E lectro- W eak measurements

1. Electro-Weakmeasurements België Nederland BND summer school 2005 Deutschland The good news: an excellent LEP I paper “Precision Electroweak Measurements on the Z Resonance” The bad news: I did not study it (and yesterday did not help) Frank Linde, september 2005, BND summerschool, Texel

2. The night after    

3. Elementary particle masses (MeV): m < 0.000003 m < 0.19 m < 18.2 e   me  0.51099890 m  105.658357 m  1777.0 mu  3 mc  1200 mt  178000 md  7 ms  120 mb  4300 Electro-weak interaction: V V neutrino menging (4) quark menging (4) e(0) 1/137.036 mW  80.42 GeV mZ  91.188 GeV mH > 114.3 GeV q l e   1 2 3 u’ d’ s’ u d s ij ij = = Strong interaction: s(mZ) 0.117 Standard Model free parameters 25 ! (“all” except gravity?)

4. Quantity Value Standard Model Pull

6. My selection A. LEP e+e collider 1. cross-section2. asymmetry3. Z-boson & W-boson decay widths & masses4. lepton universality5. infering t-quark & H-boson information B. Higgs 1. branching ratio’s 2. LEP’s screw-up? 3. discovery at LHC?4. self coupling at ILC?

7. LEP collider: EW goldmine

8.  2  s(Q)  Higgs massa (GeV/c2)  Q (GeV/c) To elucidate the theory of the electro-weak interaction For a colorful theory LEP: Nobel research

9. LEP experimental program Feynman diagrams? LEP I: Z-boson 1989 - 1995 smZ91 GeV Lpeak21031 cm2s1 Lintegrated200 pb1 LEP II: W- & H-bosons 1996 - 2000 s2mW; smax=209 GeV Lpeak1032 cm2s1 Lintegrated800 pb1 1 pb1 = 1036 cm2

10. 30 years of work! 1. cross section

11. The beam energy: specialist job E=0.2 MeV

12. The moon (tidal) effect  1 MeV

13. The beam energy: many effects Reference: resonant depolarization Complications: flux loop measurement moon effect lake effect TGV effect beam energy spread synchrotron losses  Result (LEP I): Ebeam  1.7 MeV

14. The beam intensity: luminosity Bhabha scattering e+e  e+e alternatives: e+e   e+e  e+ee+e • requirements: • high statistics • known theory • small systematics what are the requirements for a normalization process?

15. The beam intensity: luminosity E, ,  error  0.1% • trigger efficiency (99.xx  0.xx%) • systematic uncertainties in the event selection (0.xx%) • absolute acceptance i.e. xx.xx  0.xx nb

16. Reducing the systematics Measured energy distribution Fitted energy distributions N=10 Eseen = 31 GeV (X0,Y0)=(0.4,0.2) tot = 0.68 2/DF=0.94 Efit = Eseen/tot=46 GeV N=11 Eseen = 38 GeV (X0,Y0)=(0.4,0.2) tot = 0.85 2/DF=0.92 Efit = Eseen/tot=45 GeV Find the expected energy density distribution (X,Y; X0,Y0) (X0,Y0) is shower center Minimize: X0  X0 • This gives you: • shower center coordinates (X0,Y0) • observed energy fraction tot   (i;X0,Y0)  1 Efit   Ei /tot  Eseen /tot • quality of fit (figure of merit) • possibility to correct for dead channels

17. Event selection: e+e, +, +, qq identify the peaks multiplicity charged tracks topology jets planarity acoplanarity energy total energy missing energy energy balance minimal energy kinematic fits verticing neural networks 

18. The ‘real’ stuff: cuts, counting, … trigger acceptance event selection background statistics trigger acceptance event selection background statistics e+ee+e important uncertainties?

19. The ‘real’ stuff: cuts, counting, … trigger acceptance event selection background statistics trigger acceptance event selection background statistics e+e+ important uncertainties?

20. The ‘real’ stuff: cuts, counting, … trigger acceptance event selection background statistics trigger acceptance event selection background statistics e+e+ important uncertainties?

21. The ‘real’ stuff: cuts, counting, … trigger acceptance event selection background statistics trigger acceptance event selection background statistics e+eqqg important uncertainties?

22. External lines , W, Z l l l l f f Vertices  Z W Propagators W, Z Feynman rules with , W- & Z-bosons cA=½ cV=2qsin2 ½

23. e e f f  Z0 e+ e+ f f use: e+e  Z0,  ff cross section (fe)

24. e+e  Z0,  ff cross section (fe) And hence for total amplitude: With: And furthermore with: You find for the differential cross section:

25. With the following notation and approximations: and You find for the differential cross section: And hence for the total (peak) cross section: And hence for sMZ: Cross section near sMZ

26. Results: cross section

27. Results: Z-boson parameters

28. Results: # of light neutrino’s • more neutrino families: • Z-boson width larger • hadronic branching fraction smaller & therefore lower peak cross section N=2.9840 ± 0.0082

29. Direct counting of # light neutrino’s  e e+ W e e  e,, e+ Z e,, e The issue: trigger! LEP I: tricky LEP II: “easy”

30. 2. asymmetry

31. Asymmetry formula cfVcfA Af = 2 (cfV)2+(cfA)2 AfFB = ¾ AeAf

32. How to extract the asymmetry? “data” fitted d/dcos combined acceptanc& efficiency d/dcos cos -1 0 +1 which real world effects? AFB can be extracted using Born level prediction for the distribution:

33. counting or2-fit or likelihood-fit counting: 2-fit (correct for ): Likelihood-fit:

34. Results: cV & cA measurements cV cA

35. 3. Z-boson & W-boson decay widths & masses

36. p1 p1 e+ e+ px px p2 p2 W+ Z0 e e 4-vectors: Generic expression decay width: X-boson polarization sum spin states: Traces of -matrices: W-boson & Z-boson decay widths To be efficient, I perform calculation for X-boson with vertex factor: (gX/2)(cV-cA5) (in addition I work in X-boson rest frame and I mess around with u- and v-spinor states)

37. e e- p2 p1 X px     2+2 22 2 2 2 2 1 2 The amplitude p·p1= p·p2=M2/2 p1·p2=M2/2 p·p=M2

38. Use the 4-vectors: 2 2 Plug into the decay width expression: e+ p1 Z0 For the Z-boson: px p2 e e+ p1 W+ For the W-boson: px p2 e The decay width

39. W-boson Z-boson Z- & W-boson partial decay widths

40. Z-boson W-boson Z- & W-boson partial decay widths

41. Z-boson leptonic cross sections “simple” (but correct!) counting and you get branching fractions

42. W-boson cross section (LEP II) e W Z0 e+ W+ e W  e+ W+ e W e e+ W+

43. W+W event topologies “all hadronic” (4 jets) (2 jets) “all leptonic” (no jets) “simple” (but correct!) counting and you get branching fractions

44. W-mass best accuracy: 2 jets no interplay between different W-boson decay products

45. mW: screams for kinematic fit! 4-momentum conservation: (2Ebeam,0,0,0) (4) 2 W-bosons: equal mass? One condition. (1) Constraints: All hadronic: constraint improves E for jets 2-jets: three constraints for neutrino one constraint left all leptonic: hopeless (can also use the equal mass, but masses (width!) are not that equal

46. 4. lepton universality

47. The decay of the muon ()  k W  k’ p e p’ e Calculation: tedious Rewards: precision GF determination nice experiment!

48.  k  W p k’ Kinematics: p’ e e With the standard Feynman rules you get for the amplitude: Plugging this in the decay width “master” formula: • Remainder: “standard (but tedious) tricks”: • summing and averaging over the spin states • look for the appropriate trace theorem • integrate over the e(p’) + e(k’) + (k) phase space -decay calculation

49. Note: happily include in the summation non-existent -spin states (0 contribution) Spin:  0: PL  PR  0: odd #  Kinematics & me20: And finally the amplitude: -decay: trace reduction

50. 3-particle phase space yields 9-dimensional integral: Using the -function yields a 6-dimensional integral Relevant variables: EeE’, E’ and angle  between the electron and the anti-electron neutrino. 3-dimensional integral. The cos integration can be performed using: Left with: -decay: phase space integral