XXIX Ph.D in Physics Ezio TorassaPadova, April 28th 2014 Lesson #1 Measurement of the Z e W bosons properties Standard Model

XXIX Ph.D in Physics Ezio TorassaPadova, April 28th 2014 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

XXIX Ph.D in Physics Ezio TorassaPadova, April 28th 2014 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”

XXIX Ph.D in Physics Ezio TorassaPadova, April 28th 2014 Luminosity definition and measurement Integrated luminosity Efficiency (trigger + reconstruction +selection) [cm -2 sec -1 ]

XXIX Ph.D in Physics Ezio TorassaPadova, April 28th 2014 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)

XXIX Ph.D in Physics Ezio TorassaPadova, April 28th 2014 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)

XXIX Ph.D in Physics Ezio TorassaPadova, April 28th 2014 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

XXIX Ph.D in Physics Ezio TorassaPadova, April 28th 2014 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

XXIX Ph.D in Physics Ezio TorassaPadova, April 28th 2014 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

XXIX Ph.D in Physics Ezio TorassaPadova, April 28th 2014  =(  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

XXIX Ph.D in Physics Ezio TorassaPadova, April 28th 2014 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

XXIX Ph.D in Physics Ezio TorassaPadova, April 28th 2014  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:

XXIX Ph.D in Physics Ezio TorassaPadova, April 28th 2014 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)

XXIX Ph.D in Physics Ezio TorassaPadova, April 28th 2014 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

XXIX Ph.D in Physics Ezio TorassaPadova, April 28th 2014 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)

XXIX Ph.D in Physics Ezio TorassaPadova, April 28th 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

XXIX Ph.D in Physics Ezio TorassaPadova, April 28th 2014   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 __

XXIX Ph.D in Physics Ezio TorassaPadova, April 28th 2014 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

XXIX Ph.D in Physics Ezio TorassaPadova, April 28th 2014 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

XXIX Ph.D in Physics Ezio TorassaPadova, April 28th 2014  (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

XXIX Ph.D in Physics Ezio TorassaPadova, April 28th 2014 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 %

XXIX Ph.D in Physics Ezio TorassaPadova, April 28th 2014 (4) Propagator correction (vacuum polarization)   f + n loop   (3) Interference between initial state radiation and final state radiation

XXIX Ph.D in Physics Ezio TorassaPadova, April 28th 2014 EW corrections  Z/  f + n loop (1) Propagator corrections Photon exchange

XXIX Ph.D in Physics Ezio TorassaPadova, April 28th 2014 QCD corrections (1) Final state radiations (QCD FSR) (2) Vertex corrections W/  f Z*,  Contributions from virtual top terms Z*,  g W/  f ~ %

XXIX Ph.D in Physics Ezio TorassaPadova, April 28th 2014 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

XXIX Ph.D in Physics Ezio TorassaPadova, April 28th 2014 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

XXIX Ph.D in Physics Ezio TorassaPadova, April 28th 2014 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 ?

XXIX Ph.D in Physics Ezio TorassaPadova, April 28th 2014 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.

XXIX Ph.D in Physics Ezio TorassaPadova, April 28th 2014 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

XXIX Ph.D in Physics Ezio TorassaPadova, April 28th 2014 LEP luminosities LEP2 From 1990 to 1994 about 170 pb -1

XXIX Ph.D in Physics Ezio TorassaPadova, April 28th 2014 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

XXIX Ph.D in Physics Ezio TorassaPadova, April 28th 2014 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

XXIX Ph.D in Physics Ezio TorassaPadova, April 28th 2014 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).

XXIX Ph.D in Physics Ezio TorassaPadova, April 28th 2014  2 /N DoF =160/180 for the mediated ff data at LEPII

XXIX Ph.D in Physics Ezio TorassaPadova, April 28th 2014 ZZ production at LEP2  ZZ (  s) Test at 5% precision

XXIX Ph.D in Physics Ezio TorassaPadova, April 28th 2014 Produdction of W + W - bosons and M w a LEP II M Z e sin 2  W measured at LEPI  M W meas. useful for more stringent constraints. W+ W - e+ e-  W+ W - + Z* W+ W rad.corr. ZWW vertices are expected as a consequence of the non abelian structure of the SU(2) L ×U(1) Y gauge theory For the  WW measurement the main backgrounds are: -  interactions - Z*,  * decays Cancellations expected from the gauge theory have been verified with 1 %. of precision

XXIX Ph.D in Physics Ezio TorassaPadova, April 28th 2014 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  One discriminant variable is the direction of the missing momentum (ff background has small  angles)

XXIX Ph.D in Physics Ezio TorassaPadova, April 28th 2014 M W a LEP II M W can be considered a derived parameter from G F. The relation has two components: the tree level and the radiative corrections (  r). The radiative corrections are dependent from m t ed M H. 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 m t at Tevatron (180  12 GeV) still had large errors. The W mass can be obtained: from the  WW (M W ) trend having a rapid variation close to the threshold (  s ~160 GeV) through the invariant mass reconstruction

XXIX Ph.D in Physics Ezio TorassaPadova, April 28th 2014 Determination of the mass from  WW W+ W - e+ e-  W+ W - Z* W+ W - Diagrams CC03 The 4 decay modes in the table have been considered data at 161 GeV L = 10 pb -1 WW decay modeCorr (CC03) qqqq e qq  (  ) qq l DELPHI Corrections to the CC03 diagrams due to othe contributions With only 29 selected events the obtained measurement is:

XXIX Ph.D in Physics Ezio TorassaPadova, April 28th 2014 Direct reconstruction of the W mass Per  s > 2 M wi 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

XXIX Ph.D in Physics Ezio TorassaPadova, April 28th 2014 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

XXIX Ph.D in Physics Ezio TorassaPadova, April 28th 2014 The FSI reduces the hadronic channel weight with respect to the semileptonic channel LEP II combined result Contribution to the statistical and systematic errors

XXIX Ph.D in Physics Ezio TorassaPadova, April 28th 2014  M Z /M Z   M W /M W  Measurements since 1989

XXIX Ph.D in Physics Ezio TorassaPadova, April 28th 2014 Discrepancy observed in 1995 not confirmed after more precise R b measurements

XXIX Ph.D in Physics Ezio TorassaPadova, April 28th 2014 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 W Z WW WZ ZZ

XXIX Ph.D in Physics Ezio TorassaPadova, April 28th 2014 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)