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Electroweak PhysicsLecture 3

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Status so far…• 6 parameters out of 18

Extracted from σ(e+e−→ff)

Afb (e+e−→ℓℓ)

AL

R

Today 7 more!

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The Grand Reckoning

• Correlations of all yesterday’s Z peak observables from all 4 LEP experiments

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Physics Menu for Today

• The continuing legacy of LEP & SLC:

– τ-polarisation– Quark final states

• Introduction to hadron colliders…

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Key Quantities from last Lecture

• Amount of polarisation

(curly) A measures Vf, Af and sin2θW

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τ-polarisation measurement

• Parity-violation (V−A) results in longitudinal polarised fermions in e+e−→Z→ff

• At LEP τ is the only fermion whose polarisation can be measured– That’s because τaus can decay in the detector– We can look at the decay modes to determine the

polarisation

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Polarisation, Helicity & Chirality• Polarisation measures helicity states.

• Theory tells us about the chirality states– Chirality: ψL=½(1-γ5)ψ ψR=½(1+γ5)ψ

– Helicity: projection of spin on momentum: s·p

• In the relativistic limit:– left-handed chirality is same as −ve helicity– right-handed chirality is same as +ve helicity

σ+: +ve helicity of τ− (−ve for τ+)

σ−: −ve helicity of τ− (+ve for τ+)

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Polarisation Distribution

• Couplings of Z to chirality states:

• The polarisation of a τ− produced in e+e−→Z→τ+τ- depends on cosθ:

• Ae Aτ are nearly uncorrelated. Insensitive to Aτfb.

• Another measure of V−A structure, sin2θW

2 23 sin sinL W R Wg T Q g Q

( ) / 2 ( ) / 2L f f R f fg V A g V A

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τ→πντ Decays• Use momentum of π as handle on τ polarisation

• Helicity of ν is in same direction as τ-helicity– (True in limit of massless particles)

• → → Effects resulting momentum distribution of π

• In τ−→π−ν decay:– If P(τ−)=+1 momentum of π− is higher than for P(τ+)=−1

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Fit to Obtain Helicity

• Event-by-event measurement of polarisation not possible.

• Use statistical fit• Sum of:

– τ with +ve helicity– τ with −ve helicity

• In Lab Frame:

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Other Modes

• τ→ρν followed by ρ→ππ

• τ→a1ν followed by a1→πππ

• τ→μνν and τ→eνν

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Final τ-polarisation Results

• Extracted values for Ae Aτ

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Measuring Quark Final States

• Up-type and down-type quarks couple differently to Z boson

• We can try to identify the type of quark produced by looking at the properties of the jets

• Some separation can be made:

uds c

b

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b-tagging• b-quarks have a higher mass and longer lifetime

than the other quarks.• Identify b-quark jets by b-tagging• Can look for

– vertices away from the interaction point, due to long lifetime

– high-pt e or μ in the jet due to b→cℓν decays (20%)– charmed hadrons from b→cℓν decays – (61%)

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Rc and Rb Results• Was historically difficult to tag b and c quarks at

LEP

• Values of Rc and Rb were wrong initially…

• Now agree v. well with EWK prediction0q qq hadR

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Rc and Rb Results

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Forward Backward Asymmetry

• σF cross section in the forward hemisphere– Forward defined by b-quark (not bbar quark) at cosθ>0

• At tree level, angular distribution of quark is:

• Measures Z couplings to quarks, sin2θW

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Thrust

• Thrust measures the distribution of jets in a event.

• The unit vector n is where T is maximized is known at the thrust axis

• The range of T is: ½<T<1– T≈½ for an isotropic event– T=1 for an event with 2 back-to-back jets

>

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Charge of the Quark• Need to separate b quarks from bbar quarks

– Longitudinal momentum w.r.t. thrust axis– κ tunable parameter~ 0.3 →1

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AFB with quarks

• ωq is probability to estimate quark charge correctly

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Quark Asymmetries Measurements

• Corrections for QCD effects:

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Quark Asymmetry Results

• At √s=MZ:

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At SLC:

• Electron polarisation allows the measurement of ALRfb for quarks

• Differential Cross section w.r.t cosθ, including electron polarisation:

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Quark Asymmetry Results

Oh, isn’t the Standard Model great…

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Status with the Z Pole Measurements

• 13 parameters out of 18

• not bad for 5 experiments in 6 years

Extracted from σ(e+e−→ff)

Afb (e+e−→ℓℓ)

AL

R

τ polarisation asymmetry

b and c quark final states

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LEP & SLD: Before and After• Truly established the EWK theory as the correct

description of fermion interactions at √s < 100 GeV

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Next Topic: Physics at Hadron Colliders

• More physics from LEPI/SLC and LEPII still to come…

• But let’s change gear a little here and talk about physics at hadron colliders

• 3 hadron colliders– SppS collider at CERN– TeVATRON at Fermilab– LHC at CERN

• W, Z and top physics

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Super Proton Antiproton Synchrotron

• Ran from 1981 to 1984• Proton anti-proton collider• CM energy: 400 GeV• 6km in circumference• Two experiments:

– UA1 and UA2

Physics Highlight: discovery of W and Z bosons!

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W Bosons Discovered at CERN ’82

• W- bosons were discovered at CERN’s SppS collider in 1982 by the UA1 and UA2 detectors

pp W + anything W e + or +

event topology: isolated charged lepton (with high-pT) plus large amount of missing transverse energy (due to the neutrino)

very little background contamination in these event samples … they are spectacularly clean signatures

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Z Bosons Discovered at CERN ’83

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Nobel Prize for Physics 1984

• Given to Carlo Rubbia and Simon van der Meer

• “For their decisive contributions to large projects, which led to the discovery of the field particles W and Z, communicators of the weak interaction.”

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TeVatron• At Fermilab, 40km west of Chicago• Proton anti-proton collider• 1987 to 2009

– Run 1 from 1987 to 1995: √s=1.8 TeV– Run 2 from 2000 to 2009: √s=1.96 TeV

• Two experiments: CDF and DØ

Physics Highlight: discovery of the top quark

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Discovery of the Top Quark• 1995 On Friday,

February 24, 1995, at precisely 11 a.m. Central Standard Time, collaborators from DOE Fermilab’s CDF and DZero experiments simultaneously pushed the buttons on their computers submitting to Physical Review Letters their papers announcing the discovery of the top quark, the last remaining quark of the Standard Model.

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Large Hadron Collider

• 2007-2020??• At CERN in LEP tunnel• Proton-proton collisions• CM energy: 7 TeV• 4 experiments:

– ATLAS, CMS– LHCb, ALICE

Physics Highlight: ???

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Discovery of W, Z & top

• The weak vector bosons and the top quark were all discovered at Hadron Colliders

– why? because these new particles were too heavy to produce at existing e+e- machines

– hadron colliders can operate at much higher energies (less synchrotron radiation)

• The quark and gluon content of the proton means that QCD is a very important feature of hadron collider physics

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Next Lecture

• Relating the production of W, Z and top to the EW Lagrangian

• Measuring W, Z & top properties at Tevatron