Download Electroweak Physics (from an experimentalist!)

Electroweak Physics
(from an experimentalist!)
SUPA Graduate Lectures
Term 2 2005/06
Victoria Martin
SUPA/University of Edinburgh
1
The Electroweak Lagrangian
Q: How do we relate
this to observables
that we can measure
in experiments?
A: Take one piece at
a time!
Often need to
consider corrections
from other terms
2
Pull= [X(expt)-X(theory)] / X
Experimental Measurements
• Look how well EW
theory explains our
measurements!
• But what are these
measurements!?
• How do we relate
what the theory tells
us and what
experimentalists
measure?
Experiment
Theory
Observables
& PseudoObservables
3
The Blue Band Plot!
• Electroweak
theory is so
good, it
predicts the
Higgs mass
4
Course Contents
•
•
•
•
•
•
Measurements at the Z pole: LEP & SLD
LEP production of W+WMeasurements at low energy: muon lifetime, g-2
Electroweak and top physics at the Tevatron
The search for the Higgs & BSM
What the future holds
• But first, back to the theory…
5
Parameters of the Electroweak Sector
• Three key parameters:
– The two gauge coupling constants: gW and g’W
– The vacuum expectation value of the Higgs field: v
• These can be obtained through 3 measurements.
• Choose the 3 most precise:
– The electric charge, e• measured by the electric dipole moment
– The Fermi Constant, GF (precision: 0.9x10-5)
• measured by the muon lifetime
– The mass of the Z boson, MZ (precision: 2.3x10-5)
e
gW g 'W
g g'
2
W
2
W
MZ  v g  g
1
2
2
w
'2
w
1
GF 
2v 2
6
Other Useful Combinations
vgW
• Mass of the W boson: M W 
2
2
g
'
• Weak mixing angle sin 2 W  2 W 2  0.23
g 'W  gW
• Relationship between W and Z mass:
MW
MZ 
cos W
gW2
GF
1

 2
2
2 8M W 2v
7
Other Parameters in the Model
• The masses of the
fermions:
– Most influential is
m(top) due to its huge
size
• Mass of the Higgs, mH
• The EWK model tells us
nothing about these
values!
mH=(2λ)½v
λ is not specified
8
First Topic: Physics at the Z Pole
• What EWK theory
tells us about Z
• How to make and
detect Zs
• Physics Topics:
– Z mass
– Partial and Total
Widths
– Z couplings to
fermion pairs
– Asymmetries
9
Z in the Lagrangian
10
Z boson-fermion interactions
T: Weak
Isospin
T3 :Third
Component
Q: Charge
• Piece of the Lagrangian that describes fermion – Z interactions:
 f  5 (V f  Af  5 ) f Z 
• Vector coupling to Z: Vf = T3-2Q sin2θW
• Axial coupling to Z: Af = T3
11
A Z-boson factory
• LEP=Large Electron Positron
Collider @ CERN
• 1989 to 1995: LEPI
– CM energy: 88 to 94 GeV
• 7 energy points
– 17,000,000 Zs produced
– 1995: 1000 Z/h recorded by
each experiment
• 1996 to 2000: LEPII
– CM energy 161 to 209 GeV
12
LEP Experiments
• 4 experiments:
–
–
–
–
ALEPH
DELPHI
OPAL
L3
13
The Aleph Experiment
y
z
θ φ
x
14
Z bosons at LEP
15
SLC & Mark II
• SLAC Linear Collider
– Only linear collider to date
• First detector: Mark II
– 1989: First to publish
observation of e+e−→Z
16
SLC & SLD
• 1992: SLC polarised e+e− beams established!
• Mark II replaced with SLD detector
• 1992 to 1998:
600,000 Z decays
• Complementary
to LEP for some
measurements
17
Two Main Measurables
• What happens to the Z once produced?
– It decays
• What into?
– Any fermion: e, μ, τ, ν, quarks
• What can we measure?
– Two main quantities to measure:
• Cross sections to fermion final states, σ(e+e−ff)
• Decay Asymmetries eg, Afb and ALR
18
Z Boson Decaye+e−
19
Z Boson Decay +-
20
Z Boson Decay +− (e− + jet)
21
Z Boson Decay Hadrons (qq jets)
22
Decay into Fermion anti-Fermion Pairs
Z  f ( p ) f ( p ')
• At tree level not too hard to calculate!
• Vertex strength:
ig W
u ( p)  (V f  Af  5 )v( p ')
2 cos W
• Summing over the possible electron polarisations:
4

8 GF M Z
| V f |2  | Af |2
3
2

• Integrate over available phase space (p, p’) to get:

2
GF M Z3
( Z  f f )  N C
V f  Af
6 2
2

23
In reality…
• Need to include:
– Interference from the γ
– QED corrections due to
gamma radiation
– For quarks: QCD corrections
due to gluon radiation
– Fermion masses
• Correction factors:
~1
24
Total Cross Section
• The total cross section to a given fermion depends on:
– The rate for e+e− to make Zs: Γ(e+e−)
– The rate for the Z to decay to a given fermion type: Γff
– The rate for the Z to decay to anything, ΓZ
• We can parameterise this for different centre of mass
energies, s:
Parameterises final state
QED corrections in Γ(e+e−)
25
Widths
• Total width of the Z is sum of widths of everything it
can decay into:
• Hadronic modes due to quarks:
–
(top is too heavy for Z to decay into)
• Invisible modes due to neutrinos:
26
Observables extracted from σ
• Many parameters can be extracted from the
measurement of σ(e+e−→hadrons)
• Highly correlated! Choose to use just six:
– If we assume the three lepton types have the same interactions
(lepton universality), last three measurements are the same.
(Small correction to required for lepton mass difference).
27
More Ratios: R0q and R0inv
• When the type of quark can be identified, we can
define:
• Define ratio of invisible width and charged leptonic
width:
• Related to number of neutrinos, Nν:
28