Physics 391/691 - Particle PhysicsEveryone Pick Up:•Syllabus•Student Info sheet – fill it out

http://www.wfu.edu/~ecarlson/particles

8/29

https://sakai.wfu.edu/portal/site/particles

Textbook #1“Introduction to Particle Physics” by E. Carlson$25 cash or check from me

Textbook #2“2012 Review of Particle Properties” by the Particle Data Group, booklet or book, free to order online

Other Materials:•Scientific Calculator•Laptop

How This Class Will Work•I will not be giving a standard lecture

• Much of the learning will be obtained by reading the book•I will sometimes summarize the most important points at the start of class•I will primarily respond to questions/requests from your Sakai reading “quizzes”•We will spend much time in class working on problems •Often, you will be working on problems in class

•Always bring a scientific calculator to class•Probably a good idea to bring your book too, but not necessary•Be prepared to work on problems in class

Preparing for Lecture

•Read the material assigned on the web•Take the reading quiz online by 11:00 AM•Reading quizzes should show thought – they are not graded primarily on whether the answer is correct

• It can be right and not get full credit; it can be wrong and get full credit •Your answers will sometimes be used anonymously in class

Reading Assignment•Chapter 1 by Friday•Sections 2A-D by Monday

Quizzes:•Reading quiz A by Friday•Reading quiz B by Monday

The Large Hadron Collider sends numerous cylindrical bunches of protons around a large accelerator, in opposite directions, and then collides them head on.  Name at least three things the LHC could do if it wished to increase the

integrated luminosity from its current total of around 13 fb-1.

Class Participation•Class participation will be about 15% of your grade•Good comments on “reading quizzes” counts towards class participation•You will often work in groups on problems in class•You will often present your work on problems to the class

Class Attendance and Seating•If you need to miss class, email me beforehand if possible, or as soon as you get a chance•I do not grade directly on attendance

• Though it affects class participation•I will often have you work in groups of(probably) 3, so sit in groups of 3•At some point, I will probably reshuffle you

Calvin ArterAlyssa BrigemanSean CusanoSam FlynnChris LyleLoah Stevens

Homework•About 2-6 problems per homework set•Due usually on Wednesday and Friday

•Exception – due this Monday•Due at start of class

•Late homework will be penalized•Problems vary greatly in difficulty•Encouraged to talk / work on them during my office hours•What you submit should be your own work

Homework:•1.2, 5, 7, 8, 9, 14 by Monday

Exams

•Midterm and final•Midterm – 2 hours in the evening, week of Oct. 15-ish, date TBA•Final – 3 hours, 2:00 PM Dec. 11

•Honors code violations will be turned in to the honor council•Closed book but

•Formula sheet provided (maybe front and back covers of the book, for example), or •Limited self-made notes

GradesPercentage

Breakdown:Midterm 20%Final 30%Homework 30%Quizzes 5%Class Part. 15%

Grade Assigned94% A 73% C90% A- 70% C-87% B+ 67% D+83% B 63% D80% B- 60% D-77% C+ <60% F

•Curving possible, if needed

The Web

Numerous materials can be found on the web for this course•Electronic version of the book•Reading assignments, homework assignments, etc.•Test information as we get closer to midterm/final

Pandemic Plans•If there is a catastrophic closing of the university, we will attempt to continue the class:

http://www.wfu.edu/~ecarlson/particles

Emergency contacts:Web page

emailCell: 336-407-6528

Home: 336-724-2008

Today’s In-Class problemThe Large Hadron Collider (LHC) collides head-on protons distributed randomly within two bunches in

the shape of a cylinder. Assume that protons are spheres 1 fm in diameter, and if two protons overlap, they collide. As these two bunches pass through each

other, how many pp collisions will take place?

Today’s In-Class problemThe Large Hadron Collider (LHC) collides head-on protons distributed randomly within two bunches in

the shape of a cylinder. Assume that protons are spheres 1 fm in diameter, and if two protons overlap, they collide. As these two bunches pass through each

other, how many pp collisions will take place?

15 1010 p+ 15 1010 p+

9 cm 9 cm

20 m

20 m

E = 4000 GeV E = 4000 GeV

Mp = 0.938 GeV/c2

AnnouncementsEveryone Pick Up:•List of Students

8/31

XX

TP

V

v

N = number of particles per bunchA = area of bunchn = number of bunchesf = frequency at which they go around

1 2 ,X X

nN NN Ldt L f

A

V = volume the particle is inv = relative speedT = how long you wait

“It was unclear about whether the cross-section was something that we had to measure, or if it was a known, set factor and something that could be varied throughout experiments.”

“I'm also confused as to what a parameter is in terms of the 17 particles and the 18 parameters.”

•17 particles is pretty clear•We have not yet defined the theory, but when we do, it will have 18 parameters

Simple example: QED describes the behavior of electrons and positrons and how they interact with electromagnetic fields

•If I wanted to give all the constants that describe QED interactions, how many numbers would I have to give?

• Assuming we are working in units where c = = 0 = 1•We need to know the mass of the electron m•We need to know the charge of the electron - e•All other factors, like the magnetic momentof the electron, can be derived

2

22 .

2 4e

e e

m

μ S

“Can you explain the units a little more, and how every-thing being equal to one makes charge dimensionless.”

1.8: Find a dimensionless combination of e, , 0

and c. Then, setting = c = 0 = 1, find the dimensionless value of the fundamental charge e.

12 2 1 3 20

8

34 2

19

8.854 10 C kg m s

2.998 10 m/s

6.626 10 kg m /s

1.602 10 C

c

e

Important Math Equations

, is solution of 0 .

f x x a dx f a

f af x g x dx a g a

g a

1

2

3

sin cos ,

sin sin ,

cos .

k k

k k

k k

0 if 0 ,

1 if 0 .

xx

x

2 13 2 2

0 0 1 0cosf d f k dk d d f k dk d

k k k k

Problem 1.14b

2 21 1 1 11 2 1 2 1 2 1 12 2 2 20 0

.dE dE m E m E E E m m E mE

AnnouncementsErrata to Next Problem Set

9/3

1 2 1 2 1 2 3 4 4 3 4p p p p p p g p p p p p p g μ

6. Find a formula for s if particles of mass m and energy E collide with a stationary target of mass m. If you use B = 10 T magnets, how large in Earth radii would you have to make a proton collider to reach s = 8.0 TeV?

2. (b)

“Can you explain how having an anti-symetric tensor makes it have six independent components.”

•The diagonal terms are automatically zero

F F

00 00 0F F 11 22 33 0F F F

•The off-diagonal terms are related in pairs

01 10

02 20

03 30

12 21

13 31

23 32

F F

F F

F F

F F

F F

F F

1 2 3

1 3 2

2 3 1

3 2 1

0

0

0

0

E E E

E B BF

E B B

E B B

Anti-symmetric and symmetric tensors

•Anti-symmetric: A A •Symmetric: S S

Theorem: If both indices of a symmetric tensor are contracted with an anti-symmetric tensor, the result is zero

A S A S

•We can switch the indices on the anti-symmetric tensor•We can then switch the indices on the symmetric tensor•Since and are both “dummy indices” that are summed over, we can rename them

• Swap

A S A S

0

“What is a odd/even permutation (Levi-Civita).”

•A permutation is any reordering of the indices•An even permutation can be achieved by an even number of pair switchings•An odd permutation can be achieved by an odd number of pair switchings•The Levi-Civita tensor is completely anti-symmetric – it changes sign whenever you switch a pair

1 if , , , is an even permutation of 0,1,2,3 ,

1 if , , , is an odd permutation of 0,1,2,3 ,

0 otherwise.

1230 ?

Working with Levi-Civita

1 2 3 4

we know: 2 2

we want:

g g g g

p p p p

“I did not fully understand how to use four-momentum in computations.”

A particle of mass M decays to two particles. Find a general formula for the magnitude of the final three-momentum: (b) If the mass of one final particle is m and the other is 0;

Simplify we know: and are inverses of each other,

we want:

g g

g g

“I'm also a little confused by gauge transformations.”

F A A A A A

F F F