1. XXIX Ph.D in Physics Ezio TorassaPadova, May 5th 2014 Lesson #2 Asymmetry measurements and global fit Standard Model

2. XXIX Ph.D in Physics Ezio TorassaPadova, May 5th 2014 Forward-backward asymmetries  ForwardBackward e+e+ e-e- f f _ Asymmetric term

3. XXIX Ph.D in Physics Ezio TorassaPadova, May 5th 2014   s) e+e+ e-e-  Z(s) e+e+ e-e- Dominant terms

4. XXIX Ph.D in Physics Ezio TorassaPadova, May 5th 2014 G 1 (s) G 3 (s) G 1 (s) G 3 (s) For s ~ M Z 2 I can consider only the dominant terms

5. XXIX Ph.D in Physics Ezio TorassaPadova, May 5th 2014 Considering only the dominant terms the asymmetric contribution to the cross section is the product A e A f The cross section can be expressed as a function of the forward-backward asymmetry

6. XXIX Ph.D in Physics Ezio TorassaPadova, May 5th 2014 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  distribution With the likelihood method the statistical error is lower

7. XXIX Ph.D in Physics Ezio TorassaPadova, May 5th 2014 sin 2  W 0.95 0.70 0.15 0.230.240.25 AdAd AuAu AeAe At the tree level the forward-backward asymmetry it’s simply related to the sin 2  W value and to the fermion final state. A FB measurement for different f  comparison between different sin 2  W estimation

8. XXIX Ph.D in Physics Ezio TorassaPadova, May 5th 2014 For leptons decays the  angle is provided by the track direction. For quark decays the quark direction can be estimated with the jet axis  ForwardBackward e+e+ e-e- Jet The charge asymmetry is one alterative method where the final state selection is not required  forward hemisphere e+e+ e-e- Jet backward hemisphere

9. XXIX Ph.D in Physics Ezio TorassaPadova, May 5th 2014 The relation between the asymmetry measurments and the Weinberg angle it depends to the scheme of the radiative corretions: Effective Minimal subtraction Eur Phys J C 33, s01, s641 –s643 (2004) On shell

10. XXIX Ph.D in Physics Ezio TorassaPadova, May 5th 2014 sin 2  eff W and radiative corrections We considered the following 3 parameters for the QE W D :  sin  W G F A better choice are the physical quantities we can measure with high precision:  measured with anomalous magnetic dipole moment of the electron G F measured with the lifetime of the muon M Z measured with the line shape of the Z sin  W e M W becomes derived quantities related to m t e m H. 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. XXIX Ph.D in Physics Ezio TorassaPadova, May 5th 2014 Starting with the on-shell definition, including the radiative corerctions, we have: == We can avoid to apply corrections related to m t m H in the final result simply defining the Weinberg angle in the “effective scheme” H EW vertex EW loops

12. XXIX Ph.D in Physics Ezio TorassaPadova, May 5th 2014 Final Weinberg angle measurement: sin 2  eff =0.23150±0.00016 P(  2 )=7% (10.5/5) 0.23113 ±0.00020 leptons 0.23213 ±0.00029 hadrons Larger discrepancy: A l (SLD) –A fb b 2.9 

13. XXIX Ph.D in Physics Ezio TorassaPadova, May 5th 2014 A FB function of s Outside the Z 0 peak the terms with the function |  0 (s)| 2 are not anymore dominant, they became negligible. The function Re(  0 (s)) can be simplified s0s0 0 Dominant terms

14. XXIX Ph.D in Physics Ezio TorassaPadova, May 5th 2014 With different A FB measurements for different √s we can fit the A FB (s) function. We must choose the free parameters:

15. XXIX Ph.D in Physics Ezio TorassaPadova, May 5th 2014 Fit with Line shape and A FB

16. XXIX Ph.D in Physics Ezio TorassaPadova, May 5th 2014 We can decide the parameters to be included in the fit: M Z,  Z,  0 h, R l, A FB 0,lept 5 parameters fit assuming lepton universality M Z,  Z,  0 h, R e, R , R , A FB 0,e, A FB 0, , A FB 0,  9 parameters fit leptons have been considered separately (R l =  had /  l )

17. XXIX Ph.D in Physics Ezio TorassaPadova, May 5th 2014 The coupling constants between Z and fermions are identical in the SM. We can check this property with the real data. Error contributions due to: - M H, M top - theoretical incertanty on  QED (M Z 2 ) Lepton universality g V and g A for different fermions are compatible within errors

18. XXIX Ph.D in Physics Ezio TorassaPadova, May 5th 2014 DELPHI 1990 (~ 100.000 Z 0 hadronic) 1991 (~ 250.000 Z 0 hadronic) 1992 (~ 750.000 Z 0 hadronic) LEP 1990-1995 ~ 5M Z 0 / experiment LEP accelerator !  M Z /M Z  2.3 10 -5  G F /G F  0.9 10 -5  (M Z ) /   20 10 -5 9 parameters fit

19. XXIX Ph.D in Physics Ezio TorassaPadova, May 5th 2014  polarization measurement from Z   background Z bosons produced with unpolarized beams are polarized due to parity violation  from Z decay are polarized, we can measure P  from the  decays.  rest frame --   In the case of a  decaying to a pion and a neutrino, the neutrino is preferably emitted opposite the spin orientation of the  to conserve angular momentum, this is due to the left-handed nature of the neutrino. Hence, the pion will preferably be emitted in the direction of the spin orientation of the .  * is defined to be the angle in the rest frame of the  lepton between the direction of the  and the direction of the pion. The distribution of   is related to P  :  spin

20. XXIX Ph.D in Physics Ezio TorassaPadova, May 5th 2014  - left-handled  - right-handled dati background The 1/N dN/cos   distribution can not be directly measured because it is not possible to determine the τ helicity on an event-by-event basis. We can anyway measure the polarization using the spectrum of the decay products:  rest frame - - --  direction in the laboratory The pion tends to be produced - in the backward region for left-handled  – - in the forward region for right handled  – (forward/backward w.r.t.  direction in the lab.) backward In the laboratory frame the p  / p beam distribution is different for  L and  R

21. XXIX Ph.D in Physics Ezio TorassaPadova, May 5th 2014 The  polarization can be measured observing the final state particle distributions for different decays :   3     e In case of a leptonic decay the presence of two neutrinos in the final state makes this channel less sensitive to the tau helicity: The p  / p beam distribution is related to the  polarization:  - left-handled  - right-handled

22. XXIX Ph.D in Physics Ezio TorassaPadova, May 5th 2014 Fit: Compared with A  FB = ¾ A e A  P  (cos  provides one independent measurement of A e e A  The polarization is measured in several bin of the polar angle cos   between the pion and the beam direction (within 3° is a good approximation of the angle between  and beam direction)

23. XXIX Ph.D in Physics Ezio TorassaPadova, May 5th 2014 Compton Polarimeter = 75 % σ = 0.5 % Quartz Fiber Polarimeter and Polarized Gamma Counter – run on single e - beam + crosschecks = -0.02 ± 0.07 % The polarization measurement is done using the Compton scattering between electrons and polarized light. The scattering angle of the electron is related to the spin. Circular polarized light (YAG Laser, 532 nm) diffused electrons Polarization measurement

24. XXIX Ph.D in Physics Ezio TorassaPadova, May 5th 2014 With polarized beam we can measure the Left-Right asymmetry: Cross section with ‘left-handed’ polarized beam: e L - e+  ff Cross section with ‘right-handed’ polarized beam: e R - e+  ff Left-Right asymmetry at SLD 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 e L and e R with P e < 1 we measure only : A mLR = (N L -N R ) / (N L +N R ) the left-right asymmetry is given by: A LR = A mLR / P e precise measurement P e is needed ( P e = 1 )

25. XXIX Ph.D in Physics Ezio TorassaPadova, May 5th 2014 cos  new 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 A FB like at LEP: new Separating the two polarizations we can obtain new measurements:

26. XXIX Ph.D in Physics Ezio TorassaPadova, May 5th 2014 A f with A LRFB Combined with A e from A LR Asymmetry results at SLD SLD LEP leptons With only 1/10 of statistics, thanks to the beam polarization, SLD was competitive with LEP for the Weinberg angle measurement:

27. XXIX Ph.D in Physics Ezio TorassaPadova, May 5th 2014 From the experimental observables: line shape  (s) FB asymmetries A FB (s)  polarization P  (cos  ) pseudo-osservables can be extrapolated: M Z  Z   h A l FB etc.. Using a fit program (ZFITTER) with 2 loop QE W D and 3 loop QED the best fit can be obtained for the parameters of the model and for the masses having some uncertainty (m t,,m H ). 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 Global Electroweak Fit

28. XXIX Ph.D in Physics Ezio TorassaPadova, May 5th 2014 20 pseudo-osservables 5 fitted parameters With the fitted independent parameters we can obtain all the fitted pseudo-observables

29. XXIX Ph.D in Physics Ezio TorassaPadova, May 5th 2014 usage of latest experimental input: Z-pole observables: LEP/SLD results [ADLO+SLD, Phys. Rept. 427, 257 (2006)] M W and  W : latest LEP+Tevatron averages (03/2010) [arXiv:0908.1374][arXiv:1003.2826] m top : latest Tevatron average (07/2010) [arXiv:1007.3178] m c and m b : world averages [PDG, J. Phys. G33,1 (2006)]  had (5) (M Z 2 ): 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] Updated Status of the Global Electroweak Fit and Constraints on New Physics July 2011 arXiv:1107.0975v1arXiv:1107.0975v1  2 min /DOF = 16.6 / 14

30. XXIX Ph.D in Physics Ezio TorassaPadova, May 5th 2014 Updated status of the Global fit, Rencontres de Moriond QCD La Thuile, 9th-15th March 2013 Γ had QCD Adler functions at N3LO [P. A. Baikov et al., PRL108, 222003 (2012)] R b Partial width of Z→bb [Freitas et al., JHEP08, 050 (2012)] M higgs Higgs mass measurement [arXiv:1207.7214, arXiv:1207.7235]

31. XXIX Ph.D in Physics Ezio TorassaPadova, May 5th 2014

32. XXIX Ph.D in Physics Ezio TorassaPadova, May 5th 2014 m H =81 +52 -33 GeV (2002) m H =91 +58 -37 GeV (2003) m H =96 +60 -38 GeV (2004) m H =96 +31 -24 GeV (2011) 2011 2013 m H =94 +25 -22 GeV (2013) The LHC measurement m H =125.7± 0.4 GeV is compatible with the fit within 1.3 

33. XXIX Ph.D in Physics Ezio TorassaPadova, May 5th 2014 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  polarization in Z decays – Z. Phys. C 67 183-201 (1995) The ElectroWeak fit of Standard Model after the Discovery of the Higgs-like boson EPJC 72, 2205 (2012), arXiv:1209.2716