Electroweak Physics Lecture 2

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Electroweak PhysicsLecture 2
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Last Lecture

• Use EW Lagrangian to make predictions for width
  of Z boson
• Relate this to what we can measure s(ee-?ff)
• Lots of extracted quantities
• mZ, GZ
• Today look at the experimental results from
  LEPSLC

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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!
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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
• ee-?ee-
• t-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 arent the type you want, but agree
  with criteria
• esel, efficiency of selection criteria to find
  signal events
• use a detailed Monte Carlo simulation of
  physicsdetector to determine
• L, luminosity measure of ee- pairs delivered

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An example s(ee-?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,e 99
• Background 0.5
• mainly from tt-

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Measured Cross Sections

• as function of CM energy

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Use Fit to Extract Parameters

• Fit s(ee-?hadrons) as function of s with to find
  best value for parameters
• mZ
• GZ
• s0had

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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
• s(ee-?ee-)
• s(ee-?µµ-)
• s(ee-?tt-)
• Use to extract values for

Equal up to QED, QCD corrections
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Values Extracted from Total Cross Section
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Number of Neutrinos

• Use shad to extract number of neutrinos
• N(?)2.999 ? 0.011
• Only three light (m?ltmZ/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
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Angular Cross Section II

• Simplifies to
• Pe is the polarisation of the electron
• Pe1 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
  sin2?W

Asymmetries measure Vf, Af and sin2?W
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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 ee- ?(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 AZ²2A? AZ A?²
• 1 g(E) cos? cos²?
  -1 lt g(E) lt 1
• Away from resonance E gtgt MZ or E ltlt MZ
• Can neglect AZ² 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.
• At the Z pole (no ? 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
• Ratio is very nice to measure, things cancel
• Luminosity
• Backgrounds efficiencies are similar for Nf Nb
• Expression only valid for full (4p) 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(EMZ) is very sensitive to the
  couplings
• 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

• s(ee-?Z ?ff) also sensitive to Vf and Af
• decay widths ?f Vf² Af²
• combining Afb(EMZ) and ?f determination of Vf
  and Af separately

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An aside ee-?ee-

• Complication for ee-?ee- channel
• Initial and final state are the same
• Two contributions s-channel, t-channel
• and interference

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Angular Measurements of ee-?ee-
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Left-Right Asymmetry

• Measures asymmetry between Zs produced with
  different helicites

• Need to know beam energy precisely for ?
  correction

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Left Right Asymmetry II

• Measurement only possible at SLC, where beams are
  polarised.
• Experimentalists Formula
• 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

• ltPegt 100 for fully polarised beams

• ltPegt (0.244 0.006 ) in 1992
• (0.76160.0040) in 1996

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SLC ALR Results

• A0LR 0.15140.0022
• sin2?W0.230970.00027

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One more asymmetry ALRfb

• Results
• Combined result
• Equivalent to

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Status so far

• 6 parameters out of 18

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The Grand Reckoning

• Correlations of the Z peak parameters for each of
  the LEP experiments