Lesson #2 Asymmetry measurements and global fit

1. Standard Model Lesson #2 Asymmetry measurements and global fit

2. f e- e+  Asymmetric term _ f Backward Forward Forward-backward asymmetries

3. e+ e+ g(s) Z(s) e- e- Dominant terms

4. G1(s) G3(s) G1(s) G3(s) For s ~ MZ2 I can consider only the dominant terms

5. The cross section can be expressed as a function of the forward-backward asymmetry Considering only the dominant terms the asymmetric contribution to the cross section is the product Ae Af

6. The forward-backward asymmetry can be measured with the counting method: or using the “maximum likelihood fit” method: With the counting method we do not assume the theoretical q distribution With the likelihood method the statistical error is lower

7. Ad 0.95 Au 0.70 0.15 Ae 0.23 0.24 0.25 sin2W At the tree level the forward-backward asymmetry it’s simply related to the sin2W value and to the fermion final state. AFB measurement for different f  comparison between different sin2W estimation

8. Jet e- e+  Jet Backward Forward For leptons decays the q angle is provided by the track direction. For quark decays the quark direction can be estimated with the jet axis The charge asymmetry is one alterative method where the final state selection is not required Jet e- e+  Jet forward hemisphere backward hemisphere

9. Minimal subtraction On shell Effective The relation between the asymmetry measurments and the Weinberg angle it depends to the scheme of the radiative corretions: Eur Phys J C 33, s01, s641 –s643 (2004)

10. sin2qeffW and radiative corrections We considered the following 3 parameters for the QEWD :  sinqW GF A better choice are the physical quantities we can measure with high precision: a measured with anomalous magnetic dipole moment of the electron GF measured with the lifetime of the muon MZ measured with the line shape of the Z sinqW e MW becomes derived quantities related to mt e mH. The Weinberg angle can be defined with different relations. They are equivalent at the tree level but different different when the radiative corrections are considered: (1) (2) (On shell) (NOV)

11. Dr= H Starting with the on-shell definition, including the radiative corerctions, we have: EW loops EW vertex We can avoid to apply corrections related to mt mH in the final result simply defining the Weinberg angle in the “effective scheme”

12. Final Weinberg angle measurement: sin2eff=0.23150±0.00016 P(2)=7% (10.5/5) 0.23113 ±0.00020 leptons 0.23213 ±0.00029 hadrons Larger discrepancy: Al(SLD) –Afbb2.9 

13. 0 s0 AFB function of s Dominant terms Outside the Z0 peak the terms with the function |0(s)|2 are not anymore dominant, they became negligible. The function Re(0(s)) can be simplified

14. With different AFB measurements for different √s we can fit the AFB(s) function. We must choose the free parameters:

15. Fit with Line shape and AFB

16. We can decide the parameters to be included in the fit: MZ , GZ , s0h , Re , Rm , Rt , AFB0,e , AFB0,m , AFB0,t 9 parameters fit leptons have been considered separately 5 parameters fit assuming lepton universality MZ , GZ , s0h , Rl , AFB0,lept

17. Lepton universality The coupling constants between Z and fermions are identical in the SM. We can check this property with the real data. gV and gA for different fermions are compatible within errors Error contributions due to: - MH , Mtop - theoretical incertanty on aQED(MZ2)

18. LEP 1990-1995 ~ 5M Z0 / experiment DELPHI 1990 (~ 100.000 Z0 hadronic) 1991 (~ 250.000 Z0 hadronic) 1992 (~ 750.000 Z0 hadronic) 9 parameters fit LEP accelerator ! DMZ/MZ 2.3 10-5 GF/GF  0.9 10-5a(MZ) /a 20 10-5

19. n t- t rest frame t direction in the laboratory p- t polarization measurement from Ztt Z bosons produced with unpolarized beams are polarized due to parity violation t from Z decay are polarized, we can measure Pt from the t decays. backward The pion tends to be produced - in the backward region for left-handled t – - in the forward region for right handled t – (forward/backward w.r.t. t direction in the lab.) dati In the laboratory frame the pp / pbeam distribution is different for tL and tR t- left-handled t- right-handled background

20. The t polarization can be measured observing the final state particle distributions for different decays : • t pn • t  3pn • trn t mnn, enn Pt is related to the q angle of the charged track w.r.t. beam direction Different Pt (cosq) measurement from different decays channel can be added

21. Fit: Compared with AtFB = ¾ Ae At Pt (cosq) provides one independent measurement of Ae e At

22. Misura della polarizzazione Utilizza lo scattering Compton della luce polarizzata. L’angolo di scattering dipendente dallo spin dell’elettrone. • Compton Polarimeter • <Pe-> = 75 % • σ<Pe> = 0.5 % • Quartz Fiber Polarimeter and Polarized Gamma Counter – run on single e- beam + crosschecks • <Pe+> = -0.02 ± 0.07 % elettroni diffusi Luce polarizzata Circolarmente (YAG Laser, 532 nm)

23. Left-Right asymmetry at SLD With polarized beam we can measure the Left-Right asymmetry: Cross section with ‘right-handed’ polarized beam: eR-e+  ff Cross section with ‘left-handed’ polarized beam: eL-e+  ff ( Pe = 1 ) To estimate the cross section difference betwnn e-L e+ and e-R e+we need a very precise luminosity control. The e- beam polarization was inverted at SLC at the crossing frequncy (120 Hz) to have the same luminosity for eL and eR with Pe < 1 we measure only : AmLR = (NL-NR) / (NL+NR) the left-right asymmetry is given by: ALR= AmLR / Pe precise measurement Pe is needed

24. new new cos q Cross section for unpolarized beam Cross section for partial polarization Having the same luminosity and the same but opposite polarizations, the mean of P+ with P- gives the same AFB like at LEP: Separating the two polarizations we can obtain new measurements:

25. Asymmetry results at SLD • Afwith ALRFB • Combined with Ae from ALR With only 1/10 of statistics, thanks to the beam polarization, SLD was competitive with LEP for the Weinberg angle measurement: SLD LEPleptons

26. Global Electroweak Fit From the experimental observables: line shape s(s) FB asymmetries AFB(s) t polarization Pt(cos) pseudo-osservables can be extrapolated: MZ GZs0h AlFB etc.. Using a fit program (ZFITTER) with 2 loop QEWD and 3 loop QED the best fit can be obtained for the parameters of the model and for the masses having some uncertainty (mt, ,mH ). The current version of ZFITTER (in C++) is Gfitter. Global fits are performed in two versions: the standard fit uses all the available informations except results from direct Higgs searches, the complete fit includes everything

27. 20 pseudo-osservables 5 fitted parameters With the fitted parameters we can obtain also the fitted pseudo-osservables

28. Updated Status of the Global Electroweak Fit and Constraints on New Physics July 2011 arXiv:1107.0975v1 c2min /DOF = 16.6 / 14 • usage of latest experimental input: • Z-pole observables: LEP/SLD results • [ADLO+SLD, Phys. Rept. 427, 257 (2006)] • MW and GW: latest LEP+Tevatron averages (03/2010) • [arXiv:0908.1374][arXiv:1003.2826] • mtop: latest Tevatron average (07/2010) [arXiv:1007.3178] • mc and mb: world averages [PDG, J. Phys. G33,1 (2006)] • Dahad(5)(MZ2):latest value (10/2010) • [Davier et al., arXiv:1010.4180] • direct Higgs searches at LEP and Tevatron (07/2010) • [ADLO: Phys. Lett. B565, 61 (2003)], [CDF+D0: arXiv:1007.4587]

29. MW mH=81+52-33 GeV (2002) mHiggs< 193 GeV 95% C.L. mH=91+58-37 GeV (2003) mHiggs< 211 GeV 95% C.L. AbFB , AcFB , Rb , Rc mH=96+31-24 GeV (2011) mHiggs< 171 GeV 95% C.L. mH=96+60-38 GeV (2004) mHiggs< 219 GeV 95% C.L.

30. Z Physics at LEP I CERN 89-08 Vol 1 – Forward-backward asymmetries (pag. 203) Measurement of the lineshape of the Z and determination of electroweak parameters from its hadronic decays - Nuclear Physics B 417 (1994) 3-57 Improved measurement of cross sections and asymmetries at the Z resonance - Nuclear Physics B 418 (1994) 403-427 Global fit to electroweak precision data Eur. Phys J C 33, s01, s641 –s643 (2004) Measurement of the t polarization in Z decays – Z. Phys. C 67 183-201 (1995)