1. 1 Electroweak Physics Lecture 2

2. 2 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, Γ Z Today look at the experimental results from LEP&SLC

3. 3 Review of our Aim Aim: to explain as many of these measurements as possible Z pole measurements from LEP and SLC!

4. 4 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

5. 5 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 ε sel, 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

6. 6 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, N ch Sum of track momenta, E ch Efficiency,ε ~ 99% Background ~ 0.5% mainly from τ+τ−

7. 7 Measured Cross Sections as function of CM energy

8. 8 Use Fit to Extract Parameters Fit σ(e+e− → hadrons) as function of s with to find best value for parameters: m Z Γ Z σ 0 had

9. 9 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

10. 10 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

11. 11 Values Extracted from Total Cross Section

12. 12 Number of Neutrinos Use σ had to extract number of neutrinos N( ν )=2.999  0.011 Only three light (m ν ~<m Z /2) neutrinos interact with Z

13. 13 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, A fb –Left-Right Asymmetry, A LR

14. 14 Angular Cross Section y z x θ φ

15. 15 Angular Cross Section II Simplifies to: P e is the polarisation of the electron P e =+1 for right-handed helicity P e =−1 for left-handed helicity –For partial polarisation: and: depends on axial and vector couplings to the Z SM:

16. 16 Asymmetries Can measure the asymmetries for all types of fermion axial & vector couplings depend on the value of sin 2 θ W Asymmetries measure V f, A f and sin 2 θ W

17. 17 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 

18. 18 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  ) ~| A Z +A  |²~ A Z ²+2A  A Z +A  ² – ~ 1 + g(E) cos  + cos²  -1 < g(E) < 1 Away from resonance: E >> M Z or E << M Z –Can neglect |A Z |² contribution –cos  term due to  /Z interference; g(E) increases as |E-M Z | increases Near resonance: E  M Z –neglect |A  |² and 2A  A Z contributions –small cos  term due to V-A structure of A Z

19. 19 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 A fb (ℓ)=0.029 A fb (up-type)=0.103 A fb (down-type)=0.140

20. 20 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 N f N b Expression only valid for full (4 π ) acceptance N F : Number of fermions produced in forward region, θ<π/2 N B : Number of fermions produced in backward region, θ > π /2

21. 21 A fb Experimental Results P: E = M Z P  2: E = M Z  2 GeV

22. 22 Measured Value of A fb Combining all charged lepton types:

23. 23 Extracting V f and A f Large off-peak A FB are interesting to observe but not very sensitive to V-A couplings of the Z boson … … whereas A FB (E=M Z ) is very sensitive to the couplings –by selecting different final states (f = e, , , u, d, s, c, b) possible to measure the V f /A f ratios for all fermion types Use V f /A f ratios to extract sin²  W =1 - M W ²/M Z ² –V u /A u = [ 1 - (4Q u /e) sin²  W ] –V d /A d = - [ 1 + (4Q d /e) sin²  W ] –charged leptons (e, ,  ) V/A = − (1− 4 sin²  W )

24. 24 Extracting V f and A f II σ(e + e −  Z  ff) also sensitive to V f and A f –decay widths  f ~ V f ² + A f ² –combining A fb (E=M Z ) and  f : determination of V f and A f separately

25. 25 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

26. 26 Angular Measurements of e + e −  e + e −

27. 27 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

28. 28 Left Right Asymmetry II Measurement only possible at SLC, where beams are polarised. Experimentalists’ Formula: –Valid independent of acceptance –Even nicer to measure than A fb, more things cancel! : polarisation correction factor. (bunches are not 100% polarised) N R : Number of Zs produced by RH polarised bunches N L : Number of Zs produced by LH polarised bunches

29. 29 Beam Polarisation at SLC | |: (0.244 ±0.006 ) in 1992 (0.7616±0.0040) in 1996 Polarised beams means that the beam are composed of more e L than e R, or vice versa | | = 100% for fully polarised beams

30. 30 SLC: A LR Results A 0 LR = 0.1514±0.0022 sin 2 θ W =0.23097±0.00027

31. 31 One more asymmetry: A LRfb Results: Combined result: Equivalent to:

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

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