1. What we have learned from LEP and SLC? Krzysztof Doroba, Warsaw University & DELPHI Collaboration XXVIII Mazurian Lakes Conference on Physics, Aug 31 – Sep 7 2003 Precision tests of electroweak interactions-

2. Outline of the talk: Strategy of the Standard Model tests Radiative corrections LEP/SLC and detectors Z 0 line shape Z 0 decays to heavy quarks Asymmetries at the Z 0 pole Direct W mass measurement Direct Higgs search Global fit Conclusions from the tests

3. Historical introduction 1968 – Standard Model by Glashow, Salam and Weinberg unification of electromagnetic and weak interactions, existance of the weak neutral current predicted. 1973 – Neutral Currents discovered (Gargamelle experiment) to avoid flavour changing neutral currents GIM mechanizm requires existance of fourth quark (charm) 1974 – Charm quark discovered (Richter/Ting) Do the Z and W bozons realy exist with mass around 90 GeV? Constuction of at CERN. 1982 - Discovery of W and Z bosons at CERN (C.Rubia, UA1 and UA2 experiments) As the SM is renormalizable (t’Hooft and Veltman 1971) it possible to perform precise test of the model. Let us build e + e - colliders: LEP at CERN and SLC at SLAC

4. Strategy of the test. W Minimal Standard Model (MSM) describes electroweak interactions of quarks (q), leptons (l) and Higgs boson(s) (h) by exchange of first step: build LEP1 (SLC) collider at (with possible electron beam polarization at SLAC) second step: increase the energy to(LEP only) Study W and Z production Check model internal consistency Look for Higgs boson(s) and supersymetric particles and

5. Input parameters of Minimal Standard Model (MSM) -electromagnetic fine structure constant -Fermi constant- determines charged current strength - Z 0 boson mass, measured at LEP with high precision above parameters are sufficient to perform MSM calculations on the tree level. However due to high precision of the LEP/SLC measure- ments tree level is not sufficient and radiative corrections are required. This brings into the game more parameters: - fermion masses (m t ) - Higgs boson mass - strong coupling constant at(for quarks in final state)

6. Observables Each observablemeasured at LEP/SLC, With these parameters we perform fitting procedure, asking ourself: does the same set of parameters describes different observables? do the values obtained in the fit agree with those known from direct measurements? The global fit quality is the probe of the Model internal consistency!, w Where from we know the values of the parameters ? -from muon lifetime -from Hall effect -from CDF and D0 experiments we express as a function of Standard Model parameters

7. Radiative corrections Pure QED corrections factorize from electroweak part +.......... Electroweak part: Vacuum polarization Vertex correction QED:

8. Contribution from this two Particular example of vertex corrections: Influence of electroweak corrections on final result on Born level relation between Weinberg angle and W and Z masses:

9. after corrections due to vacuum polarization : effective mixing angle after (flavour dependent) vertex corrections: Flavour dependent effective mixing angle and ρ parameter. Effective coupling constants

10. This leads to improved Born approximation; the improved amplitude for the process has same form as Born amplitude for this process but with effective coupling constants: The electroweak corrections dependence is: quadratic on top quark mass logarithmic on Higgs boson mass For electroweak corrections two loop level is achieved today for most of the processes. Numerical calculations are performed using the programmes TOPAZ0 and ZFITTER.

11. LEP and detectors Large Electron Positon collider 27 km circumference peak luminosity L=2.*10 31 cm -2 s -1 (design value 1.6*10 31 ) maximum energy 208 GeV beam energy known with precision of about 2 MeV (at Z 0 peak) To operate LEP special „LEP standard model” took into account earth tides generated by moon and sun rainfalls in Jura Lake Geneva water level leakage currents from trains Four experiments have been operating at LEP (ALEPH, DELPHI,L3 and OPAL). At Z 0 peak ADLO collected about 17 M events.

13. J.Weniger, LEP fest 2000

15. LEP I running at Z 0 peak quark and antiquark fragment into two separete jets

16. LEP II running at four jets in the final state

17. SLAC Linear Collider SLC, the first linear e + e - collider ever operated with good luminosity and polarization from 1992 till 1998 had worse then LEP beam energy resolution run only at Z 0 peak (600 k events) But... its electron beam was longitudinally polarized its beam spot was much smaller (1.5μm*.7μm vs. 150μm*5μm) The designs of LEP and SLC detectors are quite similar. Slac Linear Detector (SLD) had better vertex reconstructiom (CCD vs. micro-strip) for example, due to lower repetition rate smaller beam spot But,

19. The Z 0 line shape At an experiment we measure cross section: w where N i, N i bk – number of the events and background for channel i ε i - detector efficiency L – luminosity, known from the measurement of the well known QED process - Bhabha scattering. Typical experimental errors on ΔL are below 1 per-mil Measurement is done at small angles ( approx. 25-60 mrad)

20. calculated from SM, not fitted X-section formula at Z 0 peak: H(s,s’)-radiative function Fit performed to the hadron data: M Z, Γ Z, σ 0 had, R l and to the lepton data: Γ e, Γ μ, Γ τ, or (lepton universality) Γ lept

21. ADLO results (with lepton universality) Values of M z,Г z,Г μ,Г τ,Г e,R l,... extracted with use of SM elements Observables  Pseudo-observables SM expresion for

22. The number of light neutrino families depends strongly on Predicted cross-section for two, three and four (massless) neutrino species with SM couplings

23. Z 0 decays to heavy quarks (charm and beauty) two (or more) jets are formed in process, following the quark fragmentation into hadrons. jet (initial quark) direction is established from thrust axis. in the final state we observe hadrons, not quarks. How to select Z 0 decays into particular flavour Flavour tagging: heavy flavours tagged by leptons (high p,p T ), lifetime, secondary vertex mass,.... Works well for b and c quarks. thanks to vertex detectors: b hadron on average travels 3 mm, position of the secondary vertex is measured with accuracy of 300 μm.

24. Different methods use different tags combinations to establish flavour of the initial (heavy) quark. secondary vertex mass and/or high p, p T allows to distinguish between b anc c hadrons. For tagged sample one has to know: purity (up to 96%) efficiency (up to 26%) usually requires very good Monte-Carlo program Most precise – double tag method Pseudo-observables: Most recent values: EPS Aachen 2003

25. Asymmetries at Z 0 pole Z 0 couplings to right-handed and left-handed fermions are different. for even for unpolarized e beams Z 0 is polarized along beam direction (LEP) forward (F) – e - beam direction. R (L) means right (left) handed fermions in final state For polarized electron beam (SLC): r(l) means right (left) handed electron beam polarization. - mean beam polarization

26. At the Z 0 pole: asymmetry parameter for fermion f When the couplings conform to the SM structure: Studies of asymmetry parameters provide very sensitive measurement of the,particulary good for Particulary cute- A LR at SLAC precise, direct measurement of A e with hadron events

27. Another precise measurements: LEP SLC combined vs. Standard Model EPS, Aachen 2003 LEP and SLAC measurements of A b are consistent. But the combined A b value seems to disagree with SM prediction. LEP A b (and A c ) result can be expresed in terms of

29. Direct W mass and width measurement. From CDF and D0 experiments at 1 Tev proton antiproton collider at Fermilab: From direct measurements at LEP 2: study of decay channels:or important corrections coming from: Bose-Einstein correlations color reconnection LEP 2 result: cross section for process at the treshold (161 GeV)

30. Very good agreement between electron and hadron colliders! Combined result: But NuTeV experiment measures from the ratio of the neutral to charged current interactions inandbeams: Using M Z from LEP I This indirect measurement differs more then 3σ from direct one !

32. Standard Model Higgs Search The production (and decay) of Higgs particle is predicted in the SM as a function of its (unknown) mass. For m H =115 GeV Background: WW,ZZ,2f main production channel ZH decay channels b-tagging plays essential role in Higgs search!

33. At LEP I serches in fully hadronic channels excluded by background LEP I serches in other channels - negative At LEP II main sources of background in Higgs search: Selection of Higgs candidate events: on the Monte-Carlo basis topology btag

34. Does the data sample contains signal and background or only background ? for each candidate i introduce the likelihoods ratio: Q i is estimated from topology combined with mass information. MC determines expected Q i distributions the global likelihood: s and s+b equally likely for -2ln(Q)=0

35. ADLO result by M.Duehrssen, EPS, Aachen 2003 Conclusion from further statistical analysis: m H <114.4 GeV is excluded @ 95% CL green and yellow bands indicate 1σ and 2σ limits of backround only hypotesis.

36. The Global Fit Fit of the five Standard Model parameters to all available electroweak results. Some fit results already presented: The purpose of the fit check internal consistency of the Standard Model constrain the Higgs mass Runing coupling constant -from dispersion integral and low energy e + e - data.

38. If in the global fit replace 6 parameters with then for global fit-probability=13% value fitted to the above parameters 3 σ from Standard Model prediction ! -very precise measurement at low ~20 GeV 2 Removing from fit changes χ 2 probability (to 28%) but does not influence SM parameters values much. Global EW fit with average and without OK. for global fit but problem remains...

41. Conclusions from the tests precision (above tree level) predictions of the Standard Model have been compared with experimental results from LEP and SLC. Standard Model looks fine after that comparison. SM is a well established (effective) theory. no need for New Physics. where is (if at all) the Higgs boson(s)? further measurements of M W, m t, (m H ?.....) will make tests more stringent and perhaps will show the road to New Physics. Tools: Tevatron (Run II) +......... Large Hadron Collider (2007) Next Linear Collider this talk is,by all means, not exhaustive. Supersymmetry, Grand Unification, Multi doublet Higgs Models, MSSM, TGC,... were left behind.