1 Electroweak Physics Lecture 2
Jan 14, 2016
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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: σ(e+e−→ff)
• Lots of extracted quantities– mZ, ΓZ
• Today look at the experimental results from LEP&SLC
2 2( ) f fZ f f V A
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22 2 2 2
12 1
/
ee ffZ
Z QED ZZ Z Z
se e Z f f
m R s m s m
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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
– 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
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02 2 2 2 2
1hadrons
( ) /z
hadQED z z z
sZ
R s m s m
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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
Equal up to QED, QCD corrections
00
0had had
eee ee
R
0 hadR
0 hadR
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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
x
θ φ
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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
sin2θWAsymmetries 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 +A²– ~ 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.
• 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
(cos 0) (cos 0)
(cos 0) (cos 0)fbA
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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 (4π) acceptance
NF: Number of fermions produced in forward region, θ<π/2
NB: Number of fermions produced in backward region, θ>π/2
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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
– 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 sin²W =1 - MW²/MZ² – Vu/Au = [ 1 - (4Qu/e) sin²W ]
– Vd/Ad = - [ 1 + (4Qd/e) sin²W]
– charged leptons (e, , ) V/A = − (1− 4 sin²W )
2 2 2 23 f fe e
fb Ze e f f
V AV AA E m
V A V A
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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
Correction for γ interaction
Z only contribution
• 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:
– Valid independent of acceptance
– Even nicer to measure than Afb, more things cancel!
<Pe>: polarisation correction factor. (bunches are not 100% polarised)
NR: Number of Zs produced by RH polarised bunches
NL: Number of Zs produced by LH polarised bunches
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Beam Polarisation at SLC
|<Pe>|: (0.244 ±0.006 ) in 1992
(0.7616±0.0040) in 1996
• Polarised beams means that the beam are composed of more eL than eR, or vice versa
( ) ( )
( ) ( )R L
eR L
N e N eP
N e N e
•|<Pe>| = 100% for fully polarised beams
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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…
• 6 parameters out of 18
Extracted from σ(e+e−→ff)
Afb (e+e−→ℓℓ)
AL
R
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The Grand Reckoning
• Correlations of the Z peak parameters for each of the LEP experiments