Transcript Prezentacja programu PowerPoint

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
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
Strategy of the test.
Minimal Standard Model (MSM) describes
W
electroweak interactions of quarks (q), leptons
(l) and Higgs boson(s) (h) by exchange of
first step: build LEP1 (SLC) collider at

m  0
W
M W  81 GeV
Z0
M Z  92 GeV
s  90GeV
(with possible electron beam
polarization at SLAC)
second step: increase the energy to s  160 GeV
and
(LEP only)
•Study W and Z production
•Check model internal consistency
•Look for Higgs boson(s) and
supersymetric particles
Input parameters of Minimal Standard Model (MSM)

-electromagnetic fine structure constant
GF
-Fermi constant- determines charged current strength
MZ
- Z0 boson mass, measured at LEP with high precision
 s M Z2  - strong coupling constant at
q 2  M Z2
(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 measurements tree level is not sufficient and radiative corrections are required.
This brings into the game more parameters:
mf
- fermion masses (mt)
mH
- Higgs boson mass
Radiative corrections
Pure QED corrections factorize from electroweak part
QED:
Electroweak part:
Vacuum polarization
Vertex correction
+ ..........
This leads to improved Born approximation;
the improved amplitude for the process e e  Z 0  f
has same form as Born amplitude for this process
but with effective coupling constants:
_
f
 g s  g s   g s  g s 


Ve
Ae
5
5
Vf
Af
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.
LEP and detectors
Large Electron Positon collider
• 27 km circumference
• peak luminosity L=2.*1031cm-2s-1 (design value 1.6*1031)
• 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.
LEP I running at Z0 peak
 
_
e e  Z  qq
0
quark and antiquark fragment
into two separete jets
LEP II running at s  205GeV
 


_
_
e e W W  q q q q
four jets in the final state
SLAC Linear Collider
SLC, the first linear e+e- 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. 150μm*5μm)
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)
X-section formula at Z0 peak:

s
_
s    ds' H s, s' s'
f f
calculated from SM, not fitted
H(s,s’)-radiative function
_
4 m 2f
sZ2
_
 s    peak 
_
f f

peak
_
f f

1

 _
f f 1 
QED

0
Z

 12 e  f
1

2
 M 2 2
3
Q
f
Z
Z

1
Fit performed to the hadron data:

2
s
s  M    M
2
Z
 
"   Z ""  "
Z



2
AFB
4
_
e e  qq
MZ, ΓZ, σ0had, Rl
and to the lepton data:
 Γe, Γμ, Γτ,
 
_
e e ll
or (lepton universality) Γlept
Rl 
had
NF  NB

NF  NB
lept
Values of Mz,Гz,Гμ,Гτ,Гe,Rl,... extracted with use of SM elements
Observables  Pseudo-observables
ADLO results (with lepton universality)
M Z  91.1875 0.0021GeV
Z  2.4952 0.0023GeV

0
had
N
 41.540 0.037 nb

R  20.767 0.025
0
l
0 ,l
AFB
 0.0171 0.0010
0
l

0
 had
Rl0
 s
l
sin 2 eff
SM expresion for Z
4m 2f 
Z   0 1  2  gVf
mZ 
f
2
 2m 2f
1  2

mZ


  g Af


2
 4m 2f
1  2

mZ


f
 * 1   QED   QCD


0  N
f
C
2G mZ3
12
The number of light neutrino families
Z  had  3lept  inv
inv 
Z


 Rl  3
 lept lept
N 
inv


0
depends strongly on  had
N
  
 12Rl


N 
  0
 
 lept  SM   had M Z


  Rl  3

N  2.9841 0.0083
Predicted cross-section for
two, three and four (massless)
neutrino species with SM couplings
Z0 decays to heavy quarks (charm and beauty)
_
• two (or more) jets are formed in e e  Z  q q process,
following the quark fragmentation into hadrons.
• in the final state we observe hadrons, not quarks. How to select
_
_
Z0 decays into particular flavour b b, c c, .....?
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.
0
mb  5 GeV mc  1.5 GeV
b  c

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%)
Most precise – double tag method
Pseudo-observables:
Most recent values:

Rb  b
had
usually requires very good
Monte-Carlo program
1996
c
Rc 
had
Rb  0.21638 0.00066
Rc  0.1720 0.0030
EPS Aachen 2003
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)
_
ee  Z 0  f f
 F ,R   B,R   F ,L   B,L  R   L

forward (F) – e- beam direction.
 F ,R   B,R   F ,L   B,L
 tot
R (L) means right (left) handed

  F ,L   B,R   B,L
   B fermions in final state
AFB  F , R
 F
 tot
 tot

  B,L   F ,L   B,R
FB
Apol
 F ,R
 tot
Apol 
For polarized electron beam (SLC):
ALR 
ALRFB
1 l  r
P
 tot
1

P

F ,l
  F , r    B ,l   B , r 
l r
r(l) means right (left) handed
electron beam polarization.
<P> - mean beam polarization
At the Z0 pole:
Af
0
Apol
  Af
A
0
AFB
0
LR
A
3
  Ae
4
3
 Ae A f
4
 Ae
FB , 0
pol
0
LRFB
A
3
 Af
4
asymmetry parameter for
fermion f
gVf
Af  2

gVf
g Af
g Af
g

1   Vf

g
Af


2
When the couplings conform
to the SM structure:
 1 4 Q f sin 2 efff
Studies of asymmetry parameters provide very sensitive measurement
of the sin 2 efff ,particulary good for f  lepton
Particulary cute- ALR at SLAC
e
precise, direct measurement of Ae with hadron events  sin 2 eff
0 ,b
0,c
Another precise measurements: AFB
, AFB
EPS, Aachen 2003
combined
LEP Ab  0.898 0.021
SLC Ab  0.925 0.020  Ab  0.903 0.013
Standard Model
vs.
0.935
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 sin 2 efflept
Direct W mass and width measurement.
From CDF and D0 experiments at 1 Tev
proton antiproton collider at Fermilab:
MW  80.454 0.059
From direct measurements at LEP 2:
•
cross section for process
at the treshold (161 GeV)
MW  80.40  0.22 GeV
_
• study of decay channels:WW  q q l or
important corrections coming from:
• Bose-Einstein correlations
• color reconnection
LEP 2 result:
_
_
WW  q q q q
MW  80.412 0.042GeV W  2.150 0.091GeV
Very good agreement between electron and hadron
colliders!
Combined result: MW  80.426 0.034GeV W  2.139 0.069GeV
But
NuTeV experiment measures sin 2 W
from the ratio of the
_
neutral to charged current interactions in  and  beams:
sin W  1 
2
M W2
M
2
Z
 0.2277 0.0016
Using MZ from LEP I

MW  80.136 0.084 GeV
This indirect measurement differs more then 3σ from direct one !
Standard Model Higgs Search
The production (and decay) of Higgs particle is predicted in the SM
as a function of its (unknown) mass.

main production channel

ZH decay channels
_
_
H  b b, Z  q q
_
For mH=115 GeV
_
H  b b, Z   
_
Background:
WW,ZZ,2f
_
BR( H  b b)  74%
_
H  b b, Z  l l
_
H   , Z  b b
b-tagging plays essential role in Higgs search!
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:
_
Z 0 Z 0 , W W  , q q
Selection of Higgs candidate events: on the Monte-Carlo basis
• topology
• btag
Does the data sample contains signal and background or only
background ?
• for each candidate i introduce the likelihoods Q  LS  B mH 
i
LB mH 
ratio:
• Qi is estimated from topology combined with
mass information.
• MC determines expected Qi distributions
• the global likelihood:
s and s+b equally likely for
 2 lnQ  2 lnQi   c
i
-2ln(Q)=0
ADLO result by M.Duehrssen, EPS, Aachen 2003
green and yellow bands
indicate 1σ and 2σ limits
of backround only hypotesis.
Conclusion from further
statistical analysis:
mH<114.4 GeV
is excluded @ 95% CL
The Global Fit
Fit of the five Standard Model parameters to all available
electroweak results.
( 5)
M Z2 ,  s M Z2 , M Z , mt , mH  log10  mH GeV 
   had


 s  
 0
( 5)
s 
1   l s    t s    had
with  0  1
137.0359997650
Runing coupling constant
5 
s  -from dispersion integral
 had
and low energy e+e- data.
The purpose of the fit
• check internal consistency of the Standard Model
• constrain the Higgs mass
Some fit results already presented:

mt vs. MW
lept
sin 2 eff
0,l
0,b
0,c
If in the global fit replace 6 parameters AFB
, AFB
, AFB
, Al P , Al SLD, sin 2 effl (Qhad
fb )
lept
with sin 2 eff
value fitted to the above parameters
then for global fit  2  15/ 10 d.o. f -probability=13%
sin 2 W N 
-very precise measurement at low <Q2>~20 GeV2
3 σ from Standard Model prediction !
Removing sin 2 W N  from fit changes χ2 probability (to 28%) but
does not influence SM parameters values much.
2
lept
Global EW fit with average sin eff
2
sin
W N 
and without

 2  6.4 9 d .o. f  70% prob.
OK. for global fit but sin 2 W N  problem remains...
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