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

Precision tests of electroweak interactions-

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.

WMinimal Standard Model (MSM) describes electroweak interactions of quarks (q), leptons (l) and Higgs boson(s) (h) by exchange of GeVMZ

GeVMW

m

Z

W

92

81

0

0

first step: build LEP1 (SLC) collider at GeVs 90

(with possible electron beampolarization at SLAC)

second step: increase the energy to GeVs 160 (LEP only)

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

and

Input parameters of Minimal Standard Model (MSM)

-electromagnetic fine structure constant

FG -Fermi constant- determines charged current strength

ZM - Z0 boson mass, measured at LEP with high precision

above parameters are sufficient to perform MSM calculations on thetree 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:

fm - fermion masses (mt)

Hm - Higgs boson mass

2Zs M - strong coupling constant at 22

ZMq (for quarks in final state)

Radiative corrections

Pure QED corrections factorize from electroweak part

+ ..........

Electroweak part:

Vacuum polarization

Vertex correction

QED:

This leads to improved Born approximation; the improved amplitude for the process has same form as Born amplitude for this processbut with effective coupling constants:

_0 ffZee

55

sgsgsgsg AfVfAeVe

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 programmesTOPAZ0 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,L3and OPAL). At Z0 peak ADLO collected about 17 M events.

LEP I running at Z0 peak

_0 qqZee

quark and antiquark fragment into two separete jets

LEP II running at GeVs 205

__

qqqqWWee

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.

Slac Linear Detector (SLD) had better vertex reconstructiom(CCD vs. micro-strip)

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

But,

s

mff

f

sssHdss2

_

4

_

'','

""""2

2

2

2_

_

Z

Ms

Ms

ss

Z

ZZ

Zpeak

ff

calculated from SM, not fittedX-section formula at Z0 peak:

H(s,s’)-radiative function

43

1

112

1

1222

0__

fZ

fe

ZQEDff

peak

ff QM

Fit performed to the hadron data:

MZ, ΓZ, σ0had, Rl

and to the lepton data:

Γe, Γμ, Γτ, or (lepton universality) Γlept

lept

hadlR

_

qqee

_

llee

BF

BFFB NN

NNA

ADLO results (with lepton universality)

0010.00171.0

025.0767.20

037.0540.41

0023.04952.2

0021.01875.91

,0

0

0

lFB

l

had

Z

Z

A

R

nb

GeV

GeVM

Values of Mz,Гz,Гμ,Гτ,Гe,Rl,... extracted with use of SM elementsObservables Pseudo-observables

N

sl

hadl R

0

00

leff2sin

fQCDQED

f Z

fAf

Z

fVf

Z

fZ m

mg

m

mg

m

m

1*

41

21

41

2

22

2

22

2

2

0

12

2 3

0Zf

C

mGN

SM expresion for Z

The number of light neutrino families

3

3

llept

Z

lept

inv

invlepthadZ

R

312

0

lZhad

l

SMlept

RM

RN

depends strongly on 0had

invN

N

0083.09841.2 N

Predicted cross-section fortwo, three and four (massless)neutrino species with SM couplings

Z0 decays to heavy quarks (charm and beauty)

• two (or more) jets are formed in_

0 qqZee process,following the quark fragmentation into hadrons.

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

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

__

ccbb

Flavour tagging:

• 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.

Different methods use different tags combinations to establish flavour of the initial (heavy) quark .

cb

cb GeVmGeVm

5.15 secondary vertex mass and/or high p, pT allows

to distinguish between b anc c hadrons.

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 1996

Pseudo-observables:

had

bbR

had

ccR

Most recent values: 00066.021638.0 bR

0030.01720.0 cREPS Aachen 2003

Asymmetries at Z0 pole

Z0 couplings to right-handed and left-handed fermions are different.

for_

0 ffZee 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):

tot

RBLFLBRFFBpol

tot

BF

tot

LBRBLFRFFB

tot

LR

LBLFRBRF

LBLFRBRFpol

A

A

A

,,,,

,,,,

,,,,

,,,,

rl

rBlBrFlFLRFB

tot

rlLR

PA

PA

,,,,1

1r(l) means right (left) handed electron beam polarization.<P> - mean beam polarization

At the Z0 pole:

fLRFB

eLR

feFB

eFBpol

fpol

AA

AA

AAA

AA

AA

4

3

4

34

3

0

0

0

0,

0

asymmetry parameter forfermion f

fA

2

1

2

Af

Vf

Af

Vf

f

gg

gg

A

When the couplings conform to the SM structure:

fefff

Af

Vf Qg

g2sin41

Studies of asymmetry parameters provide very sensitive measurementof the f

eff2sin ,particulary good for leptonf

Particulary cute- ALR at SLAC

precise, direct measurement of Ae with hadron events eeff2sin

Another precise measurements: cFB

bFB AA ,0,0 ,

LEPSLC

021.0898.0 bA

020.0925.0 bA

combined

013.0903.0 bA vs. 935.0

Standard Model

EPS, Aachen 2003

LEP and SLAC measurementsof 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

lepteff2sin

Direct W mass and width measurement.

From CDF and D0 experiments at 1 Tevproton antiproton collider at Fermilab:

059.0454.80 WM

From direct measurements at LEP 2:

• GeVMW 22.040.80

• study of decay channels:

lqqWW_

or__

qqqqWW

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

LEP 2 result: GeVGeVM WW 091.0150.2042.0412.80

cross section for processat the treshold (161 GeV)

Very good agreement between electron and hadroncolliders!

Combined result: GeVGeVM WW 069.0139.2034.0426.80

But

NuTeV experiment measures from the ratio of the

neutral to charged current interactions in and_

beams:

W2sin

0016.02277.01sin 2

22

Z

WW M

M

Using MZ from LEP I GeVMW 084.0136.80

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 SMas a function of its (unknown) mass.

For mH=115 GeV

%74)(_

bbHBR

Background:WW,ZZ,2f

main production channel

ZH decay channels

_

__

__

__

,

,

,

,

bbZH

llZbbH

ZbbH

qqZbbH

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:

_00 ,, qqWWZZ

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

HB

HBSi mL

mLQ

Does the data sample contains signal and background or onlybackground ?

• 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:

cQQi

i ln2ln2

s and s+b equally likely for-2ln(Q)=0

ADLO result by M.Duehrssen, EPS, Aachen 2003

Conclusion from furtherstatistical analysis:mH<114.4 GeVis excluded @ 95% CL

green and yellow bands indicate 1σ and 2σ limitsof backround only hypotesis.

The Global Fit

Fit of the five Standard Model parameters to all available electroweak results.

GeVmmmMMM H

HtZZsZhad 1022)5( log,,,,

Some fit results already presented:

Wt Mvsm .

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

5076999035.13710

1

0)5(

with

ssss

hadtl

Runing coupling constant shad5 -from dispersion integral

and low energy e+e- data.

If in the global fit replace 6 parameters )(sin,,,,, 2,0,0,0 hadfb

leffll

cFB

bFB

lFB QSLDAPAAAA

with lepteff2sin

then for global fit fod ..10/152 -probability=13%

value fitted to the above parameters

3 σ from Standard Model prediction !

-very precise measurement at low <Q2>~20 GeV2

Removing NW 2sin from fit changes χ2 probability (to 28%) but

does not influence SM parameters values much.

Global EW fit with average

lepteff2sin

lepteff2sin

and without

NW 2sin

.%70..94.62 probfod

OK. for global fit but

NW 2sin

NW 2sin problem remains...

Conclusions from the tests

• 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

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