PRECISION MEASUREMENTS

Transcription

1 PRECISION MEASUREMENTS AT Z RESONANCE Asymmetries and Constraints on Standard Model Lecture 4 12 October 2012 Shahram Rahatlou Fisica Nucleare e Subnucleare III, Anno Accademico

2 ASYMMETRIES Lineshape measurements allowed the determination of total Z width partial Z width in hadrons and leptons Z mass total of 6 parameters Several observable asymmetries sensitive to fundamental parameters of Standard Model angular distribution to spin 1 of Z boson different couplings for left and right handed fermions possibly use polarization of initial state electrons 33

3 FORWARD- BACKWARD ASYMMETRY Terms proportional to cos θw provide test of parity violation 2s π 1 N f c dσ ew dcos θ (e+ e ff) = α(s)q f 2 (1 + cos 2 θ) }{{} σ γ 8R { α (s)q f χ(s) [ G Ve G Vf (1 + cos 2 θ)+2g Ae G Af cos θ ]} }{{} γ Z interference +16 χ(s) 2 [( G Ve 2 + G Ae 2 )( G Vf 2 + G Af 2 )(1 + cos 2 θ) } +8R {G Ve G Ae } R {G Vf G Af } cos θ] {{ } σ Z Electron direction assumed as positive hemisphere Asymmetry has dependency on s Contribute only to asymmetry: canceled if integrated over solid angle Contribute only to total cross section and Z width Discrimination of fermions and anti-fermions charge for leptons A FB = N F N B, for quarks look at all info: tagging with leptons N F + N B and displaced vertices for b and c quarks (flavor tagging) e -, f + f, e + 34

4 CROSS SECTION DEPENDENCY ON POLARIZATION gl gr gl tree = ρ 0 (T3 f Q f sin 2 θw tree ) gr tree = ρ 0 Q f sin 2 θw tree, dσ Ll dcosθ dσ Rr dcosθ dσ Lr dcosθ dσ Rl dcosθ gle 2 g2 Lf (1 + cos θ)2 gre 2 g2 Rf (1 + cos θ)2 gle 2 g2 Rf (1 cos θ)2 g 2 Re g2 Lf (1 cos θ)2. L, R: polarization of initial state electron typically sum over possible polarizations At SLC polarized electron beam l, r: polarization of final state fermion Since coupling constants are different --> very different cross sections to measure 35

5 DIFFERENTIAL CROSS SECTION AND POLARIZATION [ dσ ff dcosθ = 3 [ 8 σtot ff (1 Pe A e )(1 + cos 2 θ)+2(a e P e )A f cos θ ] P e = N el! N er N el + N er P e = 0 at LEP cos θ terms vanish if integrated measure differential cross section in bins of cos θ integrate only in forward or backward hemisphere (σf and σb) 65 SLC with polarized electron beam allows measurement of each terms separately P A f = g2 Lf g 2 Rf g 2 Lf + g2 Rf Even for unpolarized beams (LEP) since Z coupling is different for L and R, there are observable LR, FB asymmetries in the final state A = 2g Vfg Af g 2 Vf + g2 Af g Vf /g Af =2 1+(g Vf /g Af ) 2 sensimve to different V and A coupling for each fermion 36

6 MIXING ANGLE FROM ASYMMETRY MEASUREMENT A f = g2 Lf g 2 Rf g 2 Lf + g2 Rf A = 2g Vfg Af g 2 Vf + g2 Af g Vf /g Af =2 1+(g Vf /g Af ) 2 g Vf g Af = 1 2Q f T f 3 sin 2 θ f eff = 1 4 Q f sin 2 θ f eff asymmetry very sensitive to mixing angle fermion charge plays important role in terms of power of measurement leptons: Q 2 = 1 up quarks: Q 2 = (2/3) 2 = 0.44 down quarks: Q 2 = (1/3) 2 = 0.11 A f ν e e L Al Family T T 3 Q ν µ µ Ac L ν τ τ L Ab 1/2 +1/2 1/2 0 1 ν er ν µr ν τr e R µ R τ R u c t +1/2 +2/3 1/2 d s b 1/2 1/3 L L u R c R t R /3 d R s R b R 0 0 1/3 L Less sensitive when smaller factor in front of sin θ sin 2 θ f eff 37

7 Utilize lifetime of decay products: larger for b and c quarks data MC uds MC udsc MC all In addition can use mass of final 10-2 state to separate b and c quarks V No. of Hemispheres uds c LIFETIME TAGGING DELPHI b s Data MC rate rate OPAL data Monte 2000 Carlo b Monte Carlo c Monte Carlo uds uds decay length 4 significance 5 L/$ 6 L V Table 5.2: b-tagging 10-6 performance of the different experiments at the cut where the R b a are performed. The lifetime tagging is combined with other information (see text). The tag is an OR-8of a secondary -6-4 vertex and -2 a lepton 0 tag tagging variable B Mass (GeV/c 2 ) No. of Hemispheres c b Data MC Mass (GeV/c 2 ) Figure 5.4: Reconstructed vertex mass from SLD for data and simulation. ALEPH DELPHI L3 OPAL SLD bpurity[%] befficiency [%]

8 LEPTON FLAVOR Γ 3 TAGGING Exploit semi-leptonic b and c decays Distinctive spectrum for leptons in final states depending on flavor of original fermion Charge of leptons correlated with parent fermion Higher momentum for leptons from b quark because of higher mass Γ 1 B + ( 40.1 ± 1.3 ) % Γ 2 B 0 ( 40.1 ± 1.3 ) % B 0 s ( 11.3 ± 1.3 ) % Γ 4 b -baryon ( 8.5 ± 2.2 ) % Γ 5 B c DECAY MODES Semileptonic and leptonic modes Γ 6 ν anything ( 23.1 ± 1.5 ) % Γ 7 l + ν l anything [a] ( 10.69± 0.22) % Γ 8 e + ν e anything ( 10.86± 0.35) % Γ 9 µ + ν µ anything ( )% Γ 10 D l + ν l anything [a] ( 2.2 ± 0.4 ) % S=1.8 Γ 11 D π + l + ν l anything ( 4.9 ± 1.9 ) 10 3 Γ 12 D π l + ν l anything ( 2.6 ± 1.6 ) 10 3 Γ 13 D 0 l + ν l anything [a] ( 6.84± 0.35) % Γ 14 D 0 π l + ν l anything ( 1.07± 0.27) % Γ 15 D 0 π + l + ν l anything ( 2.3 ± 1.6 ) 10 3 Γ 16 D l + ν l anything [a] ( 2.75± 0.19) % Γ 17 D π l + ν l anything ( 6 ± 7 ) 10 4 Γ 18 D π + l + ν l anything ( 4.8 ± 1.0 ) 10 3 Γ 19 D 0 j l+ ν l anything [a,b] ( 2.6 ± 0.9 ) 10 3 B(D 0 j D + π ) B mesons L L3 Page 4 Created: 7/30/ :47 Number of muons Data uds c fake l b#l b#c#l Number of muons Data uds c fake l b#l b#c#l Muon momentum (GeV/c) Muon transverse momentum (GeV/c) 39

9 LEFT- RIGHT ASYMMETRIES dσ ff dcosθ = 3 [ 8 σtot ff (1 Pe A e )(1 + cos 2 θ)+2(a e P e )A f cos θ ] Additional asymmetries sensitive to Af and Ae measurement P A FB = σ F σ B σ F + σ B A LR = σ L σ R 1 σ L + σ R P e F = B = Z 1 0 Z 0 A LRFB = (σ F σ B ) L (σ F σ B ) R (σ F + σ B ) L +(σ F + σ B ) R 1 P e 1 d cos d d cos d cos d d cos d(σ r σ l ) dcosθ d(σ r + σ l ) dcosθ / P f = d(σ r σ l ) dcosθ = 3 8 σtot ff = 3 8 σtot ff / d(σr + σ l ) dcosθ [ [ Af (1 + cos 2 θ)+2a e cos θ ] [ (1 + cos 2 θ)+2a e A f cos θ ] Polarization can be determined from L and R cross sections P f (cos θ) = A f(1 + cos 2 θ)+2a e cos θ (1 + cos 2 θ)+2a f A e cos θ P f = σ r σ l σ r + σ l A pol FB = (σ r σ l ) F (σ r σ l ) B (σ r + σ l ) F +(σ r + σ l ) B Measurement of polarization possible in the tau tau channel (tesina) 40

10 POLARIZED ELECTRON SLC Polarization of Electron Beam (%) Source Laser Wavelenght Optimized # # Beam Polarization SLD Data Strained Lattice Cathode for 1994 SLD Run # # Strained Lattice Cathode for 1993 SLD Run 1996 Run Strained Lattice Cathode for 1997 SLD Run # x 10 2 Z Count 60% of data in last 2 years of operation Figure 1.5: The amount of longitudinal electron polarisation as a function of the number of recorded Z decays at SLD. 41

11 b- TAGGING AT SLD Displaced secondary vertex clear signature of b decays 42

12 EXPERIMENTAL ASYMMETRIES A FB = σ F σ B σ F + σ B A LR = σ L σ R 1 σ L + σ R P e A LRFB = (σ F σ B ) L (σ F σ B ) R (σ F + σ B ) L +(σ F + σ B ) R 1 P e pol = 0 at LEP Measurement at Z pole after corrections A 0, f 3 FB = 4 A ea f A 0 LR = A e A 0 LRFB = 3 4 A f For electron final state Both asymmetries sensitive to mixing angle but ALR has larger sensitivity sin θ = 0.23 sin 2 θ = sin 4 θ = much harder to measure experimentally! 43

13 A LR ASYMMETRY AT SLD P e A LR A 0 LR sin 2 θ lept eff ±0.006 ±0.044 ± ±0.044 ± ± ± ±0.011 ± ± ± ± ± ± / ± ± ± ± ± ± ± ± ± ± ± ± ± ± / ± ± ± ± ± ± ± All combined ± ± ± ± Table 3.3: Summary of the SLD A LR measurements for all runs. Listed are the luminosityweighted mean electron polarisation ( P e ), the measured A LR,itsvaluecorrectedtotheZ-pole (A 0 LR )andsin2 θ lept eff. For P e the total error shown is dominantly systematic. For the other quantities, the errors are the statistical and systematic components respectively. The final combined result accounts for correlated uncertainties. 44

14 ion 1.5. The energy dependence of the muon and tau crosse to the hadronic A one. FB ASYMMETRY In e + e final states IN ee however, AND diagrams μμ t-channel and their interference with the s-channel diagrams ntributions are shown as a function of centre-of-mass energy L3 e + e! # e + e! (") 4. d $ / d cos + [nb] + peak!2 peak 1 peak+2 the Lepton Forward-Backward Asymmetries ry, A FB,isdefinedbythenumbersofevents,N F and N B,in forward (cos θ l > 0) or backward (cos θ l < 0) with respect 0.5 electron, A FB =(N F N B )/(N F + N B ). This definition of cceptance cuts applied on the production polar angle, cos θ, ts of A FB (l + l )requirethedeterminationofcosθ and the ptons based on their electric charges, which are determined 0 in the magnetic -1 fields of the 0.5 central 1 detectors. For µ + µ and cos + y determined from un-binned maximum-likelihood fits to the ions of the form dσ/dcos θ 1+cos 2 θ +8/3 A FB cos θ. This he available information and hence leads to slightly smaller s way the A FB measurements are insensitive to any distortions Figure 2.5: Distribution of the production polar angle, cos θ, fore + e and µ + µ events at the three principal energies during the years , measured in the L3 (left) and DELPHI (right) detectors, respectively. The curves show the SM prediction from ALIBABA [52] for e + e 45

15 INTEREFERENCE OF t- CHANNEL IN ee 1 $ [nb] L3 e + e! # e + e! (") 44 o < + < 136 o s-channel A fb 0.5 L3 e + e! # e + e! (") 44 o < + < 136 o t-channel 0 t-channel interference 0 s-channel interference ratio *s difference *s no peaking structure in cross section due to t-channel 46

16 RESULTS OF PRECISION MEASUREMENTS

17 FIT RESULTS Parameter Average Correlations [MeV] Γ ff Without Lepton Universality Γ had Γ ee Γ µµ Γ ττ Γ bb Γ cc Γ inv Γ had ± Γ ee ± Γ µµ ± Γ ττ ± Γ bb ± Γ cc ± Γ inv ± Without lepton universality Correlations χ 2 /dof = 32.6/27 m Z Γ Z σhad 0 Re 0 Rµ 0 Rτ 0 A 0, e FB A 0,µ FB m Z ± Γ Z ± σhad 0 [nb] ± Re ± Rµ ± Rτ ± A 0, e FB ± A 0,µ FB ± A 0, τ FB ± A 0, τ FB 48

18 Z BRANCHING FRACTIONS Parameter Average Correlations B(Z ff) [%] Without Lepton Universality qq e + e µ + µ τ + τ bb cc inv qq ± e + e ± µ + µ ± τ + τ ± bb ± cc ± inv ±

19 RESULTS ASSUMING LEPTON UNIVERSALITY Without lepton universality Correlations χ 2 /dof = 32.6/27 m Z Γ Z σhad 0 Re 0 Rµ 0 Rτ 0 A 0, e FB A 0,µ FB m Z ± Γ Z ± σhad 0 [nb] ± Re ± Rµ ± Rτ ± A 0, e FB ± A 0,µ FB ± A 0, τ FB ± With lepton universality Correlations χ 2 /dof = 36.5/31 m Z Γ Z σhad 0 Rl 0 A 0, l FB m Z ± Γ Z ± σhad 0 [nb] ± Rl ± A 0, l FB ± A 0, τ FB 50

20 LEPTON UNIVERSALITY % CL Standard Model Prediction A 0,l fb l + l! e + e! µ + µ! ' + '! () m t m H ) s R 0 l=% had /% ll m t =178.0 ± 4.3 GeV,m H = GeV, and α S (m 2 Z)=0.118 ± 0.003, he arrow showing the small dependence on the hadronic vacuum polarisation Z 51

21 COUPLING CONSTANTS BEFORE LEP g Vl 2002 m t m H νµ e () l + l! e + e! µ + µ! ' + '! 68% CL g Al g V 0.0 e + e - µ + µ ν e - e ν µ e - ν e - e ν e- e g A 52

22 COUPLING CONSTANTS FOR LEPTONS m t = ± 4.3 GeV m H = GeV m H g Vl l + l! e + e! µ + µ! ' + '! m t () 68% CL g Al m t =178.0 ± 4.3 GeVandm H = GeV; ± 53

23 CONSTRAINTS ON TOP LEP 200 M t Tevatron SM constraint 68% CL 50 Direct search lower limit (95% CL) Year 54

24 SM INPUT TO Z- POLE MEASUREMENTS Precision measurements at LEP rely on parameters not known a-priori coupling constants for weak, electromagnetic, and strong interaction fermion masses vector boson masses Correlation between photon, W and Z mass Higgs mass Some parameters are well known, others can be constrained from precision measurements Light fermion masses well known. Small and well calculated corrections at Z pole Photon mass fixed to be zero from QED Z mass: can be measured precisely at Z pole W mass: correlated to Z mass and Fermi Constant GF GF known with very high precision far beyond reach for mw measurements Assume GF to be fixed and treat mw as function of mz to be constrained with data m 2 W = m2 Z 2 πα GF m 2 Z 1 1 r G F ~c = 2 8 From measurement of muon lifetime Calculation at 2-loop level g 2 m 2 W Running of α = (1) 10 5 GeV 2 55

25 W AND Z MASS MEASUREMENT W J = 1 AREVIEWGOESHERE CheckourWWWListofReviews W MASS The W -mass listed here corresponds to the mass parameter in a Breit- Wigner distribution with mass-dependent width. To obtain the world average, common systematic uncertainties between experiments are properly taken into account. The LEP-2 average W mass based on published results is ± GeV [CERN-PH-EP/ ]. The combined Tevatron data yields an average W mass of ± GeV [FERMILAB-TM E]. OUR FIT uses these average LEP and Tevatron mass values and combines them assuming no correlations. VALUE (GeV) EVTS DOCUMENT ID TECN COMMENT ± OUR FIT ± k 1 pp ABAZOV 09AB D0 E cm =1.96TeV ± 0.055± k 2 ABDALLAH 08A DLPH E ee cm = GeV ± 0.034± k 3 pp AALTONEN 07F CDF E cm =1.96TeV ± 0.042± ABBIENDI 06 OPAL E ee cm = GeV ± 0.046± ACHARD 06 L3 E ee cm = GeV ± 0.043± SCHAEL 06 ALEP E ee cm = GeV ± pp ABAZOV 02D D0 E cm =1.8 TeV We use the following data for averages but not for fits ± pp AFFOLDER 01E CDF E cm =1.8TeV We do not use the following data for averages, fits, limits, etc ± AKTAS 06 H1 e ± p νe (ν e )X, s 300 GeV 80.3 ± 2.1 ± 1.2 ± CHEKANOV 02C ZEUS e p νe X, s= ± GeV BREITWEG 00D ZEUS e + p νe X, s 300 GeV ± 0.22 ± ALITTI 92B UA2 See W /Z ratio below ± 0.31 ± ALITTI 90B UA2 pp E cm =546,630GeV 80.0 ± 3.3 ± pp ABE 89I CDF E cm =1.8 TeV 82.7 ± 1.0 ± pp ALBAJAR 89 UA1 E cm =546,630GeV ± ALBAJAR 89 UA1 pp E cm =546,630GeV 89 ± 3 ± ALBAJAR 89 UA1 pp E cm =546,630GeV 81. ± 5. 6 ARNISON 83 UA1 E ee cm =546GeV BANNER 83B UA2 Repl. by ALITTI 90B Z J = 1 AREVIEWGOESHERE CheckourWWWListofReviews Z MASS OUR FIT is obtained using the fit procedure and correlations as determined by the LEP Electroweak Working Group (see the note The Z boson and ref. LEP-SLC 06). The fit is performed using the Z mass and width, the Z hadronic pole cross section, the ratios of hadronic to leptonic partial widths, and the Z pole forward-backward lepton asymmetries. This set is believed to be most free of correlations. The Z-boson mass listed here corresponds to the mass parameter in a Breit-Wigner distribution with mass dependent width. The value is 34 MeV greater than the real part of the position of the pole (in the energysquared plane) in the Z-boson propagator. Also the LEP experiments have generally assumed a fixed value of the γ Z interferences term based on the standard model. Keeping this term as free parameter leads to a somewhat larger error on the fitted Z mass. See ACCIARRI 00Q and ABBIENDI 04G for a detailed investigation of both these issues. VALUE (GeV) EVTS DOCUMENT ID TECN COMMENT ± OUR FIT ± M 1 ABBIENDI 01A OPAL E ee cm =88 94GeV ± M 2 ABREU 00F DLPH E ee cm =88 94GeV ± M 3 ACCIARRI 00C L3 E ee cm =88 94GeV ± M 4 BARATE 00C ALEP E ee cm =88 94GeV We do not use the following data for averages, fits, limits, etc ± ABBIENDI 04G OPAL E ee cm =LEP GeV ±0.032 ± ACHARD 04C L3 E ee cm = GeV ± M 7 ACCIARRI 00Q L3 E ee cm =LEP GeV ± MIYABAYASHI 95 TOPZ E ee cm =57.8 GeV ±0.28 ± pp ALITTI 92B UA2 E cm =630GeV 90.9 ±0.3 ± pp ABE 89C CDF E cm =1.8 TeV ± ABRAMS 89B MRK2 E ee cm =89 93GeV 93.1 ±1.0 ± pp ALBAJAR 89 UA1 E cm =546,630GeV 1 ABBIENDI 01A error includes approximately 2.3 MeVduetostatisticsand1.8 MeVdue to LEP energy uncertainty. 2 The error includes 1.6 MeVduetoLEPenergyuncertainty. 3 The error includes 1.8 MeVduetoLEPenergyuncertainty. 4 BARATE 00C error includes approximately 2.4 MeVduetostatistics,0.2MeV due to experimental systematics, and 1.7MeV due to LEP energy uncertainty. 5 ABBIENDI 04G obtain this result using the S matrix formalism for a combined fit to their cross section and asymmetry data at the Z peak and their data at GeV. The authors have corrected the measurement for the 34 MeV shift with respect to the Breit Wigner fits. 56

26 SM PARAMETERS TO BE EXTRACTED FROM MEASUREMENTS (m 2 Z) QED coupling constant more precisely the hadronic corrections to it (m 2 Z)! had (m 2 Z) QCD coupling constant S (m 2 Z) most precise measurement if EW sector well understood Z mass m Z And more importantly two parameters not directly accessible at LEP Higgs mass m H Top mass m t Source δ Γ Z σhad 0 Rl 0 Rb 0 ρ l sin 2 θ lept eff m W [MeV] [nb] [MeV] α (5) had (m2 Z) α S (m 2 Z ) m Z 2.1 MeV m t 4.3 GeV log 10 (m H /GeV) Theory Experiment

27 RUNNING OF α QED QED coupling constant must be determined at mz scale running due to fermion loops ",Z/W α(s) = α eµτ (s)+ α top (s)+ α (5) had (s). Lepton correction calculated with negligible uncertainty Top correction rather small and computed Light quark corrections difficult to compute perturbative QCD not feasible because of low mass measured from hadronic cross sections at low energy ee collisions Rather than α(s) determine Δαhad(s) from fit to data f ",Z/W! f /f α(s) = α(0) 1 α(s) α(0) = 1/ / [84]. The c α eµτ (m 2 Z )= uncertainty [201]. Since h α top (m 2 Z )= ( α (5) had (m2 Z) = ±

28 PSEUDO- OBSERVABLES Measurements at the Z pole both at LEP and SLC Low Q 2 νn measurements constraints on couplings Direct measurement of W mass and width from Tevatron and LEP χ 2 /dof = 32.6/27 m Z ± Γ Z ± σhad 0 [nb] ± Re ± Rµ ± Rτ ± A 0, e FB ± A 0,µ FB ± A 0, τ FB ± Direct measurement of top at Tevatron once became available 59

29 CHOOSING BEST PSEUDO- OBSERVABLES Each experimental measurement has different sensitivity to SM parameters we want to constrain. Choose those with highest sensitivity to mt and mh (through radiative corrections) small dependency on QCD corrections Parameters most sensitive to radiative corrections will be most powerful ρ 0 = m 2 W. m 2 Z cos 2 θw tree ( ) ρ f R(R f ) = 1+ ρ se + ρ f flavor κ f R(K f ) = 1+ κ se + κ f specific sin 2 θ f eff κ f sin 2 θ W g Vf ρ f (T f 3 2Q f sin 2 θ f eff ) g Af ρ f T f 3, self-energy ρ se = 3G Fm 2 W 8 2π 2 κ se = 3G Fm 2 W 8 2π 2 [ m 2 t m 2 W [ m 2 t m 2 W ( sin2 θ W cos 2 θ W cos 2 θ W sin 2 10 θ W 9 ln m2 H ( m 2 W 5 6 ) ln m2 H m 2 W ) ] + ] 60

30 SENSITIVITY TO M t AND M H () (5) had () (5) had M Z M Z % Z $ 0 had R 0 l A 0,l fb A l (P ' ) R 0 b R 0 c A 0,b fb A 0,c fb e + e! "/Z! t t W b! b e + e! "/Z W W t b! b % Z $ 0 had R 0 l A 0,l fb A l (P ' ) R 0 b R 0 c A 0,b fb A 0,c fb A b A b A c A l (SLD) sin 2 + lept eff (Q fb ) m W * % W * A c A l (SLD) sin 2 + lept eff (Q fb ) m W * % W * M t Q W (Cs) sin 2 +!!(e! e! MS ) sin 2 + W (&N) g 2 L (&N) g 2 R (&N) 1O theo /1M t &(M t )/$ meas *preliminary M t Q W (Cs) sin 2 +!!(e! e! MS ) sin 2 + W (&N) g 2 L (&N) g 2 R (&N) *preliminary O theo /1logM H &(logm H )/$ meas 61

31 Γ INV DEPENDENCY ON M t AND M H 250 Measurement m t 175 () (5) had = ± ) s = ± m H = GeV % inv Measurement m H () (5) had = ± ) s = ± m t = ± 4.3 GeV % inv 62

32 EFFECTIVE MIXING ANGLE A 0,l fb ± A l (P ' ) ± A l (SLD) ± A 0,b fb ± A 0,c fb ± Q had fb ± Average ± , 2 /d.o.f.: 11.8 / 5 m H 10 2 () had = ± () (5) m t = ± 4.3 GeV sin 2 + lept eff 63

33 mh very sensitive to red value sin 2 θ lept eff only parameter sensitive to Source of sensitivity of Higgs mass to eff α (5) had (m2 Z ) eff α (5) had (m2 Z ) Z- POLE RESULTS red value sin 2 θ lept eff m t % CL % ll m W prel. sin 2 + lept eff () R b 130 Parameter Value Correlations α (5) had (m2 Z ) α S(m 2 Z ) m Z m t log 10 (m H /GeV) α (5) had (m2 Z) ± α S (m 2 Z ) ± m Z ± m t 173± log 10 (m H /GeV) 2.05± m H 111± m H 64

34 IMPLICATION OF PRECISION MEASUREMENTS ρ f R(R f ) = 1+ ρ se + ρ f flavor κ f R(K f ) = 1+ κ se + κ f specific self-energy sin 2 θ f eff κ f sin 2 θ W g Vf ρ f (T f 3 2Q f sin 2 θ f eff ) g Af ρ f T f 3, sin 2 θ W = ± sin 2 θ lept eff = ± κ l = ± sin 2 θ b eff = ± κ b = ± ρ l = ± r w = ± ρ b = ± r = ±

35 CONSTRAINTS ON TOP AND W MASS Top-Quark Mass W-Boson Mass CDF ± 6.6 D ± 5.1 Average ± m t, 2 /DoF: 2.6 / 4 LEP1/SLD ! 10.2 LEP1/SLD/m W /% W ! 9.5 TEVATRON ± LEP ± Average ± m W, 2 /DoF: 0.3 / 1 NuTeV ± LEP1/SLD ± LEP1/SLD/m t ±

36 CONSTRAINTS ON HIGGS MASS 80.5 LEP1, SLD data LEP2 (prel.), pp! data 68% CL m W 80.4 () 80.3 m H m t 67

37 INCLUSION OF LHC m W March 2012 LHC excluded LEP2 and Tevatron LEP1 and SLD 68% CL 80.3 m H m t 68

38 IMPORTANCE OF DIRECT W AND TOP MEASUREMENTS 80.5 High Q 2 except m W /% W 68% CL 200 High Q 2 except m t 68% CL m W 80.4 m W (LEP2 prel., pp! ) m t 180 m t (Tevatron) 80.3 Excluded m H 160 Excluded m H Parameter Value Correlations α (5) had (m2 Z ) α S(m 2 Z ) m Z m t log 10 (m H /GeV) α (5) had (m2 Z) ± α S (m 2 Z ) ± m Z ± m t 178.5± log 10 (m H /GeV) 2.11± m H 129±

39 LIMIT ON HIGGS MASS Theory uncertainty () had = () (5) ± ± incl. low Q 2 data (, Excluded m H 70

40 UPDATED LIMIT ON HIGGS m h = GeV [m h < 160 GeV one-sided 95% CL] χ March 2008 Theory uncertainty α (5) α had = ± ± incl. low Q 2 data m Limit = 160 GeV probability per GeV % 5% Excluded Preliminary m H M H Including the direct LEP search data yields m h < 190 GeV at 95% CL. 71