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XXVIII Ph.D in Physics Ezio TorassaPadova, April 22th 2013 Lesson #1 Measurement of the Z e W bosons properties Standard Model.

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Presentazione sul tema: "XXVIII Ph.D in Physics Ezio TorassaPadova, April 22th 2013 Lesson #1 Measurement of the Z e W bosons properties Standard Model."— Transcript della presentazione:

1 XXVIII Ph.D in Physics Ezio TorassaPadova, April 22th 2013 Lesson #1 Measurement of the Z e W bosons properties Standard Model

2 XXVIII Ph.D in Physics Ezio TorassaPadova, April 22th 2013 in approssimazione di massa nulla per tutte le particelle di stato iniziale e finale (m  0, E  |p| )  p 1 = [E,p,0,0];  p 2 = [E,-p,0,0];  p 3 = [E, p cos ,p sin ,0];  p 4 = [E,-p cos ,-p sin ,0];  s= ( p 1 + p 2 ) 2 = ( p 3 + p 4 ) 2 = 4E 2 ;  t= ( p 1 - p 3 ) 2 = ( p 4 - p 2 ) 2 = - ½ s (1 - cos  );  u= ( p 1 - p 4 ) 2 = ( p 2 - p 3 ) 2 = - ½ s (1 + cos  );  s + t + u = m m m m 4 2  0 (2 variabili indipendenti). s,t,u – le variabili invarianti di Mandelstam e-e- b a e+e+ e-e- b a e+e+  Introduzione

3 XXVIII Ph.D in Physics Ezio TorassaPadova, April 22th 2013 e+e+ ++ e-e-  -- canale “ s ” e+e+ e+e+  e+e+ e+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). Canale “s” e canale “t”

4 XXVIII Ph.D in Physics Ezio TorassaPadova, April 22th 2013 Luminosity definition and measurement Integrated luminosity Efficiency (trigger + reconstruction +selection) [cm -2 sec -1 ]

5 XXVIII Ph.D in Physics Ezio TorassaPadova, April 22th 2013 Based on low angle Bhabha scattering event counting e- e+e+ e+e+  e-e- e + e -  e + e - Dominated by the photon exchange “t cannel”:  (deg) Region used by the luminometer:  1-10 deg e+e+ e-e-  “s channel”  e+e+ e-e- Luminosity measurement LEP Bhabha Homi Jehangir, indian theoretica physicist (Bombay 1909 – monte Bianco 1966)

6 XXVIII Ph.D in Physics Ezio TorassaPadova, April 22th 2013 e+e+ e-e-  t)   s) e+e+ e-e-  (s)-  (t)  (t)-  (t)  (s)-  (s) Z(s)-  (s) Z(s)-  (t) Z(t)-  (s) Z(t)-  (t) Z(s)-Z(s) Z(s)-Z(t) Z(t)-Z(t)  Z(s) e+e+ e-e- e+e+ e-e- Z  t) (non polarized emectrons)

7 XXVIII Ph.D in Physics Ezio TorassaPadova, April 22th 2013 Coasting beams with crossing angle  and beam currents x y x z y o  Luminosity (rate) insensitive to offsets in x and z, but sensitive to offsets in y:  See S. Van der Meer, ISR-PO/68-31, June 18 th, 1968  Now the trick: scan the offset while measuring the rate, over the whole non-zero range, then integrate the result: Rate vs offset, taken from Potter in Yellow report CERN v1 Van der Meer scan

8 XXVIII Ph.D in Physics Ezio TorassaPadova, April 22th 2013 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) QE W D (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. Standard Model

9 XXVIII Ph.D in Physics Ezio TorassaPadova, April 22th 2013 Standard Model The QE W D Lagrangian (cfr. Halzen, Martin, “Quarks & leptons”, cap ): L QE W D = L gauge + L fermioni + L Higgs + L Yukawa => Fermions – Vector bosons interaction term L fermioni = L lept + L quark => Fermions – Scalar boson interaction term

10 XXVIII Ph.D in Physics Ezio TorassaPadova, April 22th 2013  =(  1,  2,  3 ) : Pauli matrixes g g’ a b v = |  GiGi Parameters of the model 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

11 XXVIII Ph.D in Physics Ezio TorassaPadova, April 22th 2013 Small oscillation around the vacuum. For we neglect terms at order > 2 nd After the symmetry breaking : 2 complex Higgs fields 1 real Higgs field - 3 DOF 4 massless vector bosons 1 massless + 3 massive vector bosons + 3 DOF

12 XXVIII Ph.D in Physics Ezio TorassaPadova, April 22th 2013  W Weinberg angle g g’ v  e Millikan experiment (ionized oil drops) G F  lifetime  W Gargamelle (1973) asymmetry from scattering electron charge Fermi constant sin 2  W  0.23 ( error  10 % ) M W  80 GeV M Z  92 GeV UA1 pp √s = 540GeV (1993) M W = 82.4±1.1 GeV M Z = 93.1±1.8 GeV Before the W and Z discovery we had strong mass constraints: Historical measurements: The mass of the vector bosons are related to the parameters:

13 XXVIII Ph.D in Physics Ezio TorassaPadova, April 22th 2013 The Z° boson can decay in the following 5 channels with different probabilities:  p=0,20 (invisible) e - e + p=0,0337 p v = 0,0421 Z°  -  + p=0,0337 p v = 0,0421  -  + p=0,0337 p v = 0,0421 q  q p=0,699 p v = 0,8738 The differences can be partially explained with the different number of quantum states:  includes the 3 different flavors: e, ,   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 m t >M Z ) “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 Z 0 boson decay (channels and branching ratios)

14 XXVIII Ph.D in Physics Ezio TorassaPadova, April 22th 2013 Z 0 boson decay (selection criteria) e + e -  Z 0  e + e - Efficiency  96 % Contamination  0.3 % (  +  - events) e + e -  Z 0  hadrons Charged track multiplicity  3 E 1 ECAL > 30 GeV E 2 ECAL > 25 GeV  < 10 o Efficiency  98 % Contamination  1.0 % (  +  - events) Nucl. Physics B 367 (1991) events (hadronic and leptonic) collected between August August 1990 N ch Fraction of √s a) Charged track multiplicity  5 b) Energy of the event > 12 %  s

15 XXVIII Ph.D in Physics Ezio TorassaPadova, April 22th 2013 e + e -  Z 0   +  - e + e -  Z 0   +  - Charged track multiplicity  6 E tot > 8 GeV, p T missing > 0.4 GeV  > 0.5 o etc. Charged track multiplicity = 2 p  1 e p  2 > 15 GeV IP Z < 4.5 cm, IP R < 1.5 cm  < 10 o Association tracker- muon detector E HCAL < 10 GeV (consistent with MIP) E ECAL < 1 GeV (consistent with MIP)  Efficiency  99 % Contamination: ~1.9 % (  +  - events) ~1.5 % (cosmic rays) Efficiency  70 % Contamination: ~0.5 % (  +  - events) ~0.8 % (e + e - events) ~0.5 % (qq events)

16 XXVIII Ph.D in Physics Ezio TorassaPadova, April 22th input variables: P and P t 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 Quark flavor separation Classification using neural network MC uds MC c MC bReal data

17 XXVIII Ph.D in Physics Ezio TorassaPadova, April 22th 2013   s) e+e+ e-e-  (s)-  (s)  Z(s) e+e+ e-e- Z(s)-Z(s) Z 0 line shape The line shape is the cross section  (s) e + e -  ff with √s values arround M Z Can be observed for one fermion or several together (i.e. all the quarks) _ f f f f __

18 XXVIII Ph.D in Physics Ezio TorassaPadova, April 22th 2013 g Vf = I 3f - 2 Q f sin 2  W g Af = I 3f Resonance term (Breit – Wigner) ( I  Q e Q f ) ( terms proportional to ( m f / M z ) 2 have been neglected ) The expected line shape from the theory is a Breit-Wigner function characterized by 3 parameters: Mass (M Z ) – Width (  Z ) – Peak cross section (  0 ) With unpolarized beams we must consider the mean value of the 4 different helicity Branching ratios  f /  Z are related to Q f and I 3f

19 XXVIII Ph.D in Physics Ezio TorassaPadova, April 22th 2013 We can take the values of the parameters reported in the PDG and calculate the expected value of the partial widths  f  3 families  2 families g Vf = I 3f - 2 Q f sin 2  W g Af = I 3f  3 families

20 XXVIII Ph.D in Physics Ezio TorassaPadova, April 22th 2013  (s) e + e -  hadrons  Born (s)  (s) experimental cross section 00 Branching ratios e+e+ e-e- Process  ff /  Z (%) B.R. exp. (%) Neutrinos ±0.06 Leptons ±0.02 Hadrons ±0.06

21 XXVIII Ph.D in Physics Ezio TorassaPadova, April 22th 2013 Radiative corrections The radiative corrections modify the expected values at the tree level: Z*,   Relevant impact: decreases the peak cross section of ~30% shift √s of the peak of ~100 MeV QED corrections 1-z = k 2 /s fraction of the photon’s momentum (1) Initial state radiation (QED ISR) (2) Final state radiation (QED FSR) Z*,   G(s’,s) = function of the initial state radiation Initial state radiation correction: ~ 0.17 %

22 XXVIII Ph.D in Physics Ezio TorassaPadova, April 22th 2013 (4) Propagator correction (vacuum polarization)   f + n loop   (3) Interference between initial state radiation and final state radiation

23 XXVIII Ph.D in Physics Ezio TorassaPadova, April 22th 2013 EW corrections  Z/  f + n loop (1) Propagator corrections Photon exchange

24 XXVIII Ph.D in Physics Ezio TorassaPadova, April 22th 2013 QCD corrections (1) Final state radiations (QCD FSR) (2) Vertex corrections W/  f Z*,  Contributions from virtual top terms Z*,  g W/  f ~ %

25 XXVIII Ph.D in Physics Ezio TorassaPadova, April 22th 2013 Line shape Interference EW- QED M Z  Z  0 QED ISRQED Interference IS-IF Photon exchange QED FSRQCD FSR EW vertex Breit-Wigner modified by EW loops

26 XXVIII Ph.D in Physics Ezio TorassaPadova, April 22th 2013 Padova 4 Aprile 2011 Ezio Torassa M Z  Z  0 h,  0 e,  0 ,  0  M Z  Z  e  h,  e  e,  e  ,  e   PDG 2010

27 XXVIII Ph.D in Physics Ezio TorassaPadova, April 22th 2013 Padova 4 Aprile 2011 Ezio Torassa  inv =  Z –  had - 3  lept - 3  The number of the neutrino families can be added in the fit. The result is compatible only with N=3 We can also extract the width for new physics (emerging from Z decay):  Z,  had,  lept can be measured   can be estimated from the SM The result is compatible with zero or very small widths. Number of neutrino families We can suppose to have a 4 th generation family with all the new fermions heavier than the Z mass (except the new neutrino). How to check this hypothesis ?

28 XXVIII Ph.D in Physics Ezio TorassaPadova, April 22th 2013 Gamma-gamma interactions The gamma-gamma interactions produce two leptons with small energy (W  << E beam ) and small angles, most of them are not detected. At the Z 0 peak the gamma-gamma cross section is about 150 nb. After the selection (p T,  cuts) is reduced to a non resonant 6 nb background.

29 XXVIII Ph.D in Physics Ezio TorassaPadova, April 22th 2013 QED was assumed for the ISR function H(s,s’) and the interference IF-FS function  (s,s’) QE W D was assumed for the interference QED-EW function   Z (s) QCD was assumed for the QCD FSR correction With the cross section measurements at higher energies (  s= GeV), the interference term can estimate from the data. Residual dependence from the model

30 XXVIII Ph.D in Physics Ezio TorassaPadova, April 22th 2013 LEP luminosities LEP2 From 1990 to 1994 about 170 pb -1

31 XXVIII Ph.D in Physics Ezio TorassaPadova, April 22th 2013 qq(  ) WW ZZ  s Center of mass energy after the initial state radiation Relevant ISR contributions (radiative return to the Z 0 peak) Searches beyond the Standard Model have more sensitivity to the non radiative events:  s /s > 0.85 ff(  ) production at LEP2

32 XXVIII Ph.D in Physics Ezio TorassaPadova, April 22th 2013 Jet Identification of ISR photon and  s´ estimation (SPRIME) Search of ISR candidates: Sarch of signal inside calorimeters, luminometer included, with E  >10 GeV (not associated to charged tracks) Jet 1 and Jet 2 reconstruction Photon inside the beam pipe hypothesys Energy and momentum conservation: None ISR photon detected ISR photons are emitted at low angle, they mainly induce polar angle unbalance (R  unbalance is neglected) R z

33 XXVIII Ph.D in Physics Ezio TorassaPadova, April 22th 2013 One ISR photon detected If the photon is coplanar with the two jets (  > 345 o ) 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 Z 0 (cross section peak).

34 XXVIII Ph.D in Physics Ezio TorassaPadova, April 22th 2013  2 /N DoF =160/180 for the mediated ff data at LEPII

35 XXVIII Ph.D in Physics Ezio TorassaPadova, April 22th 2013 ZZ production at LEP2  ZZ (  s) Test at 5% precision

36 XXVIII Ph.D in Physics Ezio TorassaPadova, April 22th 2013 Produzione dei bosoni W + W - e misura di M w a LEP II M Z e sin 2  W misurati a LEPI  M W permette la definizione di vincoli piu’ stringenti. W+ W - e+ e-  W+ W - + Z* W+ W rad.corr. I vertici ZWW previsti come conseguenza della strutta non abeliana della teoria di gauge SU(2) L ×U(1) Y esistono Per ricavare  WW occorre distinguere il segnale WW dal fondo: ff(  ) ff(gg) - Le cancellazioni previste dalla teoria di gauge sono state verificate al livello dell’ 1 %. -

37 XXVIII Ph.D in Physics Ezio TorassaPadova, April 22th 2013 Decadimenti adronici La caratteristica è la ricostruzione di 4 jets. Talvolta anche gli eventi ff possono fornire 4 jets. I jets dovuti a radiazione di gluoni sono caratterizzati da un piccolo angolo e da una bassa energia. La variabile D è in grado di discriminare permettendo la riduzione del fondo: - Decadimenti semileptonici La caratteristica è la ricostruzione di 2 jets ed un leptone energetico ed isolato. Decadimenti totalmente leptonici La caratteristicha è la ricostruzione di 2 leptoni energetici isolati di carica opposta. L’esempio in figura riporta solo 2 tracce cariche ma il leptone puo’ anche essere un  Una variabile discriminante è la direzione del momento mancante che per il fondo ff ha piccoli angoli 

38 XXVIII Ph.D in Physics Ezio TorassaPadova, April 22th 2013 M W a LEP II M W si può considerare una grandezza derivata da G F, il cui valore è conosciuto con precisione. La relazione è semplice a livello (  r=0) mentre con le correzioni di polarizzazione del vuoto risulta dipendente da m t ed M H. Una precisa misura della massa del W permette una ulteriore verifica del modello ed allo stesso tempo fornisce dei limiti per le masse del top e dell’Higgs. All’inizio di LEP II le misure dirette di m t al Tevatron (180  12 GeV) avevano ancora errori piuttosto grandi. La massa del W può essere ottenuta: dall’andamento  WW (M W ) che in prossimità della soglia  s ~160 GeV varia rapidamente mediante la ricostruzione della massa invariante.

39 XXVIII Ph.D in Physics Ezio TorassaPadova, April 22th 2013 Determinazione della massa da  WW W+ W - e+ e-  W+ W - Z* W+ W - Diagrammi CC03 Lo stato finale in 4 fermioni, oltre ai contributi dei diagrammi CC03, può ricevere contributi da altri diagrammi elettrodeboli. Tali contributi sono stati considerati con dei termini di correzione della sezione d’urto (v. Tabella). La sezione d’urto così corretta è stata confrontata con l’andamento previsto in funzione della massa M W Dati 1996 a 161 GeV L = 10 pb -1 WW decay modeCorr (CC03) qqqq e qq  (  ) qq l l DELPHI Contributi, interferenza inclusa, di altri diagrammi che generano 4 fermioni mediante il coinvolgimento di 0,1 o 2 bosoni vettori massivi Vengono selezionati 29 eventi ( ) da cu si ricava:

40 XXVIII Ph.D in Physics Ezio TorassaPadova, April 22th 2013 Ricostruzione diretta della massa Per  s > 2 M W è possibile ricostruire direttamente la massa dai decadimenti. La ricostruzione ottenuta solo con le tracce osservate non ha una sufficiente risoluzione. Applicando dei vincoli quali la conservazione dell’energia e dell’impulso del centro di massa la risoluzione migliora significativamente. La ricostruzione si effettua solo per i decadimenti adronici e semileptonici, per quelli totalmente leptonici non si dispone di sufficienti vincoli (rispetto ai semileptonici manca l’asse del jet che determina la direzione del W opposto). DELPHI Dati 1998 a 189 GeV L = 150 pb -1

41 XXVIII Ph.D in Physics Ezio TorassaPadova, April 22th 2013 FSI: Final State Interaction I due W decadono a distanze di frazioni di fm nel caso adronico contribuiscono le interazioni dei partoni nello stato finale FSI

42 XXVIII Ph.D in Physics Ezio TorassaPadova, April 22th 2013 L’FSI riduce il peso del canale adronico rispetto al canale semileptonico Risultato combinato LEP II Contributi agli errori statistici e sistematici

43 XXVIII Ph.D in Physics Ezio TorassaPadova, April 22th 2013  M Z /M Z   M W /M W  Measurements since 1989

44 XXVIII Ph.D in Physics Ezio TorassaPadova, April 22th 2013 Discrepancy observed in 1995 not confirmed after more precise R b measurements

45 XXVIII Ph.D in Physics Ezio TorassaPadova, April 22th 2013 EWK physics at LHC LEP 170 pb -1 at the Z 0 peak  e+e-  ~ pb → 5 M Z 0 / experiment LHC 25 fb-1  pp  ~ pb → 750 M Z 0 / experiment

46 XXVIII Ph.D in Physics Ezio TorassaPadova, April 22th 2013 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) Z Physics at LEP I CERN 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) Measurement of the mass and width of the W boson in e + e - collision at  s =189 GeV Phys. Lett. B 511 (2001)


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