Lesson #1 Measurement of the Z e W bosons properties

1. Standard Model Lesson #1 Measurement of the Z e W bosons properties

2. 3 2 4 1 e- a a e-  e+ b e+ b Introduzione s,t,u – le variabili invarianti di Mandelstam • p1 = [E, p, 0, 0]; • p2 = [E, -p, 0, 0]; • p3 = [E, p cos, p sin, 0]; • p4 = [E, -p cos, -p sin, 0]; • s = ( p1 + p2 )2 = ( p3 + p4 )2 = 4E2; • t = ( p1 - p3 )2 = ( p4 - p2 )2 = - ½ s (1 - cos); • u = ( p1 - p4 )2 = ( p2 - p3 )2 = - ½ s (1 + cos); • s + t + u = m12 + m22 + m32 + m42 0 (2 variabili indipendenti). in approssimazione di massa nulla per tutte le particelle di stato iniziale e finale (m  0, E  |p| )

3. e+ e+ e+ +   canale “t” e+ - e+ canale “s” e- Canale “s” e canale “t” • si chiamano processi di “canale s” quelli, come e+e- +-, in cui la particella emessa e riassorbita ( in questo caso) ha come quadrato del quadri-momento il valore s, la variabile di Mandelstam che caratterizza il processo; • viceversa, si chiamano processi di “canale t” quelli, come e+e+ e+e+, in cui la particella scambiata ( anche in questo caso) ha come quadrato del quadri-momento il valore t; • talvolta, il processo (ex. e+e- e+e-) è descritto da più diagrammi di Feynman, di tipo s e t; in tal caso si parla di somma di “diagrammi di tipo s” o di “tipo t” (+ interferenza).

4. Integrated luminosity Efficiency (trigger + reconstruction +selection) [cm -2 sec -1 ] Luminosity definition and measurement

5. e+ g e+ e- g e- Luminosity measurement LEP Based on low angle Bhabha scattering event counting e- e+e- e+e- q e+ e- Dominated by the photon exchange “t cannel”: e+ “s channel” q (deg) 45. 90. Region used by the luminometer:  1-10 deg Bhabha Homi Jehangir, indian theoretica physicist (Bombay 1909 – monte Bianco 1966)

6. e+ e+ g(s) Z(s) e+ e- e- e+ g(t) Z(t) e- e- (s)-(s) (t)-(t) (s)-(t) (non polarized emectrons) Z(s)-(s) Z(s)-(t) Z(t)-(s) Z(t)-(t)Z(s)-Z(s) Z(s)-Z(t)Z(t)-Z(t)

7. Rate vs offset, taken from Potter in Yellow report CERN 94-01 v1 • Now the trick: scan the offset while measuring the rate, over the whole non-zero range, then integrate the result: Van der Meer scan x See S. Van der Meer, ISR-PO/68-31, June 18th, 1968  z • Coasting beams with crossing angle  and beam currents y • Luminosity (rate) insensitive to offsets in x and z, but sensitive to offsets in y: yo x

8. Standard Model Standard Model The standard Model is our particle interaction theory It’s based on the two non –abelian gauge groups: QCD (Quantum CromoDynamics) : color symmetry group SU(3) QEWD (Quantum ElectroweakDynamics) : symmetry group SU(2)xU(1) We have one theory but many Monte Carlo programs because the cross section for every possible process is not a trivial calculation also starting from the “right” Lagrangian.

9. Standard Model The QEWD Lagrangian (cfr. Halzen, Martin, “Quarks & leptons”, cap.13 - 15): LQEWD = Lgauge + Lfermioni+ LHiggs + LYukawa Lfermioni= Llept+ Lquark => Fermions – Vector bosons interaction term => Fermions – Scalar boson interaction term

10. s=(s1,s2,s3) : Pauli matrixes g g’ a b Parameters of the model Gi Removing the mass of the fermions and the Higgs mass we have only 3 residual free parameters: g g’ v is the minimum of the Higgs potential v = | F | =

11. After the symmetry breaking : Small oscillation around the vacuum. For we neglect terms at order > 2nd 2 complex Higgs fields 1 real Higgs field - 3 DOF 4 massless vector bosons 1 massless + 3 massive vector bosons + 3 DOF

12. UA1 pp √s = 540GeV (1993) MW = 82.4±1.1 GeV MZ = 93.1±1.8 GeV Fermi constant electron charge WWeinberg angle g g’ v  Historical measurements: e Millikan experiment (ionized oil drops) W Gargamelle (1973) asymmetry from scattering GF lifetime The mass of the vector bosons are related to the parameters: sin2W  0.23 ( error  10 % ) MW  80 GeV MZ  92 GeV Before the W and Z discovery we had strong mass constraints:

13. Z0 boson decay (channels and branching ratios) The Z° boson can decay in the following 5 channels with different probabilities:  p=0,20 (invisible) e- e+ p=0,0337 pv= 0,0421 Z° - + p=0,0337 pv= 0,0421 - + p=0,0337 pv= 0,0421 qq p=0,699 pv= 0,8738 • The differences can be partially explained with the different number of quantum states: • nn includes the 3 different flavors: e , m , t • qq includes the 5 different flavors: uu , dd , ss , cc , bb for every flavor there’re 3 color states ( tt is excluded because mt >MZ) • “partially explained” : 0,20 > 3 × 0,0337 and 0,699 > 15 × 0,0337 • we will see later they are depending also to the charge and the isotopic spin

14. Z0 boson decay (selection criteria) e+e- Z0  hadrons Nucl. Physics B 367 (1991) 511-574 150.000 events (hadronic and leptonic) collected between August 1989 - August 1990 Fraction of √s Nch a) Charged track multiplicity  5 b) Energy of the event > 12 % s Efficiency  96 % Contamination  0.3 % ( + - events) e+e- Z0 e+e- Efficiency  98 % Contamination  1.0 % (+ - events) • Charged track multiplicity  3 • E1ECAL > 30 GeV E2ECAL > 25 GeV •  < 10 o

15. Charged track multiplicity = 2 • p1 e p2 > 15 GeV • IPZ < 4.5 cm , IPR < 1.5 cm •  < 10 o • Association tracker- muon detector • EHCAL < 10 GeV (consistent with MIP) • EECAL < 1 GeV (consistent with MIP)  e+e- Z0  +- Efficiency  99 % Contamination: ~1.9 % (+ - events) ~1.5 % (cosmic rays) e+e- Z0  +- Efficiency  70 % Contamination: ~0.5 % (m+m- events) ~0.8 % (e+e- events) ~0.5 % (qq events) • Charged track multiplicity  6 • Etot > 8 GeV , pTmissing > 0.4 GeV •  > 0.5 o • etc.

16. Quark flavor separation Classification using neural network • 19 input variables: • P and Pt of the most energetic muon • Sum of the impact parameters • Sphericity , Invariant mass for different jets • 3 output variables: • Probability for uds quarks • Probability for c quarks • Probability for b quarks MC c MC uds MC b Real data

17. _ The line shape is the cross section s(s) e+e- ff with √s values arround MZ Can be observed for one fermion or several together (i.e. all the quarks) e+ e+ g(s) Z(s) e- e- Z0 line shape f f _ _ (s)-(s) f f Z(s)-Z(s)

18. gVf = I3f - 2 Qf sin2qW gAf = I3f Resonance term (Breit – Wigner) With unpolarized beams we must consider the mean value of the 4 different helicity The expected line shape from the theory is a Breit-Wigner function characterized by 3 parameters: Mass (MZ) – Width (Z) – Peak cross section (0) ( I  QeQf ) ( terms proportional to ( mf / Mz )2 have been neglected ) Branching ratios f / Z are related to Qf and I3f

19. We can take the values of the parameters reported in the PDG and calculate the expected value of the partial widths f gVf = I3f - 2 Qf sin2qW gAf = I3f  3 families  3 families  2 families  3 families

20. sBorn(s) s0 s(s) experimental cross section Branching ratios s(s) e+e- hadrons e- e+

21. Z*, g g g Z*, g Radiative corrections The radiative corrections modify the expected values at the tree level: QEDcorrections Initial state radiation correction: (1) Initial state radiation (QED ISR) G(s’,s) = function of the initial state radiation 1-z = k2/s fraction of the photon’s momentum • Relevant impact: • decreases the peak cross section of ~30% • shift √s of the peak of ~100 MeV (2) Final state radiation (QED FSR) ~ 0.17 %

22. f g g g g (3) Interference between initial state radiation and final state radiation (4) Propagator correction (vacuum polarization) + n loop

23. f Z/g Z/g EW corrections (1) Propagator corrections + n loop Photon exchange

24. Z*, g W/Z/g/f Z*, g g (2) Vertex corrections Contributions from virtual top terms Z*, g W/Z/g/f ~ 1 + 0.9 % QCD corrections (1) Final state radiations (QCD FSR)

25. Line shape QED ISR QED Interference IS-IF Breit-Wigner modified by EW loops Interference EW- QED Photon exchange QED FSR QCD FSR EW vertex MZ Z 0

26. Ezio Torassa MZ Z 0h , 0e , 0 , 0 MZ Z Geh , GeGe , GeG , GeG PDG 2010

27. Ezio Torassa Number of neutrino families We can suppose to have a 4th generation family with all the new fermions heavier than the Z mass (except the new neutrino) . How to check this hypothesis ? The number of the neutrino families can be added in the fit. The result is compatible only with N=3 Ginv = GZ –Ghad - 3Glept - 3Gn We can also extract the width for new physics (emerging from Z decay): GZ ,Ghad , Glept can be measured Gn can be estimated from the SM The result is compatible with zero or very small widths.

28. Gamma-gamma interactions The gamma-gamma interactions produce two leptons with small energy (Wgg << Ebeam) and small angles, most of them are not detected. At the Z0 peak the gamma-gamma cross section is about 150 nb. After the selection (pT , Df cuts) is reduced to a non resonant 6 nb background.

29. Residual dependence from the model • QED was assumed for the ISR function H(s,s’) and the interference IF-FS function (s,s’) • QEWD was assumed for the interference QED-EW function sgZ(s) • QCD was assumed for the QCD FSR correction With the cross section measurements at higher energies (s= 130-200 GeV), the interference term can estimate from the data.

30. LEP2 LEP luminosities From 1990 to 1994 about 170 pb-1

31. s  Center of mass energy after the initial state radiation Relevant ISR contributions (radiative return to the Z0 peak) Searches beyond the Standard Model have more sensitivity to the non radiative events: s /s > 0.85 ff(g) production at LEP2 qq(g) WW ZZ

32. Jet Jet Identification of ISR photon and s´ estimation (SPRIME) Search of ISR candidates: Sarch of signal inside calorimeters, luminometer included, with Eg>10 GeV (not associated to charged tracks) None ISR photon detected Jet 1 and Jet 2 reconstruction Photon inside the beam pipe hypothesys Energy and momentum conservation: R z ISR photons are emitted at low angle, they mainly induce polar angle unbalance (R unbalance is neglected)

33. One ISR photon detected If the photon is coplanar with the two jets ( Sa > 345o ) his direction is used. Considering the low resolution of the calorimeters the energy momentum balance is used to estimate the energy of the photon otherwise a second undetected photon inside the beam pipe is considered. ISR photon spectrum s = 130 GeV The photon emission at the energy of s – 91 GeV increases because the process is traced back to the Z0 (cross section peak).

34. 2/NDoF =160/180 for the mediated ff data at LEPII

35. Test at 5% precision ZZ production at LEP2 sZZ(s)

36. e+ W+ n e- W - Produdction of W+W- bosons and Mw a LEP II MZ e sin2W measured at LEPI  MW meas. useful for more stringent constraints . W+ W+ Z* g + + rad.corr. + W - W - ZWW vertices are expected as a consequence of the non abelian structure of the SU(2)L×U(1)Ygauge theory Cancellations expected from the gauge theory have been verified with 1 %. of precision For the sWW measurement the main backgrounds are: - gg interactions - Z*, g* decays

37. Hadronic decays The characterisctic is the reconstruction of 4 jets. Sometime also two fermions from a Z decays can produce 4 jets due to gluon emission but radiative jets have small angle and energy. Variable D can discriminate this background. - Semileptonic decays The characteristic is the reconstruction of 2 jets and one energetic and isolated lepton. Total leptonic decays The characteristic is the reconstruction of 2 energetic and isolated leptons with opposite charge. The example in figure shows only two tracks but the lepton can also be the t. One discriminant variable is the direction of the missing momentum (ff background has small q angles)

38. MW a LEP II • MW can be considered a derived parameter from GF . The relation has two components: the tree level and the radiative corrections (Dr). • The radiative corrections are dependent from mt ed MH. • The precise measurement of the W mass is important to verify the SM theory and • to provide limits for the top and Higgs masses. At the beginning of LEP II direct • measurement of mt at Tevatron (18012 GeV) still had large errors. • The W mass can be obtained: • from the sWW(MW) trend having a rapid variation close to the threshold (s~160 GeV) • through the invariant mass reconstruction

39. W+ e+ W+ W+ Z* g n e- W - W - W - Determination of the mass from sWW Diagrams CC03 The 4 decay modes in the table have been considered. Corrections to the CC03 diagrams due to othe contributions 1996 data at 161 GeV L = 10 pb -1 With only 29 selected events the obtained measurement is: DELPHI

40. Direct reconstruction of the W mass Per s > 2 Mwi is possibile to reconstruct directly the invariant mass. The reconstruction can be obtained in the hadronic decay and in semileptonic decay. In the semileptonic decay the momentun and the center of mass energery constraints are used. DELPHI Dati 1998 a 189 GeV L = 150 pb -1

41. FSI: Final State Interaction The distance decay between the two W is fraction of fm In the hadronic decay channel the interatcion between partons in the final state are relevant FSI

42. LEP II combined result Contribution to the statistical and systematic errors The FSI reduces the hadronic channel weight with respect to the semileptonic channel

43. Measurements since 1989 DMW/MW 5.2 10-4 DMZ/MZ 2.3 10-5

44. Discrepancy observed in 1995 not confirmed after more precise Rb measurements

45. EWK physics at LHC LEP 170 pb-1 at the Z0 peak se+e-~ 3 104 pb → 5 M Z0 / experiment LHC 25 fb-1 spp~ 3 104 pb → 750 M Z0 / experiment W Z WW WZ ZZ

46. Quarks & Leptons – Francis Halzen / Alan D. Martin – Wiley International Edition The Experimental Foundation of Particle Physics – Robert N. Cahn / Gerson Goldhaber Cambridge University Press Determination of Z resonance parameters and coupling from its hadronic and leptonic decays - Nucl. Physics B 367 (1991) 511-574 Z Physics at LEP I CERN 89-08 Vol 1 – Radiative corrections (p. 7) Z Line Shape (p. 89) Measurement of the lineshape of the Z and determination of electroweak parameters from its hadronic decays - Nuclear Physics B 417 (1994) 3-57 Measurement and interpretation of the W-pair cross-section in e+e- interaction at 161 GeV Phys. Lett. B 397 (1997) 158-170 Measurement of the mass and width of the W boson in e+e- collision at s =189 GeV Phys. Lett. B 511 (2001) 159-177 http://www.pd.infn.it/~torassa/dottorato/2014/