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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

2

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

2

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