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Precision tests of electroweak interactions-
What we have learned from LEP and SLC?
Krzysztof Doroba, Warsaw University DELPHI
Collaboration
XXVIII Mazurian Lakes Conference on Physics,
Aug 31 Sep 7 2003
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Outline of the talk

• Strategy of the Standard Model tests
• Radiative corrections
• LEP/SLC and detectors
• Z0 line shape
• Z0 decays to heavy quarks
• Asymmetries at the Z0 pole
• Direct W mass measurement
• Direct Higgs search
• Global fit
• Conclusions from the tests

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Historical introduction

• 1968 Standard Model by Glashow, Salam and
  Weinberg
• unification of electromagnetic and
  weak interactions,
• existance of the weak neutral
  current predicted.
• 1973 Neutral Currents discovered (Gargamelle
  experiment)
• to avoid flavour changing neutral
  currents GIM mechanizm
• requires existance of fourth
  quark (charm)
• 1974 Charm quark discovered (Richter/Ting)
• Do the Z and W bozons realy exist
  with mass around 90 GeV?
• Constuction of at
  CERN.
• 1982 - Discovery of W and Z bosons at CERN
• (C.Rubia, UA1 and UA2 experiments)
• As the SM is renormalizable (tHooft and Veltman
  1971)
• it possible to perform precise test of the model.
• Let us build ee- colliders LEP at CERN and SLC
  at SLAC

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Strategy of the test.
Minimal Standard Model (MSM) describes
electroweak interactions of quarks (q), leptons
(l) and Higgs boson(s) (h) by exchange of
W
first step build LEP1 (SLC) collider at
(with possible electron beam polarization at SLAC)
second step increase the energy to
(LEP only)

• Study W and Z production
• Check model internal consistency
• Look for Higgs boson(s) and
• supersymetric particles

and
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Input parameters of Minimal Standard Model (MSM)
-electromagnetic fine structure constant
-Fermi constant- determines charged current
strength
- Z0 boson mass, measured at LEP with high
precision
- strong coupling constant at
(for quarks in final state)
above parameters are sufficient to perform MSM
calculations on the tree level. However due to
high precision of the LEP/SLC measure- ments tree
level is not sufficient and radiative corrections
are required. This brings into the game more
parameters
- fermion masses (mt)
- Higgs boson mass
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Observables
Each observable
measured at LEP/SLC,
we express as a function of Standard Model
parameters
,

• With these parameters we perform fitting
  procedure, asking ourself
• does the same set of parameters describes
  different observables?
• do the values obtained in the fit agree with
  those known from
• direct measurements?

The global fit quality is the probe of the Model
internal consistency!
w
Where from we know the values of the parameters ?
-from muon lifetime
-from Hall effect
-from CDF and D0 experiments
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Radiative corrections
Pure QED corrections factorize from electroweak
part
QED
..........
Electroweak part
Vacuum polarization
Vertex correction
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Particular example of vertex corrections
Contribution from this two
Influence of electroweak corrections on final
result

• on Born level relation between Weinberg angle

and
W and Z masses
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• after corrections due to vacuum polarization

effective mixing angle

• after (flavour dependent) vertex corrections

Flavour dependent effective mixing angle and ?
parameter.
Effective coupling constants
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This leads to improved Born approximation the
improved amplitude for the process
has same form as Born amplitude for
this process but with effective coupling
constants

• The electroweak corrections dependence is
• quadratic on top quark mass
• logarithmic on Higgs boson mass

For electroweak corrections two loop level is
achieved today for most of the processes.
Numerical calculations are performed using the
programmes TOPAZ0 and ZFITTER.
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LEP and detectors

• Large Electron Positon collider
• 27 km circumference
• peak luminosity L2.1031cm-2s-1 (design value
  1.61031)
• maximum energy 208 GeV
• beam energy known with precision of about 2 MeV
  (at Z0 peak)

• To operate LEP special LEP standard model took
  into account
• earth tides generated by moon and sun
• rainfalls in Jura
• Lake Geneva water level
• leakage currents from trains

Four experiments have been operating at LEP
(ALEPH, DELPHI,L3 and OPAL). At Z0 peak ADLO
collected about 17 M events.
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J.Weniger, LEP fest 2000
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LEP I running at Z0 peak
quark and antiquark fragment into two separete
jets
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LEP II running at
four jets in the final state
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SLAC Linear Collider

• SLC, the first linear ee- collider ever
• operated with good luminosity and polarization
  from 1992 till 1998
• had worse then LEP beam energy resolution
• run only at Z0 peak (600 k events)
• But...
• its electron beam was longitudinally polarized
• its beam spot was much smaller (1.5µm.7µm vs.
  150µm5µm)

The designs of LEP and SLC detectors are quite
similar.
But,

• for example, due to
• lower repetition rate
• smaller beam spot

Slac Linear Detector (SLD) had better vertex
reconstructiom (CCD vs. micro-strip)
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The Z0 line shape
At an experiment we measure cross section
where Ni, Nibk number of the events and
background for channel i
w
ei- detector efficiency
L luminosity, known from the measurement of the
well known QED process - Bhabha scattering.
Measurement is done at small angles ( approx.
25-60 mrad)
Typical experimental errors on ?L are below 1
per-mil
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X-section formula at Z0 peak
calculated from SM, not fitted
H(s,s)-radiative function
Fit performed to the hadron data
MZ, GZ, s0had, Rl
and to the lepton data
Ge, Gµ, Gt, or (lepton universality) Glept
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Values of Mz,?z,?µ,?t,?e,Rl,... extracted with
use of SM elements Observables ?
Pseudo-observables
ADLO results (with lepton universality)
SM expresion for
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The number of light neutrino families
depends strongly on
Predicted cross-section for two, three and four
(massless) neutrino species with SM couplings
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Z0 decays to heavy quarks (charm and beauty)

• two (or more) jets are formed in

process,
following the quark fragmentation into hadrons.

• in the final state we observe hadrons, not
  quarks. How to select
• Z0 decays into particular flavour

Flavour tagging

• jet (initial quark) direction is
• established from thrust axis.

• heavy flavours tagged by leptons
• (high p,pT), lifetime, secondary
• vertex mass,....

Works well for b and c quarks. thanks to vertex
detectors
b hadron on average travels 3 mm, position of the
secondary vertex is measured with accuracy of
300 µm.
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secondary vertex mass and/or high p, pT allows
to distinguish between b anc c hadrons.
Different methods use different tags combinations
to establish flavour of the initial (heavy)
quark .

• For tagged sample one has to know
• purity (up to 96)
• efficiency (up to 26)

usually requires very good Monte-Carlo program
Most precise double tag method
Pseudo-observables
Most recent values
EPS Aachen 2003
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Asymmetries at Z0 pole
Z0 couplings to right-handed and left-handed
fermions are different.
for
even for unpolarized e beams Z0 is polarized
along beam direction (LEP)
forward (F) e- beam direction. R (L) means
right (left) handed fermions in final state
For polarized electron beam (SLC)
r(l) means right (left) handed electron beam
polarization. ltPgt - mean beam polarization
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asymmetry parameter for fermion f
At the Z0 pole
When the couplings conform to the SM structure
Studies of asymmetry parameters provide very
sensitive measurement of the
,particulary good for
Particulary cute- ALR at SLAC
precise, direct measurement of Ae with hadron
events
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Another precise measurements
EPS, Aachen 2003
combined
Standard Model
LEP SLC
vs.
LEP and SLAC measurements of Ab are consistent.
But the combined Ab value seems to disagree
with SM prediction.
LEP Ab (and Ac ) result can be expresed in
terms of
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Direct W mass and width measurement.
From CDF and D0 experiments at 1 Tev proton
antiproton collider at Fermilab
From direct measurements at LEP 2
cross section for process at the treshold (161
GeV)

• study of decay channels

or

• important corrections coming from
• Bose-Einstein correlations
• color reconnection

LEP 2 result
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Very good agreement between electron and
hadron colliders!
Combined result
But
NuTeV experiment measures
from the ratio of the
neutral to charged current interactions in
and
beams
Using MZ from LEP I
This indirect measurement differs more then 3s
from direct one !
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Standard Model Higgs Search
The production (and decay) of Higgs particle is
predicted in the SM as a function of its
(unknown) mass.
Background WW,ZZ,2f
main production channel
ZH decay channels
For mH115 GeV
b-tagging plays essential role in Higgs search!
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At LEP I serches in fully hadronic channels
excluded by background
LEP I serches in other channels - negative
At LEP II main sources of background in Higgs
search

• Selection of Higgs candidate events on the
  Monte-Carlo basis
• topology
• btag

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Does the data sample contains signal and
background or only background ?

• for each candidate i introduce the likelihoods
• ratio
• Qi is estimated from topology combined with
• mass information.
• MC determines expected Qi distributions
• the global likelihood

s and sb equally likely for -2ln(Q)0
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ADLO result by M.Duehrssen, EPS, Aachen 2003
green and yellow bands indicate 1s and 2s
limits of backround only hypotesis.
Conclusion from further statistical
analysis mHlt114.4 GeV is excluded _at_ 95 CL
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The Global Fit
Fit of the five Standard Model parameters to all
available electroweak results.
Runing coupling constant
-from dispersion integral and low energy ee-
data.

• The purpose of the fit
• check internal consistency of the Standard Model
• constrain the Higgs mass

Some fit results already presented
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If in the global fit replace 6 parameters
with
value fitted to the above parameters
then for global fit
-probability13
-very precise measurement at low ltQ2gt20 GeV2
3 s from Standard Model prediction !
Removing
from fit changes ?2 probability (to 28) but
does not influence SM parameters values much.
Global EW fit with average
and without
problem remains...
OK. for global fit but
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Conclusions from the tests

• this talk is ,by all means, not exhaustive.
  Supersymmetry,
• Grand Unification, Multi doublet Higgs Models,
  MSSM, TGC,...
• were left behind.

• precision (above tree level) predictions of the
  Standard Model
• have been compared with experimental results
  from LEP and
• SLC.
• Standard Model looks fine after that comparison.
  SM is a well
• established (effective) theory.
• no need for New Physics.
• where is (if at all) the Higgs boson(s)?
• further measurements of MW, mt, (mH? .....) will
  make tests
• more stringent and perhaps will show the road
  to New Physics.
• Tools Tevatron (Run II) .........
• Large Hadron Collider (2007)
• Next Linear Collider

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