Electroweak Physics Lecture 2 1 Last Lecture Use

Electroweak Physics Lecture 2 1

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 – m. Z, ΓZ • Today look at the experimental results from LEP&SLC 2

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− • τ-polarisation • Quark final states 4

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 5

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− 6

Measured Cross Sections • as function of CM energy 7

Use Fit to Extract Parameters • Fit σ(e+e−→hadrons) as function of s with to find best value for parameters: • m. Z • ΓZ • σ0 had 8

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 9

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 10

Values Extracted from Total Cross Section 11

Number of Neutrinos • Use σhad to extract number of neutrinos • N(ν)=2. 999 0. 011 • Only three light (mν~<m. Z/2) neutrinos interact with Z 12

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 13

Angular Cross Section y z θ φ x 14

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: 15

Asymmetries • Can measure the asymmetries for all types of fermion • axial & vector couplings depend on the value of sin 2θW Asymmetries measure Vf, Af and sin 2θW 16

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 1/2 e+e- (cos ) ~ 1 + cos² 17

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+2 A 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 2 A AZ contributions – small cos term due to V-A structure of AZ 18

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 19

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 20

Afb Experimental Results • P: E = MZ • P 2: E = MZ 2 Ge. V 21

Measured Value of Afb • Combining all charged lepton types: 22

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 sin² W =1 - MW²/MZ² – Vu/Au = [ 1 - (4 Qu/e) sin² W ] – Vd/Ad = - [ 1 + (4 Qd/e) sin² W] – charged leptons (e, , ) V/A = − (1− 4 sin² W ) 23

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 24

An aside: e+e− • Complication for e+e− channel… – Initial and final state are the same – Two contributions: s-channel, t-channel – … and interference 25

Angular Measurements of e+e− 26

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 27

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! 28

Beam Polarisation at SLC • Polarised beams means that the beam are composed of more e. L than e. R, or vice versa • |<Pe>| = 100% for fully polarised beams |<Pe>|: (0. 244 ± 0. 006 ) in 1992 (0. 7616± 0. 0040) in 1996 29

SLC: ALR Results A 0 LR = 0. 1514± 0. 0022 sin 2θW=0. 23097± 0. 00027 30

One more asymmetry: ALRfb • Results: • Combined result: • Equivalent to: 31

Status so far… Extracted from σ(e+e−→ff) Afb (e+e−→ℓℓ) ALR • 6 parameters out of 18 32

The Grand Reckoning • Correlations of the Z peak parameters for each of the LEP experiments 33