SuperSymmetry
and Higgs
Standard Model
Higgs in the Standard Model
Problems with the Standard Model
Minimal Supersymmetric Standard Model (MSSM)
Higgs in the MSSM
MSSM particle spectrum
Results of SUSY searches
Project
Presentations
Tests of the Standard Model - EPS 2005 - July 25 - Sijbrand de Jong
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Sijbrand de Jong
Abdelhak Djouadi
Nicolo de Groot
YOU
1
Wednesday 14 Dec
10.00 - 11.00 : Lecture 1: Summary of SM (SdJ)
11.15 - 12.45 : Exo: γ gymnastics & loop calculation
13.45 - 15.15 : Lecture 2: The Higgs mechanism in the SM (Djouadi)
15.45 - 17.00 : Exo: Higgs production and decay
16.45 - 17.30 Lecture 2: Problems of the SM and SUSY solutions
Thursday 15 Dec.
09.30 - 10.15 10.30 - 11.15 Lectures 3 Abdelhak Djouadi
11.30 - 12.45
Exercises
14.00 - 14.45 15.00 - 15.45 Lectures 4 Abdelhak Djouadi
16.00 - 17.30
Exercises
Friday 16 Dec.
09.30 - 10.15 10.30 - 11.15 Lectures 5 Nicolo de Groot
11.30 - 15.00
Project
15.00 - 16.00
Project presentations
16.00
Drinks
Tests of the Standard Model - EPS 2005 - July 25 - Sijbrand de Jong
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• YOU are going to do the work
But we are going to assist (if not insist)
Each lecture session is followed by an exercise session
Assistants (any ≥2 combination of):
Tim Dijkstra
(Hylke Kroes)
Marcel van Kessel
Jan Willem Wagenaar
Emphasis on quantitative understanding of the MSSM
Calculate Feynman diagrams etc. yourself (exercises)
Determine a search strategy yourself
(project)
Tests of the Standard Model - EPS 2005 - July 25 - Sijbrand de Jong
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N
Number of events
Measurement
=
L
Luminosity
Accelerator
σ
Cross section/Decay width
Theory
Fermi’s Golden Rule
σ=∫ |M|2 dLips
M: matrix elements calculable with Feynman diagrams
Tests of the Standard Model - EPS 2005 - July 25 - Sijbrand de Jong
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u
u
u
d
d
d
c
c
c
s
s
s
t
t
t
b
b
b
g1
g2
g3
g4
Standard
Model
g5
g66
g7
g8
W+
Z
γ
W−
νe
νµ
ντ
e
µ
τ
Tests of the Standard Model - EPS 2005 - July 25 - Sijbrand de Jong
H
5
The U(1)×SU(2) Standard Model in a schematic form for 1 fermion type (electron)
s
m
r
e
t
s In following
s
a
m mass terms are
O
N
included “by hand’
Lagrangian invariant under the following U(1)×SU(2) transformation
g1 and g2 coupling strengths of hypercharge and weak interaction
Tests of the Standard Model - EPS 2005 - July 25 - Sijbrand de Jong
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Feynman Rules: Fermions
Lfermion= Ψ(iγµ∂µ-m)Ψ
Fourier space
pµ ↔ i∂
µ
Free solutions: particles Ψ=us(p)e-ipx
Dirac spinors:
Anti-particles Ψ=vs(p)e-ipx
mponents !
o
c
4
Complication: the γ matrices
Chiral projections (1±γ5)/2 g5=iγ0γ1γ2γ3
Tests of the Standard Model - EPS 2005 - July 25 - Sijbrand de Jong
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Feynman Rules: Gauge Bosons
Lgauge=−1/4FµνFµν +1/2MV2AµAµ
Fµν = ∂µAν - ∂νAµ
Free particle solution: Aµ=εµ e-ipx
For the (MV=0) photon the qµqν term is not there
εµqµ=0 for on-mass-shell photons
Tests of the Standard Model - EPS 2005 - July 25 - Sijbrand de Jong
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Feynman Rules: Fermion-Gauge Boson Interaction
Lint= −e Ψ γµ Aµ (vf-af γ5) Ψ
Electromagnetic coupling constant: e(mZ)≈1/128
Weak mixing angle: sW= sinθW, sin2θW≈0.21
Weak isospin: If, If3=+1/2 up quark and neutrino’s
If3=−1/2 down quarks and charged leptons
Tests of the Standard Model - EPS 2005 - July 25 - Sijbrand de Jong
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Feynman Rules: Tree level example: e− e− → e− e−
(Møller Scattering)
q
Tests of the Standard Model - EPS 2005 - July 25 - Sijbrand de Jong
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Feynman Rules: Tree level example: e+e− → µ+µ−
Tests of the Standard Model - EPS 2005 - July 25 - Sijbrand de Jong
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Feynman Rules: Take traces
Tests of the Standard Model - EPS 2005 - July 25 - Sijbrand de Jong
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Feynman Rules: Phase Space Integration
1
Tests of the Standard Model - EPS 2005 - July 25 - Sijbrand de Jong
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Feynman Rules: Putting it together
Tests of the Standard Model - EPS 2005 - July 25 - Sijbrand de Jong
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Exercise 1:
Proof the following relations:
Exercise 2:
Calculate
Tests of the Standard Model - EPS 2005 - July 25 - Sijbrand de Jong
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Exercise 1: Gamma matrices contractions and traces
Tests of the Standard Model - EPS 2005 - July 25 - Sijbrand de Jong
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Exercise 2:
Calculate
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Exercise 2:
Calculate
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Exercise 2:
Calculate
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Exercise 2:
Calculate
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Exercise 2:
Calculate
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Exercise 2:
Calculate
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