work intersects
both theory and experiment. He
obtained his PhD from Harvard
University in 2007.
37
Beyond the Atom: Remodelling Particle Physics
Appendix A
Particle Zoo Cards
p
PROTON
mass: 938 MeV
spin-½
Q = +1
S=0
Σ
*-
Δ
DELTA MINUS
mass: 1232 MeV
spinQ = -1
S=0
Σ
SIGMA MINUS
mass: 1197 MeV
spin-½
Q = -1
S = -1
Ξ
0
Ξ
XI STAR ZERO
mass: 1532 MeV
spinQ=0
S = -2
Σ
SIGMA PLUS
mass: 1189 MeV
spin-½
Q = +1
S = -1
discovered: 1953
38
mass: 1315 MeV
Κ
0
KAON (K ZERO)
mass: 498 MeV
spin-0
Q=0
S = +1
Σ
Κ
-
SIGMA ZERO
mass: 1193 MeV
mass: 135 MeV
discovered: 1949
Ξ
*-
XI STAR MINUS
mass: 1535 MeV
spinQ = -1
S = -2
discovered: 1962
π
+
discovered: 1947
0
PION (PI ZERO)
spin-0
Q=0
S=0
discovered: 1959
discovered: 1962
+
XI ZERO
spin-½
Q=0
S = -2
discovered: 1953
*0
π
0
discovered: 1960
discovered: 1954
-
mass: 1387 MeV
spinQ = -1
S = -1
discovered: 1919
-
SIGMA STAR MINUS
PION (PI PLUS)
mass: 140 MeV
spin-0
Q = +1
S=0
discovered: 1947
n
NEUTRON
mass: 940 MeV
spin-½
Q=0
S = -1
spin-½
Q=0
S=0
discovered: 1956
discovered: 1932
KAON (K MINUS)
mass: 494 MeV
η
ETA
mass: 548 MeV
spin-0
Q = -1
S = -1
spin-0
Q=0
S=0
discovered: 1947
discovered: 1961
Beyond the Atom: Remodelling Particle Physics
Appendix A
Particle Zoo Cards continued
-
Ξ
XI MINUS
mass: 1322 MeV
spin-½
Q = -1
S = -2
0
Δ
*+
Σ
spinQ = +1
S = -1
discovered: 1960
DELTA ZERO
KAON (KBAR ZERO)
mass: 1231 MeV
Κ
0
KAON (K PLUS)
mass: 494 MeV
spin-0
Q = +1
S = +1
Λ
discovered: 1947
Δ
++
mass: 498 MeV
spin-0
Q=0
S = -1
π
-
LAMBDA
mass: 1116 MeV
spin-½
Q=0
S = -1
PION (PI MINUS)
mass: 140 MeV
spin-0
Q = -1
S=0
discovered: 1947
Δ
+
discovered: 1947
discovered: 1954
Κ
mass: 1383 MeV
discovered: 1952
spinQ=0
S=0
+
SIGMA STAR PLUS
DELTA PLUS
mass: 1235 MeV
spinQ = +1
S=0
discovered: 1954
Σ
*0
SIGMA STAR ZERO
mass: 1384 MeV
spinQ=0
S = -1
discovered: 1951
discovered: 1960
ETA PRIME
NOBEL PRIZE
mass: 958 MeV
Murray Gell-Mann
DELTA DOUBLE
PLUS
mass: 1231 MeV
spinQ = +2
S=0
discovered: 1954
Ω
-
OMEGA MINUS
mass: 1672 MeV
spinQ = -1
S = -3
discovered: 1964
η’
spin-0
Q=0
S=0
discovered: 1964
39
Beyond the Atom: Remodelling Particle Physics
Appendix B
Particle Physics Equations and Constants
Description
Equation
Variables
Si Unit
FM – force acting on charged object moving in
magnetic field
q – quantity of charge on object
v – speed of charged object
B – magnetic field strength
N
Newton's 2nd
Law
Fnet – net force acting on object
m – mass of object
a – acceleration of object
N
kg
m/s2
Centripetal
Acceleration
aC – centripetal acceleration
v – linear speed of orbiting object
R – radius of orbit
m/s2
m/s
m
Kinetic Energy
EK – kinetic energy
m – mass of object
v – linear speed of object
J
kg
m/s
Electric Field
Strength
EQ – magnitude of electric field
k – Coulomb’s constant
Q1 – charge on object one
Q2 – charge on object two
r – radial distance between objects
J
Nm2/C2
C
C
m
Relativistic
EnergyMomentum
Relation
E – total energy
E0 – rest-mass energy
p – relativistic momentum
c – speed of light
J
J
kgm/s
m/s
Rest-Mass
Energy
E0 – rest energy
m – mass of object (aka “rest mass”)
c – speed of light
J
kg
m/s
Relativistic
Momentum
p – relativistic momentum
γ – Lorentz factor
m – mass of object
v – speed of object
kgm/s
Lorentz Force
kg
m/s
γ – Lorentz factor
Lorentz Factor
v – speed of object
c – speed of light
Name
C
m/s
T
Symbol
Value
m/s
m/s
Si Unit
-19
elementary charge
e
1.602x10
Coulomb's constant
k
9.00x109
Nm2/C2
Speed of Light
c
3.00x108
m/s
40
C
Beyond the Atom: Remodelling Particle Physics
03 Perimeter Explorations
Beyond the Atom: Remodelling Particle Physics
Teacher's Guide
AUTHOR TEAM
Dave Fish
Physics Teacher, Sir John A Macdonald Secondary School and
Educational Consultant, Perimeter Institute for Theoretical Physics
Roberta Tevlin
Physics Teacher, Danforth Collegiate and Technical Institute and Teacher
Network Coordinator, Perimeter Institute for Theoretical Physics
Damian Pope
Senior Manager of Educational Outreach,
Perimeter Institute for Theoretical Physics
SCIENCE ADVISORS
Cliff Burgess
McMaster University and Perimeter Institute for Theoretical Physics
Rolf Landua
Head of CERN Education Group
Eric Mazur
Harvard University Balkanski Professor of Physics and of Applied Physics
TEACHER CONTRIBUTORS
John Atherton, Alpha II Alternative School Toronto, Ontario
James Ball, John F. Ross Collegiate Vocational Institute, Guelph, Ontario
Peter Dobias, O'Gorman High School, Timmins, Ontario
Dave Doucette, Richmond Hill High School, Richmond Hill, Ontario
Dwight Dunfield, Fredericton High School, Fredericton, New Brunswick
Darlene Fitzner, Sir Winston Churchill High School, Calgary, Alberta
Philip Freeman, Richmond Secondary School, Vancouver, British
Columbia
Patrick Kossmann, Greenall School, Balgonie, Saskatchewan
Lisa Lim-Cole, Uxbridge Secondary School, Uxbridge, Ontario
Chris Nichols, Castle View High School, Castle Rock, Colorado, USA
Barry Panas, St. John's-Ravenscourt School, Winnipeg, Manitoba
Nanouk Pare, John Abbott College, Montreal, Quebec
David Vrolyk, Sir John A. Macdonald Secondary School, Waterloo,
Ontario
EDITORIAL PROJECT MANAGEMENT
Kevin Martindale
John Yip-Chuck
New Leaf Media
COVER DESIGN
Gabriela Secara
3D IMAGES
Steve Kelly
PRINTER
Denison Print
VIDEO PRODUCER
Damian Pope
Senior Manager of Educational Outreach
Perimeter Institute for Theoretical Physics
VIDEO DEVELOPMENT, PRODUCTION, AND POST PRODUCTION
Show Communications
EXECUTIVE PRODUCER
Greg Dick
Director of Educational Outreach
Perimeter Institute for Theoretical Physics
COPYRIGHT
Published by Perimeter Institute for Theoretical Physics, 31 Caroline
Street North, Waterloo, Ontario, Canada, N2L 2Y5. Copyright © 2013 by
Perimeter Institute for Theoretical Physics.
All rights reserved. No part of this work covered by the copyright herein,
except for any reproducible pages including in this work, may be
reproduced, transcribed, or used in any form or by any means—graphic,
electronic, or mechanical, including photocopying, recording, taping, Web
distribution, or information storage and retrieval systems—without the
written permission of Perimeter Institute for Theoretical Physics.
For permission to use material from this text or product, submit a request
online to Perimeter Institute.
The information and activities presented in this book have been carefully
edited and reviewed for accuracy and are intended for their instructional
value. However, the publisher makes no representation or warranties of
any kind, nor are any representations implied with respect to the material
set forth herein, and the publisher takes no responsibility with respect to
such material. The Publisher shall not be liable for any general, special,
consequential or exemplary damages resulting, in whole or in part, from the
readers' use of, or reliance upon, this material.
EDITOR
Tom Moss Gamblin
INTERIOR DESIGN AND COMPOSITION
Anna-Marie Hatayer
Elizabeth Goheen
41
Beyond the Atom: Remodelling Particle Physics
ACKNOWLEDGMENTS
Special thanks to the teachers who attended:
• Einstein Plus 2011, Perimeter Institute
• The 2011 PTRA summer institute, Omaha, Nebraska
• The OTF Physics Camp in August 2011, Sudbury
• The September 2011 meeting of the Physics Teachers Alliance (GTA)
The QuarkNet program at Fermilab for permission to modify their
activity on the top quark. In particular, Marjorie Bardeen, Rob Grimm
(William Fremd High School, Palatine, Illinois, USA), and Tom Jordan.
The physics department at Lancaster University for their computer
simulation of Higgs boson detection
Mick Storr and Goronowy Tudor-Jones and the High School Teachers
program at CERN.
IMAGE CREDITS
CERN including the ALTAS and CMS detectors for use of LHC and
detector images on pp. 1, 3, 7, 14, 28, 29, 30, 31
Brookhaven National Laboratory for use of omega-minus image on p. 15
Fermilab for top quark image on p. 20 and Standard Model image on p. 27
Particle Data Group, Lawrence Berkeley National Laboratory of use of
supersymmetry image on p. 31
National Museum of Science and Industry (UK) for use of cathode ray tube
image on p. 21
iStockphoto/Banks Photos for the PET (Positron Emission Tomography)
scan of a human brain on p. 24.
Perimeter Institute for Theoretical Physics gratefully acknowledges the
support of the Government of Ontario and the Government of Canada.
42
Perimeter Institute
Perimeter Institute for Theoretical Physics is an independent, nonprofit, research institute whose mission is to make breakthroughs
in our understanding of our universe and the forces that govern
it. Such breakthroughs drive advances across the sciences and
the development of transformative new technologies. Located
in Waterloo, Ontario, Canada, Perimeter also provides a wide
array of research training and educational outreach activities to
nurture scientific talent and share the importance of discovery
and innovation with students, teachers, and the general public.
In partnership with the Governments of Canada and Ontario,
Perimeter is a successful example of public-private collaboration in
scientific research, training, and outreach.
Perimeter Explorations
This series of in-class educational resources is designed to help
teachers explain a range of important topics in physics. Perimeter
Explorations is the product of extensive collaboration between
international researchers, Perimeter Institute’s outreach staff and
science educators. Each module has been designed with both,
expert and less experienced teachers in mind, and thoroughly
classroom tested.
Perimeter Explorations 03 Beyond the Atom:
Remodelling Particle Physics Teacher’s Guide includes:
- Teacher’s Guide in printed form
- Teacher’s Support Material CD-ROM with the teacher’s guide
in PDF format and modifiable versions of the student activities
To order other Perimeter Institute Educational Outreach Resources,
please visit our online store at www.perimeterinstitute.ca
Follow us on Twitter @Perimeter
Perimeter Institute for Theoretical Physics
31 Caroline Street North
Waterloo, Ontario
Canada N2L 2Y5
Tel: +1 519 569 7600
Fax: +1 519 569 7611
Made in Canada
© 2013 Perimeter Institute for Theoretical Physics
ISBN 978-1-927633-00-7
9 781927 633007