Lecture 15
Some simple points
Talk about WS6
Toy Models
Why is the free Lagrangian for a real scalar
22
1
2 m
But for a complex scalar (no factor of )?
( ) m 2
A free complex scalar can be thought of as a linear combination of two
real scalars (re
Physics 637 2013F
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Pauli and Dirac Algebra
1. Pauli Trace Algebra: Here I will use the notation that for a 3-
vector v , The bold
face indicates the combination with sigma matrices: v = v and 12
Physics 637 2013F
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Working with SU(2) and O(3) Transformations
1. Calculating rotations using Pauli Matrices: Recall that
i
R2 (v , ) = exp( 2 v ) = cos iv sin . The Pauli matrices satisfy
2
2
2
2
x =
Lecture 5
Field Lagrangians
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Lagrangian
Hamiltons Principle
The equation of motion is an stationary point of the Lagrangian (in
classical mechanics also minimizes)
Mechanics Example:
For a 1d particle with potential V
Lecture 11
Annhilation:
e2
t
e2
M 2 = i
u
QED Calculations continued
More about Phase Space
M 1 = i
e + e
v2 E1 ( p1 k2 ) E2u1
iq
t
u
2
| M | = 2e
| M 2 |unpol = 2e 4
u
t
*
2 Re( M 1M 2 )unpol = 0
2
1 unpol
(k2 , E2 )
(k1 , E1 )
v2 E2 ( p1 k1 ) E1u1
i
Lecture 6
Lagrangian Formulation of Field Theory
Classical E&M as a Gauge Theory.
The Main approach to modeling QFT we will use is the
Lagrangian formulation
To derive predictions we will use Feynman Diagrams
Gauge
Theories
String Theory and Duality;
E
Quark potential
Lecture 4
can be
of
Upshot of Worksheet 1
Review of Quark Model and SU(3) Flavor Symmetry
Some more review on Dirac algebra and trace calculations.
qq
e
urrent
A rotation can be represented by the product of two reflection
with planes i
Lecture 2
Symmetries and Representations for some Nonabelian Groups
Basic calculational methods
Trace calculations; Fierz identities; Completeness expansions
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Some Group Theory Terminology
If A Lie algebra has a finite
Lecture 3
Fierz Identities
Review of Quark Model and SU(2) Flavor Symmetry
Fierz identities transform tensor products into products with
the indices permuted.
They are handy tools for reducing arbitrary products of
tensors
SU(2)
ab cd = 1 ad cb + 1 i
Lecture 1
Learning Goals for 637
About 637
Introduction
Review of Symmetry
Gain a working knowledge of tools for calculating cross sections.
Group Theory: SU(2), SU(3), SO(3)
Feynman Diagrams
Phase space
Structure Functions
Basic model building w
Physics 637 Homework HEP #2 Due October 8, 2013
1. Finish up parts 2cde of worksheet 4 (Phase Space/Compton Scattering) and hand in
completed worksheet with assignment.
2. Consider the scattering ( p1 ) e ( p2 ) ( p3 ) e ( p4 ) . In the rest fra
Physics 637 Homework HEP #3
Due November 14
1
1. If =
is a complex doublet field which is an isospin representation of a
2
SU(2) gauge theory. Show that for an arbitrary you can represent it in terms of the 4
real parameters cfw_ 1 , 2 , 3 , accord
Physics 637 Homework HEP #2 Due October 8, 2013
(solutions)
1. Finish up parts 2cde of worksheet 4 (Phase Space/Compton Scattering) and hand in
completed worksheet with assignment.
See posted worksheet solutions
2. Consider the scattering ( p1 ) e ( p
Physics 637 Homework #1 Due Sept 12, 2013
1. Consider a set of Heaviside-Lorentz units where 0 = 0 = 1 ( c = 1) and we express
all physical quantities in terms of powers of GeV. For each of the following physical
quantities determine.
(a) What power of Ge
Physics 637 Homework HEP #1
1. Consider a set of Heaviside-Lorentz units where = 0 = 0 = 1 ( c = 1) and we
express all physical quantities in terms of powers of GeV. For each of the following
physical quantities determine.
(a) What power of GeV are the fo
Physics 637 2013F
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Charged Current Scattering: Center of Mass
1. Consider the three reactions below in the center of mass frame at sufficiently
high energy that you can use the approximation me , m
Lecture 8
Feynman Diagrams
Feynman Diagrams I; Phase space.
Go over worksheet
This is the main calculational tool we will use to obtain
predictions for a fundamental theory.
In particular we will use it to calculate cross sections and
decay widths (to
Lecture 7
Review
Quantum E&M as a Gauge Theory.
The Lagrangian for a charged scalar field is
L = ( D ) * ( D ) m2 | |2 1 F F
4
This Lagrangian is invariant under the coupled gauge
transformation:
' = eiqf
A A ' = A f
The same works for other kinds
Outline
49 Years of the Higgs Boson
David Atwood ISU
October 23 2013
10/23/2013
David Atwood ISU
1
The Idea
How it Works
The Standard Model as a Broken Gauge Theory
Milestones of the Standard Model
Is the Higgs Boson Discovered?
What is The Higgs Boson Go
Lecture 19
Weak Interaction of Leptons
Physics 637 2013 F David Atwood
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Physics 637 2013 F David Atwood
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0.814 MeV
0.863 MeV
Physics 637 2013 F David Atwood
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Physics 637 2013 F David Atwood
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Beta Decay of a Muon I
( p1 ) ( p2 ) e ( p3 ) ( p4 )
Work
Neutrino Beam + Electron Target with a Muon in
Final State
Lecture 20
Inverse muon decay example
Intermediate Vector Boson Hypothesis
Some features of this kind of reaction?
They only have charged current diagrams
They are directly related to muon de
Lecture 21
Tangent 1: Concerning question 2
Some Tangents
Intermediate Vector Boson Hypothesis
Pathologies of 4 fermi theory
Pathologies of raw IVB
You might want to do 2b before 2a since it is easier
From an earlier lecture, recall that 3bdy phase space
Physics 637 2013F
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Model 4
1. Consider a model with a SU(2) gauge symmetry and a complex scalar field
1
=
which is a doublet representation of this group (i.e. isospin=1/2 field).
2
In this
Lecture 18
Why Does Particle Physics need SSB?
• Weinberg and Salam constructed the Standard Model in 1967
where SSB is an essential element of the theory.
• What drove them to put this craziness at the heart of the
theory to explain weak interactions?
Model 3 Summary: Charged Real Scalar Fields with
U(1) Gauge Symmetry
Lecture 16
Symmetry of Lagrangian
Lagrangian
Model 4
Model 4
L = | D |2 V (| |2 ) 1 F F
4
U (1) :
eiq ( x )
V ( ) = | | + | | (| | )
2
1
2
2
22
1
4
A A ( x )
2 > 0 Symmetry is preser
Physics 637 2013F
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Non-
Abelian Gauge
1. Scalar Gauge Theories: Let be a SU(2) doublet scalar field.
a) What is the Lagrangian if the SU(2) is not a gauge symmetry
so this it is just a fr
Physics 637 2013F
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Scalar Feynman Diagrams
1. Scalar Exchange: Suppose that there exists a neutral scalar h (perhaps a higgs
or something like that) where the Feynman rule for the e+ e h vertex is