Transcript Electroweak Physics (from an experimentalist!)

Electroweak Physics
Lecture 2
1
Last Lecture
• Use EW Lagrangian to make predictions for width of Z
boson:
2
( Z  f f )  V f  A f
2
• Relate this to what we can measure: σ(e+e−→ff)
2
ee  ff
s

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
1
 
Z
 e e Z  f f  2
mZ RQED s  m2 2  s2 / m2  Z
Z
Z
Z




• Lots of extracted quantities
– mZ, ΓZ
• Today look at the experimental results from LEP&SLC
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Review of our Aim
• Aim: to explain as
many of these
measurements as
possible
Z pole measurements
from LEP and SLC!
3
Physics Topics
• Total cross section to quarks and leptons
– Number of neutrinos
• Angular cross sections
– Asymmetries
• Between forward and backward going particles
• Between events produced by left and right electrons
– e+e−e+e−
• τ-polarisation
• Quark final states
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Measuring a Cross Section
• Experimentalists’ formula:
• Nsel, number of signal events
– Choose selection criteria, count the number that agree
• Nbg, number of background events
– Events that aren’t the type you want, but agree with criteria
• εsel, efficiency of selection criteria to find signal events
– use a detailed Monte Carlo simulation of physics+detector to
determine
• L, luminosity: measure of e+e− pairs delivered
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An example: σ(e+e−→quarks)
• Select events where the final state is two quarks
• In detector quarks appears as jets
• Simple selection criteria:
• Number of charged tracks, Nch
• Sum of track momenta, Ech
• Efficiency,ε ~ 99%
• Background ~ 0.5%
• mainly from τ+τ−
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Measured Cross Sections
• as function of CM energy
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Use Fit to Extract Parameters
• Fit σ(e+e−→hadrons)
as function of s with
to find best value for
parameters:
• mZ
• ΓZ
• σ0had
0
  Z  hadrons    had
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RQED
s2z
(s  mz2 )2  s 22z / mz2
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Energy of the Beam
• Critical to measurement:
– How well do you know the
energy of the beam, s ?
• At LEP, it was required to
take into account:
– The gravitational effect of the
moon on tides
– The height of the water in Lake
Geneva
– Leakage Currents from the TGV
to Paris
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Leptonic Cross Sections
• Leptonic cross sections measured in a similar way:
• σ(e+e−→e+e−)
• σ(e+e−→μ+μ−)
• σ(e+e−→τ+τ−)
• Use to extract values for
0


Re0  had  had
ee
 ee0
Equal up to QED, QCD corrections
 had
R 
 
0
 had
R 

0
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Values Extracted from Total Cross Section
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Number of Neutrinos
• Use σhad to extract
number of neutrinos
• N(ν)=2.999  0.011
• Only three light
(mν~<mZ/2) neutrinos
interact with Z
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Cross Section Asymmetries
• Results so far only use the total number of events
produced
• Events also contain angular information
• Cross section asymmetries can be used to exploit the
angular information
– Forward Backward Asymmetry, Afb
– Left-Right Asymmetry, ALR
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Angular Cross Section
y
z
θ φ
x
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Angular Cross Section II
• Simplifies to:
• Pe is the polarisation of the electron
• Pe=+1 for right-handed helicity
• Pe=−1 for left-handed helicity
– For partial polarisation:
• and:
• depends on axial and vector couplings to the Z
• SM:
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Asymmetries
• Can measure the asymmetries for all types of fermion
• axial & vector couplings depend on the value of sin2θW
Asymmetries measure
Vf, Af and sin2θW
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Forward-Backward Asymmetry I
• At Z energies the basic Feynman diagrams are:
– Z exchange (dominant, due to resonance effect)
–  exchange (becomes more important ‘off-peak’)
•  exchange is a pure vector: parity conserving process
– the angular distribution of the final state fermions only involves
even powers of cos
–  is the angle between the outgoing fermion direction and the
incoming electron
– for spin 1   spin 1/2 e+e-
(cos) ~ 1 + cos²
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Forward-Backward Asymmetry II
• Z exchange is a V-A parity violating interaction
– the angular distribution of the final state fermions can involve
odd and even powers of cos 
– (cos) ~| AZ +A |²~ AZ²+2A AZ +A²
–
~ 1 + g(E) cos + cos²
-1 < g(E) < 1
• Away from resonance: E >> MZ or E << MZ
– Can neglect |AZ|² contribution
– cos term due to /Z interference; g(E) increases as |E-MZ|
increases
• Near resonance: E  MZ
– neglect |A|² and 2A AZ contributions
– small cos term due to V-A structure of AZ
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Forward-Backward Asymmetry III
• Asymmetry between fermions that go in the same
direction as electron and those that go in the opposite
direction.
 (cos   0)   (cos   0)
Afb 
 (cos   0)   (cos   0)
• At the Z pole (no γ interference):
• SM values for full acceptance
• Afb(ℓ)=0.029
• Afb(up-type)=0.103
• Afb(down-type)=0.140
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Forward Backward Asymmetry Experimentally
• Careful to distinguish here between fermions and anti-fermions
• Experimentalists’ formula:
NF: Number of fermions
produced in forward
region, θ<π/2
NB: Number of fermions
produced in backward
region, θ>π/2
• Ratio is very nice to measure, things cancel:
– Luminosity
– Backgrounds + efficiencies are similar for Nf Nb
• Expression only valid for full (4π) acceptance
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Afb Experimental Results
• P:
E = MZ
• P 2: E = MZ  2 GeV
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Measured Value of Afb
• Combining all charged
lepton types:
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Extracting Vf and Af
• Large off-peak AFB are interesting to observe but not very
sensitive to V-A couplings of the Z boson …
• … whereas AFB(E=MZ) is very sensitive to the couplings
 Ve Ae   V f Af
Afb  E  mZ   3  2
2 
2
2

V

A
V

A
e  f
f
 e



– by selecting different final states (f = e, , , u, d, s, c, b)
possible to measure the Vf/Af ratios for all fermion types
• Use Vf/Af ratios to extract sin²W =1 - MW²/MZ²
– Vu/Au = [ 1 - (4Qu/e) sin²W ]
– Vd/Ad = - [ 1 + (4Qd/e) sin²W]
– charged leptons (e, , ) V/A = − (1− 4 sin²W )
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Extracting Vf and Af II
• σ(e+e−Z ff) also sensitive to Vf and Af
– decay widths f ~ Vf² + Af²
– combining Afb(E=MZ) and f: determination of Vf and Af separately
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An aside: e+e−e+e−
• Complication for e+e−e+e− channel…
– Initial and final state are the same
– Two contributions: s-channel, t-channel
– … and interference
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Angular Measurements of e+e−e+e−
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Left-Right Asymmetry
• Measures asymmetry between Zs produced with
different helicites:
Measured: Z+γ
Z only contribution
Correction for γ interaction
• Need to know beam energy precisely for γ correction
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Left Right Asymmetry II
• Measurement only possible at SLC, where beams are
polarised.
• Experimentalists’ Formula:
NL: Number of Zs
produced by LH
polarised bunches
NR: Number of Zs
produced by RH
polarised bunches
<Pe>: polarisation
correction factor.
(bunches are not
100% polarised)
– Valid independent of acceptance
– Even nicer to measure than Afb, more things cancel!
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Beam Polarisation at SLC
• Polarised beams means that the beam are composed of
more eL than eR, or vice versa
N (eR )  N (eL )
Pe
N (eR )  N (eL )
•|<Pe>| = 100% for fully
polarised beams
|<Pe>|: (0.244 ±0.006 ) in 1992
(0.7616±0.0040) in 1996
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SLC: ALR Results
A0LR = 0.1514±0.0022
sin2θW=0.23097±0.00027
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One more asymmetry: ALRfb
• Results:
• Combined result:
• Equivalent to:
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Status so far…
Extracted from σ(e+e−→ff)
Afb (e+e−→ℓℓ)
ALR
• 6 parameters out of 18
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The Grand
Reckoning
• Correlations of the
Z peak parameters
for each of the LEP
experiments
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