Electroweak tests of the Standard Model IDPASC school LHC Physics Lesson #1 Electroweak tests of the 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.

Standard Model LQEWD = Lgauge + Lfermioni + LHiggs + LYukawa 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

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

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

Historical measurements: electron charge W Weinberg angle Fermi constant 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: UA1 pp √s = 540GeV (1993) MW = 82.4±1.1 GeV MZ = 93.1±1.8 GeV Before the W and Z discovery we had strong mass constraints: sin2W  0.23 ( error  10 % ) MW  80 GeV MZ  92 GeV

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

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 Nch Fraction of √s 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

 e+e-  Z0  +- e+e-  Z0  +- 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)  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.

Classification using neural network 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 uds MC c MC b Real data

Z0 line shape (s)-(s) Z(s)-Z(s) 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) _ g(s) e+ e- f Z(s) e+ e- f _ _ (s)-(s) f f Z(s)-Z(s)

Mass (MZ) – Width (Z) – Peak cross section (0) 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) Resonance term (Breit – Wigner) ( I  QeQf ) ( terms proportional to ( mf / Mz )2 have been neglected ) gVf = I3f - 2 Qf sin2qW gAf = I3f Branching ratios f / Z are related to Qf and I3f

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

e+ e- Branching ratios s(s) e+e-  hadrons sBorn(s) s0 Process ff / Z (%) B.R. exp. (%) Neutrinos 20.54 20.00±0.06 Leptons 10.33 10.10±0.02 Hadrons 69.13 69.91±0.06 Branching ratios s(s) e+e-  hadrons sBorn(s) s(s) experimental cross section s0 e+ e-

Radiative corrections The radiative corrections modify the expected values at the tree level: QED corrections Initial state radiation correction: (1) Initial state radiation (QED ISR) G(s’,s) = function of the initial state radiation Z*, g g 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) Z*, g g ~ 0.17 %

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

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

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

Line shape MZ Z 0 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

MZ Z 0h , 0e , 0 , 0 MZ Z Geh , GeGe , GeG , GeG PDG 2010 Padova 4 Aprile 2011 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. Padova 4 Aprile 2011 Ezio Torassa

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.

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

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

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

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

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

sin2W 0.95 0.70 0.15 0.23 0.24 0.25 Ad Au Ae 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

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  Forward Backward e+ e- Jet The charge asymmetry is one alterative method where the final state selection is not required Jet e-  e+ Jet hemisphere forward backward hemisphere

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)

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)

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

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) –Afbb 2.9 

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 s0

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

Fit with Line shape and AFB

MZ , GZ , s0h , Re , Rm , Rt , AFB0,e , AFB0,m , AFB0,t 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

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)

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

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. t rest frame t- p- n t direction in the laboratory 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

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

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

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

Cross section for unpolarized beam 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: new new

Asymmetry results at SLD Af with 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

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

Discrepancy observed in 1995 not confirmed after more precise Rb measurements

Quarks & Leptons – Francis Halzen / Alan D 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

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)