Precision electroweak physics at LEP

I ~ g l l I l~J mgl|'kql [ 1 1 gt

PROCEEDINGS SUPPLEMENTS

Nuclear Physics B (Proc. Suppl.) 37B (1994) 3-22 North-Holland

Precision E l e c t r o w e a k P h y s i c s at L E P A. Blondel a * ~L.P.N.H.E. Ecole Polytechnique, 91128 Palaiseau France Progress in precision measttcements of electroweak observables at LEP continues steadily. The highlights of 1993 are: a new scan of the Z Iineshape with precise beam energy determination lead to a measurement of the Z width with 1.5 I0 -s precision; first results on absolute cross-sections with high precision luminosity monitors; high efficiency btagging with mlcro-vertex detectors leading to I% measurements of the Z --+ bb partial width, and to forward-backwaxd b asymmetry with jet charge. All other electrowesk measurements benefit from improved statistics. The basic symmetries of the Standard Model (SM) are verified, and electroweak radiative effects axe now measvLted with a precision of a few 10 -3. The results axe compared with other precision electroweak meastttements from SLC, neutrino scattering, and the p~ colllders. The consequences of the recent evidence for the top quark are drawn out. Precision data begin to set significant limits on the I-Iiggs Boson mass, and on alternative extensions to the Standard Model.

1. I n t r o d u c t i o n LEP performance has improved steadily since 1989. The typical integrated luminosity recorded by the experiments has been: 1.2 pb -1 in 1989, 7. pb -1 in 1990, 13. pb -1 in 1991, 23. pb -1 in 1992, 35. pb -1 in 1993. It is hoped to reach 50. pb -1 in 1994. The luminosity improvement is a product of several factors: i) overall efficiency, now as .high as 60%; ii) increase in 1992 of the number of bunches per beam from 4 to 8 with the "Pretzel" scheme; iii) better alignment, monitoring and tuning procedures allowing now a high b e a m - b e a m tune shift of 0.04; iv) the luminosity life time, now well in excess of 10 hours. Present records (01/08/94) are a peak luminosity of 2 103t/cm2/s, (above design!), and integrated daily luminosity of .93 p b - 1 / d a y . Finally, the precise determination of the beam energy by resonant depolarization is essential for accurate measurement of the Z mass and width (see below). D a t a were recorded by the four L E P experiments with efficiencies around 90%, at center-of-mass energies around the Z pole. Scanning of the Z line shape took place in 1989, 90, 91 and 93, d a t a were taken only at the peak of the resonance in 1992 and 94. No d a t a has been recorded above 95 GeV center-of-mass energy. The cross-sections decreasing very quickly, a very large step in energy is required to make this operation worthwhile. This should happen sometime in 1996, when the W pair threshold is in reach with the addition of a large number (over 200) superconducting R F cavities. The results given here are based on the 1989-1993 d a t a presented at the 1994 Glasgow conference a total of 8 million visible Z decays, table 1, and include preliminary numbers. *Mailing Address: CERN, PPE division 1994 - Elsevier Science B.V.

SSDI 0920-5632(94)00607-5

II A I D I L I O tLEPI ~q:

'90-'91 '92 '93 prel. total t + / - : '90-'91 '92 '93 prel. total

451 680 653 1784 55 82 79 216

356 697 677 1730 37 69 71 177

423 677 658 1758 40 58 62 160

454 733 653 1840 58 88 81 227

1684 2787 2641 7112 190 297 293 780

Table 1

LEP experiments statistics in units of 10 z events used for the analysis of the Z line shape and lepton forward-backward asymmetries.

2. A s y n o p s i s o f t h e m e a s u r e d

quantities

The building blocks of electroweak physics at the Z are measured cross-sections for various final states, forward-backward and polarization asymmetries. Assuming that Z and photon exchange are the only processes t h a t occur, they can all be expressed in terms of the chi~al couplings, or, more commonly, the vector and axial-vector couplings. In the SM:

gvl

=

(gL1+gRl)=I~l-2Q1sin20w

(1)

gAj

=

(g~1

(2)

-

gRl) = -r~i.

The Z --* f f partial width is given by: P] :

~x Mz (gLy~ + g~12). 6sin 2 0wcos 2 0w

(3)

The total width is the sum over all open channels. Within very good limits, only the fermions of the first three generations, with the exception of the top quark, contribute to the cross-section.

4

A. Blondel/Precision Electroweak Physics at LEP

Around the Z pole, the photon exchange is only a correction to the Z-channel which dominates the cross-section, and can the be written as: ~rl _-- 127r(hc) 2

sF~F! (s - M2) 2 +

r~ "

(4)

.2~_

One can easily see that forward-backward asymmetries or polarization asymmetries are sensitive the following asymmetry of couplings: - t l -=

gls - 91I ¥ -

29v 9 i + 9L

For unpolarized asymmetry is:

beams the forward-backward

A ( ~ _~ 3 ~.~i.

(6)

For the tau lepton, the polarization of the final state fermion is measurable, as a function of polar angle. For unpolarized beams: 2coaO

~(~os0)

_~

.A~ + l+coj2 0 2.o~0

A

.,4

(7)

A_

1 + l+co,~O..~r

from which one can derive both M.~ and .A~. Interesting observables are obtainable ff longitudinal beam polarization is available. The Left-Right asymmetry of Z production [1,2] ~ L

ALR --

-

--

O'R

-

~L

~

+ ~a

~,

(8)

-

+

4

t.(9)

is the polarization of the e+e - system. The values of Neutral Current couplings and their sensitivity to sin ~ 0~eft are given in table 2.

f // e-

d

• The running of the QED coupling constant fromq2=0toq2 =MS ' • The isospin-breaking loop corrections to the W and Z propagators. They are absorbed conveniently in the p parameter, p -- 1 + Ap. • The running of the Z and W self-energies, absorbed in the parameters &aQ and A r ew. • The Z --* bb vertex correction.

The forward-backward polarized asymmetry [3]: =

2.1. A s t r a t e g y o f t e s t s a n d r a d i a t i v e effects One can organize the measurements at LEP in two broad classes: i) the measurements providing tests of the SU(2)L × U(1) gauge structure, and ii) the measurements which probe electroweak radiative effects. The main consequence ofSU(2)L X U(1) invariance is Universality: the couplings of all particles with the same quantum numbers are the same. This is best tested with leptons. Also, the chiral couplings of the g to the fermion f obey the formula of equation 2. After correcting for radiative effects, the same value of sin 2 0w should match all measured couplings. Besides QED radiative effects (emission of real or virtual photons) which are conceptually straightforward, LEP observables are sensitive to electroweak (propagator or vertex) radiative effects. Electroweak corrections are sensitive to heavy, yet undiscovered, particles, such as the top quark or the Higgs boson, in an inclusive way. There are four [4-9] main radiative effects at the Z pole, plus one when including the W mass:

Isf

Qs

9at

1/2 -1/2 1/2 -1/2

0 -1 2/3 -1/3

1/2 -1/2 1/2 -1/2

O.4I

gvt 1/2 -0.04

A!

o~,~ o~,,

1 0.16

0 -7.9

0.19

0.69

-3.5

-0.35

0.94

-0.6

Table 2 Numerical va/ues of quantum numbers, Neutral Current couplings, chiral coupling asymmetry ,41 and sensitivity o f ~$ for the four types o f fermions. The ra/ue o f sin 2 0~fr is 0.23.

The propagator corrections modify equation 2 by an overall scaling factor p and a global change of sin28w, in an universal way. Non-universal corrections are small and - with the notable exception of the Z - * bb vertex - insensitive ~ to heavy physics. Furthermore, all asymmetries with unpolarized beams and the most precise asymmetry with polarized beams are proportional to the electron coupling .A,, while the sensitivity to sin s 0w of hadronic asymmetries is contained in the A , term (see table 2). It is therefore convenient to express all asymmetry measurements at LEP in terms of the effective weak m i ~ n g angle [10] defined as: sin s

1 - gga~ w ) e~$ = ~(1

(10)

where the ratio ~ is extracted from pole asymmetries. This defimtion absorbs vertex corrections for leptons, but not for quarks. See [5,6,11] for various avatars of the concept: This sin 2 0~ff and the MS definition [12] s i n ~ O~_~(q2) are very dose [9,13]. The relations between the observables, the Fermi constant GF and the QED running constant

A. Blondel /Precision Electroweak Physics at LEP

Quantity

Main Technologies

5

Physics Outputs

Relative Precision

line shape Mz

Absolute energy scale relative cross-sections line shape fit (QED rad. corr.)

input

5.10 - s

Fz

Relative energy scale relative cross-sections line shape fit (QED ra~i. corr.)

Ap

1.5 10 - a

peak,O

N~.~

Absolute cross-sections

O'had

3. 10 - s

test SU(2)L × U(1) Rl ~

~h~d

lepton, haAron event selection

r~

Rb = rh~d rt

b-tagging

asymmetries

test universality f ( ~ . , sin ~ 0~~, 6,b)

4. 10 - a 2. 10 - a

~¢b

10 -2

" ~ 0w e~f sm

2. 10 - s

Table 3 Synopsis o f precision n e u t r a / c u r r e n t observables at the Z pole.

c~(M~) - I : 128.8 =k 0.1 [14] can be written in terms of these universal electroweak corrections Ap, A s q , A r ew and in terms of 6~b as [9,8,15,16]:

M~ =

~ro~(M~) J~G~(1 + Ap)(1 + a~q)sin ~ 0 ~ cos~ 0 ~ ' GFM 3

rL

24v%

rb

:

M~v

:

[1 + Ap] ]I + (gV____L_l)2](1 +

.

gAL ~

3 ::-~);

r~(l+6.b); lra(M~)

(11)

V~GF(1 - at--)(1 - .~,--~. Mz )" Table 3 summarizes the main observables, their physics output and the most critical technique involved. W i t h this specific choice I these observables axe ahnost uncorrelated, from b o t h points of view of statistical and systematic errors. 3. T h e Z l i n e s h a p e The measurements of cross-sections by the four LEP detectors are reported in [17-19,21]. 3.1. L u m i n o s i t y m e a s u r e m e n t The determination of luminosity is based on counting low angle Bhabha events e+e - ~ e+e - . Lu-

mlnosity monitors consist of two electromagnetic calorimeters, with good spatial resolution, positioned very accurately neax the beam pipe. Bhabha events appear as two back-to-back electromagnetic showers, carrying the full beam energy each, as shown on figure 2. A thorough discussion of the luminosity measurement can be found in the line-shape publications by the experiments, and in ref. [22-24]. For a minimum angle 0mi,~ of 29 mrad, the selected crosssection exceeds 100 nb. The statistical accuracy is better than 10 - a . The main experimental challenge comes from the 1/82mi,~ dependence of the selected Bhabha cross-section. An uncertainty on the inner radius R of the sensitive region of the luminosity calorimeter induces an error on the measured crosssection: A O'Bhabha --2× O'Bhabha

AR - R

For the typical value of R (5 cm) a precision well under 25 p m is requested to match the statistical accuracy. The LEP experiments have upgraded their luminosity monitors to provide high precision knowledge of the inner edge. The A L E P H Silicium calorimeter (SiCAL) [23] was operational from the

6

A. Blondel/Precision Electroweak Physics at LEP

D E L P H I (preliminary) 40 f (a)

~'

Hadrons

* 1990

/

.1992

• 1991

\

[

i 0

L ' ' I

87 Los

....

I,,

89

88

,,l,

,,+1.,.,1

90

91

....

92

I ....

93

I , ,~L~LJ~

94

• L

i|

95 96 VS (GeV)

1

(b)

b

,I

0"9587" ~

88

....

I ....

89

[ ....

90

I ....

91

I ....

92

I ....

93

II,

94

,,I

....

95

96

vs (GeV)

Figure 1. The D E L P H I hadronic cross-sections as a function o f center-of-mass energy. The square points show the considerable statistical improvement from the 1993 scan.

Figure 2. A luminosity event in the A L E P H SiCAL luminosity monitor. Left: front view (x-y): The showers o f the electron (side A) and positron (side B) are displayed on the same graph. The Silicinm pads are represented with dots o f size proportional to the energy collected. The ring shows the radial pad row at which the clusters are reconstructed. right: side view (r-z) o f the two showers, with the corresponding energy profiles.

i

middle of 1992 d a t a onwards. A SiCAL event is shown on figure 2. Sical is a silicon-tungsten sandwith with precision machined planes of silicon pads for energy readout. The fiducial cut 0,n=,~ is made on pad boundaxies, where the position resolution is optimum. The radius of the pad boundaries is known with a precision of better than 10 microns. The other experiments have made similar improvement to thei~ lvmlnosity measurement: OPAL with a detector similar to the ALEPH Sieal, operational in 1993, giving a precision of 0.07%!; L3 with a precision silicon tracker positioned in front of the BGO luminosity calorimeter, operational in 1993, obtains a 0.16% precision; DELPHI with a silieium telescope operational in 1993, and a lead/scintillator/silicium sandwich that should be operational in 1994. The breakdown of experimental systematic errors for the ALEPH, OPAL and L3 is shown in table 4. At low angles the Z contribution is less than 5.10 -4. The Z-~ interference vanishes at the Z pole, but can be as large as 6.10 - s off the pole, leading to a small correction that affects only the Z mass. Other low angle QED processes such as e+e - --~ ~f'f, are small (2 10 - s ) , and well calculable. The calculation of radiative corrections to the Bhabha scattering cross-section itself is made delicate by the interplay of experimental cuts with higher order pro-

Hadron Calorlmoter Barrel

Lumtnoe/ty ~ RB24

Active lead dngs

Figure 3. Side view of the L3 detector, showing the new low

angle s ~ c o n

l u l n i n o s i t y tracker (SLUM)

cesses, that are not simulated. No single event generator has a complete account of the corrections, so the estimate presently involves a combination of: i) event generation with BHLUMI [25] a multi-photon O ( a ) Monte-Carlo with exclusive exponentiation (many radiative photons are generated, assuming successive occurrence of the first-order process); ii) complete electroweak first-order QED calculations [26]; iii) estimate of higher order processes by leading-log and second order calculations [27,28]. The present estimate of the theoretical error is -4- 0.25% for a minimum angle of 25 mrad, larger than the experimental one. Hard work is taking place to reduce the error.

A. Blondel /Precision Electroweak Physics at LEP

[

~exp. O'ha d

c%

~rr

A(*) FB A(~) FB

]

ALEPH

DELPHI

7

]

L3

[

OPAL

'92

'93 prel.

'92

'93 prel.

'92

'93 prel.

'92

'93 prel.

o.15% 0.14% 0.4% 0.5% 0.3%

0.09% 0.14% 0.4% 0.5% 0.3%

0.38% 0.13% 0.59% 0.37% 0.63%

0.28% 0.13% 1.2% 0.5% 0.8%

0.5 % 0.15% 0.3 % 0.5% 0.7 %

0.16% 0.11-0.14% 0.25-0.76% 0.45-0.57% 0.54%

0.41% 0.20% 0.22% 0.19% 0.44%

0.07% 0.20% 0.35% 0.22% 0.51%

0.0029 0.001

0.0029 0.001

0.003

0.003

0.001

0.002

0.0005

0.0005

0.0017

0.002

0.002 0.002 0.003

0.005 0.001 0.004

0.002 0.001 0.002

0.002 0.001 0.002

Table 5 The experimental systematic errors for the analysis o f the Z//he shape and lepton forward-backward asymmetries. The errors quoted do not include the common uncertainties due to the LEP energy calibration and to the theoretical error on the Bhabha cross-section calculation. For L3 cross-sections the range o f errors corresponds to the different center-of-mass energies. For the treatment o f correlations between the errors for different years see [17-19,21].

source

Backgrounds Beam particles - "Physics" sources Trigger eft. Reconstruction Radial rid. cuts: - mech. precision - beam position - long. position - asymmetry cuts Shower param, and Energy cuts Acoplanarity cut Or: evt selection Simulation stat. TOTAL exp. error -

Syst. err. ( 1 0 - 4 ) ALEPH OPAL

L3

0.3

0.1

-

1.

.1

-

<0.01

.02 0.1

-

2.9 3.0 2.6

3.6 2.1 0.6 2.6

3.6 0.5

3.8 -

3.5

-

6.0 9.5

-

3.7 7.2

-

3.3 -

6.0 -

-

9.0 10. 15.6

Table 4 Systematic errors for the A L E P H Si-Cal, OPAL SiW and L3 Si-tracker+BGO luminosity measurement.

3.2. S e l e c t i o n o f h a d r o n i c a n d l e p t o n i c e v e n t s Decays of the Z into q~ pairs are not separately identified, but generically labelled as hadroCts. The selection efficiency is very large, typically 97% to 99%, and the resulting systematic errors rather small, see table 5. Energy dependent corrections come from the subtraction of the "two-photon" background, and from energy variation of the selection efficiency, leading to systematic errors of less than

1 MeV on the g width. Leptonie decays of the Z, e+e - --4 e+e - , e+e - --4 p + p - and e+e - --* 7"+r - , offer much simpler topologies than hadronic decays. They are however less frequent (1:20), and, since they have fewer tracks, are easier to miss. The experimental uncertainties are summarized in table 5. The e+e - mode is affected by t - c h a n n d Bhabha scattering process, which has to be subtracted. Complete higher order calculations are available [29], so the procedure introduces a negligible systematic error. 3.3. T h e b e a m e n e r g y The LEP data were taken in 1990-1991 at seven different center-of-mass energies interspaced by 1 GeV from 88.25 GeV to 94.25 GeV. In 1992 all data were taken at the Z pole. In 1993 a scan of the Z line shape was performed again at the energies of 89.4 91.2, 93 GeV. The 1993 energies were chosen i) to minimize the statistical error on l~z, ii) to obtain beam polarization that allows precise energy calibration by resonant depolarization for all three points [30]. Transverse spin Polarization builds up in a storage ring by the Sokolov-Ternov effect [31], and was observed in LEP for the first time in 1990 [32]. Resonant depolarization has been used previously in e+e machines, providing accurate measurements of the masses of the J/~b, ~b', T, T ' , at VEPP4 in Novosibirsk [33,34], at DORIS in Hamburg [35], at CESR in Cornel] [36]. It was first performed in LEP in 1991 [37].

8

A. Blondel/Precision Electroweak Physics at LEP

LEP TIDE EXPERIMENT

E [MeV] 44717

13_

i

44717.5

44718

44718.5

............. ~:.~ ................. ~+.:.iF:.

11Nov~r~ber19~

200

44719

:~.......

AE/E

•

(ppm)

- -

MEASUREMENTS

by resonant depolarization

T H E O R Y of t e n ' e s t r i a l t i d e s

100

e-

Cl

r 0.5 ~

0

t

-100

tJ o

+ -0.5

-200 101.48

101.481

101.482

101.483

101.484

, 4

//

Figure 4. Measurement of the width of the artificial depolarizing resonance, showing a width o f 200 KeV.

The spin precession frequency is determined as follows: a fast kicker generates a periodic perturbation to the beam (and its spin). If the perturbation is in resonance with the spin precession, one observes a sharp decrease or even reversal of the measured polarization. The spin tune L, is directly related to the beam energy by the anomalous magnetic moment a~ = g,-2 = 1.1596521884(43). 10 - s and the mass 2 m~ = 0.51099906(15) MeV of the electron: ge -- 2 Ebeara _ Ebeam . ~' : ae7 -- ~ me 0.4406486(1)

,,I

(12)

At the Z pole, v : 103.5. The intrinsic resolution of the method is better than 200 KeV [38], figure 4. However, energy measurements are delicate and performed only seldom, four times in 1991. In 1993, they were made more compatible with normal physics operation, and performed 25 times, roughly a third of physics fills. The extrapolation to the whole scan data requires tracing in time the properties of the magnets, current, field, temperature, as well as the geometrical properties of the ring. The analysis of the accumulated data is performed in collaboration by the accelerator physicists and members of the LEP collaborations within the LEP Energy working group [39]. The most spectacular source of energy variations comes from ground motion. Because of the strong focusing of LEP, these movements are amplified by a factor of nearly 10 4, SO that a small expansion

,,

I

,

8

,

,

I, 12

,

,1

, /6

,

,

I 20

,

,

,

I 24

Day time (hrs) Figure 5. Beam energy variations measured over 24 hours compared to the expectation from the tides.

by +10 -8 leads to a potential error on the Z mass and width of 10 MeV. Terrestrial tides [40] are one strong cause of such variations and were indeed observed [41], figure 5. All known sources of fluctuations being removed, the LEP energy calibrations of 1993 still show a full swing of more than 10 MeV of the beam energy. Careful investigations of the beam orbit measurements [42,43] show that the observed energy jumps are correlated with orbit movement, especially visible in september 1993 when a century record of rMnfall took place! The present knowledge of the beam energy leads to systematic errors of 4 MeV on the Z mass, and 3 MeV on the Z width, before correction with the orbit. It is hoped to reduce these errors to less than two MeV when the analysis of the measured orbits is complete. 3.4. F o r w a r d - b a c k w a r d a s y m m e t r i e s for Leptons The lepton forward-backward asymmetry "A(L) is ~FB a steep function of center-of-mass energy, as can be seen on figure 6. This leads to some sensitivity to initial state radiation and beam energy uncertainties, which induces a correlation with the Z mass. The lepton forward-backward asymmetry can also be used to constrain the Z-photon interference term. For these reasons, the line shape fit includes the leptonic forward-backward asymmetries. The initial state radiation effect is treated with

A. Blondel /Precision Electroweak Physics at LEP

0.6

I

'

~

•

I

'

I

a) e+e"

'

< 0.2

0.4

o

0.2

-0.2

I

'

I

'

I

9

'

.........,

0.025

/"

................................"*....

\

0

s °%"".... '°'°.. . M, ...

.,;~---.,-" "....

• "-....

-0.4 ,

88 i

~o.2

0.02

,

90 '

I

,

,

92 94 ~s (GeV) '

I

'

l

~

0.1

i

I

,

90

88 ,

i

I

,

I

92 g4 ~ s (GeV ,

i

,

0.015

~

",

i':o.os

0

e ".

i

0.01

0

eL,

j

i ::

...... e÷e_ ......... ~i~=:"

i"r

-0.2 0.00~,

-0.05

~20.7 ~

'

'20.8"

"

"20.9

-0.4

88

90

92 94 ~/s (GeV)

-OA

88

90

92

94

,~s (aeV)

Figure 6. The OPAL fitted forward-backward asymmetries for electron, muon, tau and inclusive lepton final states. The lines are the results o f a global fit to the//he shape and lepton asymmetries. great detail in [45], and implemented in fitting formulae, such as HIZA [47] and ZFITTEK [48], together with photon exchange terms. It is believed that the QED corrected Z pole asymmetry, of equation 6, can be extracted from the measured one with an accuracy of 0.0008 [45]. The uncertainty in the absolute energy scale of LEP does not affect the extracted asymmetry: it is only sensitive to the distance of the scan points from the Z peak, which is determined from those same s c a n points. However, a 10 MeV point-to-point error results in an uncertainty of 0.0008 on A (l) F B , fully correlated for the three lepton types. Because of the interference with the t-channel, the dependence of the e+e - asymmetry on beam energy is of opposite sign than for the other two leptons, figure 6. The effect is thus reduced in the average lepton asymmetry. $.5. R e s u l t s o n t h e Z Hne s h a p e O n c e the cross-sections, asymmetries and energies are determined, a fit is performed according to unfold the pure Z contribution, from the photon contribution and the initial state radiation. Two difl'erent fits are usually performed: First, a fit to verify lepton universality. This requires nine parameters: Mz, Fz, ~..p~k,0 had , R,, R~, P~, ~A(') F B , ~A0') -'FB, A(r) F B " The results of such fits can be found in table 6. and shown on figure 7. The accuracy of the test is 0.35%. Within this precision, the values of RL and A F(L) B for all leptons are consistent with each other,

"

' 21

v.,

Figure 7. One standard deviation contours (39~ probability) in the D . ( l ) plane. The S M prediction for Mz : 91.1895 GeV, Mt : 150 GeV, MH : 300 GeV, ~ , : 0.123 is shown as a dot. The arrows correspond to S M predictions for 50 < Mt(GeV) < 250, 60 < MH(GeV) < 1000 and as(M~) = 0.123 ± 0.006. The arrows point towards increasing Mr, MH and a , .

with a maximum discrepancy of two standard deviations for A ~ ; . The three leptonic widths give consistent values and support lepton universality. One can thus make this assumption and fit for one leptonic width Fz defined as the partial Z decay width into a pair of massless leptons, and one asymmetry A (l) F B " The result is shown in table 7. The correlations between these parameters, given in table 8, are small. The LEP averages are performed taking into account the common systematic errors: i) the beam energy errors; ii) a common error of 0.25% on absolute-cross sections from the theoretical uncertainty on O ' B h a b h a . iii) a common uncertainty of 0.0008 on lepton asymmetries due to the accuracy of the QED radiation. The agreement between experiments is acceptable, as shown by the values o f x s for 3 degrees of freedom given in table 7. One can extract from these numbers the values of Nv, so t h a t the line shape results for LEP can be summarized as: Mz

:

91.1895-4- 0.0017± 0.0040LSp

Fz

:

2.4969 ± 0.0027± 0.0027L~.p

Nv

:

2 . 9 8 8 ± 0.010±0.019th.

Rz

=

20.795± 0.040

(13)

This clearly is consistent with three species of light neutrinos (with mass smaller than Mz/2). An important derived parameter is the leptonic

10

A. Blondel/Precision Electroweak Physics at LEP

R~ R~ R~ FB X 10 4 A(,) A(F~ x 104 FB x 104 A(~)

ALEPH

DELPHI

20.674-0.13 20.91±0.14 20.69±0.12

20.964-0.16 20.60±0.12 20.64+0.16

212 ±53 189 ±38

207 +73 128 ±36

253 ±42

209:1:56

L3

OPAL

Average

X2i

20.904-0.13 20.85+0.10 20.914-0.13 over lepton s

20.864-0.07 20.82+0.06 20.75±0.07 20.795-4-0.040

3.0 1 4.5 :i 2.3 1.4

109 +81 132 +47

60 4-66 124 4-34

156 ±34 143 ±21

4.1 ' 2.0

299 173

193 4-43

230 ±26

2.1

170 4-16

8.0

20.944-0.13 20.93+0.14 20.704-0.17 average

average over leptons

Table 6 Lepton universality test, Rt and A(L) "'FB are extracted from the 9-parameter fits to the data of the four L E P experiments.

Mz(MeV) rz(MeV) crpe~k'°" b ' had

(n)

Rl A (z) x 10'

ALEPH

DELPHI

L3

OPAL

Average

X2 j

91191.54-3.3 2495.9±5.5 41.59+0.08 20.730±0.078 216+25

91186.94-3.3 2495.1±5.2 41.26±0.13 20.690±0.090 160±28

91190.04-3.6 2504.0±5.1 41.45+0.11 20.859+0.088 168±35

91186.24-3.6 2494.6±5.5 41.48±0.12 20.8644-0.076 137+24

91188.7+1.7+4 2497.6±2.7±2.7 41.494-0.05+0.10 20.795±0.040 170+14±8

1.6 2.2 4.7 3.4 t 5.5

Table 7 Line shape parameters from the four LEP experiments [17-19,21], combined according to [44].

I~Z Mz

Fz

peak,0 O'had

0.031

Rl

A (L) FB

0.003

0.01

0.04

-0.091

0.001

0.002 0.002

peak,0 O'had

Rl

0.114

0.004

Table 8 Average correlation coefficients for the parameter set o f table 7.

partial width: I't = 83.964-0.18 MeV.

(14)

LFrom the average value of A(~ one can derive a value of the effective weak mixing angle: sin 2 0~ft = 0.23107 4- 0.00090

(15)

4. P a r t i a l w i d t h s i n t o s p e c i f i c f l a v o u r s Because it belongs the same multiplet as the heavy top quark, the Z --r bb partial width receives a specific vertex correction, sensitive uniquely to the top_ quark mass [49]. In order to measure the Z--* bb partial width, or the b forward backward asymmetry, the first step is identification of b events, or "btagging", b-tagging is interesting for many reasons:

besides allowing electroweak measurements, it is a key tool in selecting clean b samples for study of exclusive b-quark properties, B ° B ° mixing, and even as a secondary tool for search for the Higgs boson, which is expected to decay primarily into b-quarks, if it not too heavy. The topic has received the devoted attention of a large fraction of the LEP experimentalists, with many new techniques and refinements. A good review can be found in [50]. The best quantity to measure is Rb = rla~d r~ ~ where the b-vertex correction is nicely isolated with little theoretical uncertainty [16] The methods group in three categories: tagging with leptons, event shape or displaced vertex. The oldest technique is b-tagging with high P, P± leptons. Leptons are identified among all charged tracks in hadronic events, and selected on their longitudinal or transverse momentum with respect to the nearest jet. Charm decay background is separated statistically from a global fit to the lepton distributions. As a result, the b partial width that is extracted this way is strongly correlated with assumptions made on the charm decays. The efficiency is reduced to less than 10% by i) the leptonic branching ratio ( 40% for either b into electron or muon) and ii) the high P, P± cuts necessary to isolate a pure sample. Typically, a purity of 80% can be reached with an efficiency of 5%. The heavy flavours analyses

A. Blondel/Precision Electroweak Physics at LEP

~:.i~.i

~......... '..

i~#iiiiii~iii~!ii!!!~!!:7:::

+i++i:?

. . . . .

::::~

~

::::i:~!!i~!~ili~ii~iii~ii~ii~iiii~ii~i~i~ili~i ~i~

]c+

11

- ~-/~ +

/

it

::::::::::::::::::::::::: :.:::.:::: :!

~

z•

OPAL

..... !

I

~J"

,$

~'i~

,...=

-30

-20

i

-10

0

DecoyLength

Figure 8. A fu//y reconstructed example ofa Z --, bb event. Here a B, is/dentified by its decay B, --* ~b~q~. The ~bt decays into two muons and the q~ into two K's. Left: front view (x-y). Right: expanded view o f the vertex showing the V D E T hits, and the reconstructed primary and secondary vertices. using lepton tagging are described in ref [51-54]. Event shapes analyses have in principle the advantage of using an events. Various kinematical variables can be reconstructed in jets that are sensitive to the presence of a heavy, fast object decaying isotropically. An efficient variable is the boosted sphericity product and variations thereof. Such analyses are described in [55-57]. Vertex tagging is the area where most progress has been accomplished in the last year. The tool of identification is now the long (1.5 ps) life time of the b-hadrons, associated with their large decay multiplicity. As a consequence, events containing a b-quark tend to contain several charged tracks originating from a secondary vertex situated several millimeters from the main interaction point, as can be seen in a beautiful example of a fully identified b event shown on figure 8. To perform this task, the LEP experiments are equipped with high precision vertex detectors. The LEP experiments have used various characterization of the detached secondary vertex properties: A L E P H [59] and D E L P H I [61] have used the product of probabilities of the tracks to extrapolate back to the vertex, while OPAL [60] selects signal and background control samples on the basis of impact parameter significance 5/,r(5), figure 9. The L3 detector is being upgraded to include a vertex detector to be operational in 1994. Since the production and decay of b-hadrons is not very well known, the tagging efficiency cannot be calculated with certainty. However, there are two

10

2O Significance

30

Lies.

Figure 9. Decay length significance distribution in OPAL. The events with forward tag provide the b signal and those w/th backward tag a control sample for resolution and light quark background.

b's per Z --* bb event, and use is made of the double tag method to measure the tagging efficiency from the data, by comparing the rates of single tagged and double tagged events. Only backgrounds and hemisphere correlations have to be calculated from Monte-Carlo. The backgrounds come mostly from light quarks which fake the tag. u, d, s quarks can fake a lepton tag because of misidentified hadron, or the vertex tag because of secondary vertices (strange particle decays or secondary interactions). Charm constitutes the more serious background, as it is a source of prompt leptons, and of secondary vertices albeit with lower multiplicities. The charm background estimates require good knowledge of charm production and are presently the dominant source of systematic error. The hemisphere correlations are mostly of geometrical nature, since the two b quarks in an event are emitted back-to-back, and tend to hit the detector inhomogeneities in a correlated manner. However there are some physical reasons for correlation as well, namely the gluon emission that affects both sides of an event. Better control of systematics can be obtained by calibrating one of the tagging methods against another (mixed tag). The most precise methods are those using the vertex tag, and the least precise systematically are those using event shape variables. The results are summarized in table 9. The experimental results in this table have been corrected to a set of common input parameter values, and the average performed taking into account corn-

12

A. Blondel/Precision Electroweak Physics at LEP

Method High p, P± lepton tag

Event shape variables: Microvertex tag:

Experiment ALEPH

ro

l~h6d

modeling error

value

exp. error

0.216

± 0.006

+ 0.005

L3

0.2187

± 0.008

± 0.008

OPAL

0.2252

± 0.011

± 0.007

DELPHI

0.2145

± 0.0089

± 0.0066

ALEPH (mixed)

0.228

± 0.0054

± 0.004

L3

0.222

± 0.003

4- 0.007

DELPHI

0.2214

4- 0.0020

± 010028

ALEPH

0.2187

± 0.0022

± 0.0026

OPAL

0.2171

± 0.0021

=t= 0.0021

average for SM rhAd I'.

0.2192

=t: 0.0018

Table 9 r~ measurements at LEP. The numbers have been shifted to a c o m m o n set o f parameters and the averages rhad have been c o m p u t e d as described in [44,89]. T h e y are therefore not necessarily identical to the numbers given by the experiments. Errors that would result from floating the charm partial width are not shown.

mon sources of errors, by the LEP electroweak working group [44,89]. The main background to b-tag being charm, there is a large correlation between the b and c partial widths. If the measurement of .Xx_ l~h.d is to be interpreted within the SM, ~ is essentially fixed to its rhsd SM value, even ff one let sin 20~fr and f~b float independently of each other. On the other hand it is also interesting to measure .£_L and ~had r~ independently. rhad In this case, the result of table 9 becomes:

rb -

rhad Fc ~had

-

=

~({~}) = ( w +

0.22024- 0.0020

0.15834-

0.0098

(16)

with a correlation of-0.40 between these two numbers. r polarization In the case of the r lepton, the charged decay provides us with a final state polarization analyzer. The ALEPH [62], DELPHI [63], OPAL [64] and L3 [20] collaborations have presented results for the following five decay channels: v --~ m,¢ (B.R. 12%), ~- -* evev~ (B.R. t8%) r ~ #v~,vr (B.R. 18%), ~" -~ pvr --, 7r-~r°t,~ (B.R. 24%), ~- --~ a l v r --~ ~r-lr+~r°t,r (B.R. 8%). The analyses do not distinguish here the nature of the charged hadron, channels with Kaons are included as well, but have very similar spin properties. The extraction of the r polarization is illustrated in figure 10. For the lepton and lr channels, all the information is contained in the momentum spectrum 4.1.

of the charged particle, which is fitted to a linear combination of the distributions for positive and negative helicities. For p and al decays, the fun information must be retrieved by a full analysis of the decay products, as shown by Roug~ [67], and developed in [68]. For the r --~ pvr decay, the r helicity affects the distributions of both r and p decay angles, in a way that depends on the lr-lr ° mass. This set of observables, (~}, defines the final state. The probability density functions for the -t-1 helicity, W+({~}), are used to build an optimal variable -

W-)l(W+ +

w-)({~}),

and at

the r polarization. For the at, the decay is defined by six variables. Full use of the density function in this set makes the al channel more sensitive than the leptonic one. By analyzing the polarization as a function of polar angle one can derive both the average r polarization, 7)~ and the forwazd-baekwaxd polarization • pol(r) asymmetry AFB , as shown in figure 11. The results in the individual ehanneis from the LEP experiments are summarized in table 10. The measurements are compatible with each other. It can be seen also that experimental systematic errors on are now almost as large as the statistical ones. Improvements will require ingenuity! Systematic errors on A, are, on the other hand, very small. The extraction of 7~ assumes that the r decays through maximally parity violating V-A charged current. The errors in table 10 do not allow for possible violation of this assumption. It is possible, however, to place constraints on t h e r neutrino helicity ( by studying the correlation between the helicities of the

A. Blondel/Precision Electroweak Physics at LEP

1250"

Data

~a) 1000- L ~ 750

~ J-[ MonteCaxlo

13

12501 (b)

"~ackground

t~

0.2

ALEPH preliminary

...... ' \

500. -'-:..- h=+l

90-91-92 data

250'" " ~ ~ °o~

0:5 0.~5 i EJE~m

¢J

700

(c)

400

5- -i -0.2

250

.......i..~...i..L~ :.:_j::

200

-0.4

150

300

...,-J

200

~'---...

0.25

0.5

~':~-.-?:: 0.75 1

0

cos0

1

0

~.~.~.;-. Figure 11. Angular dependence o f the ~" polarization in A L E P H . The fines show the result o£ a fit to equation 7 in case one does (dotted //ne) or does not (£ull line) assume lepton universality.

-12-'

-1

-6.5

6

o15

Figure 10. Extraction o f the T polaxization in a) r ~ Iz~'t,vr ; b) "1"---, ev~vr; c) r ---, 7rvr; d) r ---, pvr decays. The fu///ine is the resu/t o f the/it, which is a//near sum o f the c o m p o n e n t s due to posiave (dotted line) or negat/ve (dashed line) r helieities. two ~"s in an event. The A R G U S [69] (at DESY) and ALEPH [70] collaborations have performed such analyses, yielding: ~ v ~ = - 1 . 2 5 ± 0.23±o:1s o os (ARGUS) and ~vr : - 0 . 9 9 ± 0.07 ± 0 . 0 4 (ALEPH). This confirms beautifully that the ~- family has the same muitiplet structure as the electron and muon. If one uses this empirical value for the v~ helicity, an common error of AT~r = 0.015 has to be added to the results of table 10. The polarization results can be expressed as a measurement of the T and electron couplings, or of sin 2 ~ : ~4~ : 0 . 1 4 3 + 0 . 0 1 0

sin28~:0.2320±0.0013

.4~

sin 2 8~~ : 0.2330 ± 0.0014

: 0.135 ± 0.011

-1

100

5o ....;.%.

100 e ,~

o.,o s

(d)

300

600 500

Oo%5

The values of J[r and .4, are essentially uncorrelated, and in good agreement with lepton universality. 4.2. Q u a r k a s y m m e t r i e s In principle the quark asymmetries ~FB A(g) offer better sensitivity to the measurement of couplings and sin 2 8~w fr than the leptonic forward-backward asym-

metries, as well as better event statistics. However, it is difficult to tag specific quark final states and to measure their charge. Inclusive hadronic charge asymmetry measurements have been carried out by A L E P H [71,72], D E L P H I [73] and OPAL [74]. The method is based on the premise, first suggested by Feynman [75] that the original quark chaxge is carried out by the resuiting jet of particles. This property has been since then verified in several reactions where the original quark flavour is known, in paxticuiar (anti)neutrino or muon deep inelastic scattering [76]. The method used by A L E P H and D E L P H I is described here. OPAL used a different one, based on the three highest momentum particles, with somewhat better statistical sensitivity. Each event is separated in two hemispheres, according to the thrust axis. The momentum weighted hemisphere charge is constructed: QF,B

--

~F,B Pl~i qi ~F,B P~i

(17)

where qi is the charge of particle i, p]li its momentum

14

A. Blondel/Precision Electroweak Physics at LEP

Channel eueuv ~uuu~. ~ru~ pu~ alu~

ALEPH -214 ± -123± -148± -90± -144±

DELPHI

65 ± 55± 26± 24± 42=k

33 27 11 18 22

-130 ± -33± -192± -119± -184±

all

137 ± 12 :t: 8

144 4-

all

127 ± 16 ± 5

140 ±

OPAL

~ x 103 76 ~ 81 6 8 ± 41 3 8 ± 40 2 8 ± 31 6 6 ± 59 .A~ x 103 18 ± 16 A~ x l0 s 28 4- 3

L3

- 8 5 ± 58 ± -80± 54± -143± 37± - 1 5 7 ± 244N.A.

45 33 30 15

- 1 2 7 ± 79 ± -254± 72± -128± 36± - 1 6 6 ± 28 4-250±128±

24 28 28 17 34

153 ± 19 ± 13

144 :i: 13 ± 15

122 ± 30 ± 12

154 ± 20 ± 12

Table 10 Results o f the r polarization analyses for individuM channds from the LEP experiments• For A L E P H and L3 values o f individual channels, only 1992 data are shown. STATUS

s/u

EW Prog.

QCD

cuts

• 2 eft sm 0w

0.315+0.045

EXPOSTAR

NO

NO

0.23174-0.00134-0.0011

DELPHI

89-90 publ. 89-92 prel. 90-91 publ.

OPAL

90-91 publ.

0.3154-0.045 0.2854-0.050

ZFITTER ZFITTER

YES YES

NO S<0.12

0.2345-£0.00304-0.0027 0.23214-0.00174-0.0028

EXPT. ] ALEPH

I

Average I

0.23204-0.00114-0.0011

Table 11 S u m m a r y o f the determination of sin 2 0~~r from inclusive haclronic charge asymmetries at LEP.

projected on the thrust axis, and ~ is a parameter that is varied for systematic checks. Maximum sensitivity is found for ~ -- 1. A good estimate of charge for each event is the difference between the forward and backward hemisphere QFB = QF - QB. A significant average charge asymmetry, (QFB), is observed for the inclusive hadronic event sample. The expected charge asymmetry is given by: =

~

6 A (f) F! f

FB

rhad"

(18)

q u a r k flavors

Where 61, the charge separation, is the average charge difference between quark and antiquark hemisphere: 61 : ( Q / - Q ~ - ) The forward backward asymmetries, see equation 6, are all positive, but the signs of the charge separations are different. This results in a large cancellation~ already at patton level. The experimental uncertainties are small but the interpretation of (QFB) in terms of sin2 0~w is affected by the uncertainty in the calculation of the charge separations. This is estimated by varying the parameters of the hadronization models, and by comparing various models. The experiments find different values for the charge separations, which can be traced to a different choice of input parameters in the simulation, and of the decay tables for heavy fla-

voted particles. The most critical parameters in the simulation of light quark charges, are those controlling pair production of strange particles and baryon pairs. Improved understanding of particle composition and correlations in jets will help reducing these errors. The decay tables of heavy particles will remain incompletely known, and the solution is probably to measure directly the heavy quark jet charges, by means of tagged events. ALEPH has presented a preliminary analysis [721, where the fragmentation systematic error is reduced by using a direct measurement of the b jet charge, based on lepton and lifetime tagged b samples, as well as a constraint obtained by measuring the quantity (QF" QB). It can easily be shown that, for a sample consisting only of one type of quarks f, and up to small correlation terms, 62

(QF' QB) -~ _ ! . 4

(19)

This method can be used for a selected b sample to measure 6b. In the inclusive sample, (QF" QB) measures a weighted sum of the squares of the charge separations, but still constrains usefully some of the fragmentation parameters (unfortunately not strange particles and baryon pair production!).

A. Blondel /Precision Electroweak Physics at LEP

. . . .

i

,

,

i

i

I

. . . .

I

. . . .

I

. . . .

I

. . . .

I

. . . .

I

. . . .

.

2OOO 1750

y o.~

. . . .

I

. . . .

I

•

15

I

. . . .

I

,

i

. . . .

I

. . . .

i

. . . .

I

. . . .

I

. . . .

I

I

0.15 e,~,'~ f ~

1~oo

It

i~o

l

0.1

t

÷ K± 0.05

,.o

IV\

500

+ -0.05

° . 0 ~ , i ' ~

'~.,~ 'o'.,. . . . o,

-0,1

. . . .

0.1

m2 (CeV/c) a

,

t~

0.2

,

,

,

0..3

I

0.4

. . . .

I

0.5

. . . .

0.6

I

I,J

0.7 cosOp

Figure 12. Mass reconstruction with the D E L P H I RICH.

Figure 13. Measured charged K a sym m et ry in DEL-

The results ate expressed in terms of sin 2 0~~. QCD corrections and B mixing are automatically taken into account by the method. The present status is given in table 11. By selecting events with a fast K ± and A an enriched sample of signed s i events can be obtained. This is possible in DELPHI thanks to the particle identification provided by the Ring Imaging Cerenkov [77]. The mass of a particle of momentum P is measured by the Cerenkov angle 0c as: m : P.n.cosOc. Kaons axe well separated for momentum between 10 and 18 GeV, as shown in figure 12. The expected purity for this mass range is 42% ors quarks of the right sign, and expected asymmetry is -0.04. A significant asymmetry is measured, figure 13. Similar, though less precise analysis is obtained with A's. Fast K ° and neutrons, detected in the hadron calorimeter, provide an unsigned tag for s~ and dd events. This can be combined with jet charge to measure the down-quaxk asymmetry. The measured asymmetries [78] axe consistent with the SM value 0.0937:

leptons. High P± leptons tag b quarks, low P± leptons axe enriched in c quarks. Another possibility for b's is the life-time tag and for c the recognition of a high momentum D meson.

K± :

0.118

A : 0.135 K ° , n : 0.111

"4-0.031star. -4- 0.016syst. "[-0.0~stat"

-4- 0.037syst.

q-0.031stat. -I-0.068 --0,054 s y s t .

4.3. H e a v y q u a r k a s y m m e t r i e s The asymmetry can also be measured for individual quark species if one is able to: • Tag the specific quark flavour. This can be done for b and c quarks by means of their semi-leptonic decays, which produce prompt

PHI.

• Measure the scattering angle. The thrust axis of the event is usually used as measure of the original quaxk-antiquaxk direction before fragmentation. • Assign an orientation to the event axis defined above. In the selection with leptons or with D mesons, the sign of the lepton or the fiavour of the meson can be used. In case the event is recognised by life-time tag, one can use the jet charge (as in the inclusive sample) to measure in a statistical way the asymmetry. All LEP collaborations have performed an analysis using lepton tagging [51,79,81,80]. There the prompt lepton sample axe analysed in a global way to extract simultaneous way the b and c partial width, the direct and cascade semi-leptonlc branching f~actions, the inclusive B ° - B ° rni~ng and the b and c asymmetries. The asymmetry has to be corrected for QCD radiation [82] (3% correction) and for the experimental effects associated with the event axis determination and its orientation with a lepton (a few%). ALEPH [83], DELPHI [84] and OPAL [85] have presented the asymmetry measured fiom jet-chaxge in the lifetime-tagged lepton sample. The weakness of the inclusive jet charge asymmetry described above, namely the dependence upon fragmentation

A. Blondel/Precision ElectroweakPhysics at LEP

16

parameters, is avoided by determining the b charge from the d a t a using the charge correlation between opposite hemispheres, equation 19. As mentioned before, no QCD correction is necessary with this method. The charm asymmetry is also measured with D mesons by ALEPH [86], DELPHI [87], OPAL [88]. The averaging of these results is a very delicate enterprise. A preliminary procedure is attempted by the LEP eleetroweak working group [44,89]• The results are corrected for photouie effects to obtain the pole asymmetries:

:~2neff SIH o w

combined LEP-SLD data A~,

P~

0.2320 + 0.0013

p~B

AFB(bb) AvB(cc) QFB ALR(SLC)

A(~)0 FB

--

=

0.0967 + 0.0038

•

i e-

0.2330 ~: 0.0014

i~

0.23268± 0.00068 0.2310 + 0.0021

_~'

~--

0.2320 _+0.0016

i

0.2294 _+0.0010

-e-

Average A(b) o FB

0.23107_+ 0.00090

I~ ::::i ..

AMt-~4MIV

0.23167+0.00040 250

0.0760+ 0.0091

:

The correlation between these numbers is 0.08. They - 2 neff can be expressed as measurements of sm v, :

200

~/do, = 8 Q~ P=0.178

~"

150

E I O0

• 2 eft sm 0~ =

0.23268

+0.00068 (from b)

sin s 0~¢r =

0.2310

+0.0021 (from c)

0.225

0240

Figure 14. Summary of measurements of sin s 8~vff from the forward-backward asymmetries o£1eptons, polarization, inclusive quarks, heavy quarks asymmetry and the SLC polarization asymmetry. Also shown is the SM prediction as a function o f Mr.

(21)

LFrom LEP data, combining the measurement of A(b)0FS = }.4¢Jtb and the value .A, = 0.135 + 0.011 obtained from leptonic asymmetries and ~- polarization (see below), one can derive .Ab = 0.955 + 0.086. The two values are consistent with the SM expectation .A~ = 0.94. 4.4. S u m m a r y o n sin20~v~ The different values of sin20 eft measured from asymmetries and ~ polarization at LEP and SLC [91] are summarized on figure 14. Even though it is also possible to extract an equivalent value of sin28~ff from other measurements in the framework of the minimal SU(2)L × U(1) model, and in particular from Fe or Mw, asymmetries constitute a direct way to obtaiJa a value that corresponds exactly to the defiuition of equation 10. The measurements presented before average to: • 2 ~eff sm ~w = 0.23167+ 0.00040

0 235

sin2(~w~

(20)

The b forward-backward polarized asymmetry, defined in equation 9 can be measured if the beams are polarized. This has recently been done at SLC [90], both with lepton tag and the combined vertext a g / j e t charge method. For 5. 104 Z decays with 63% polarization, one finds: APOl(b) FB ----- .A~ = 0.93 + 0.14.

0.230

(22)

This number will play an important role in the determination of electroweak radiative effects.

e # r lepton

gvl -0.0370 + - 0 . 0 3 0 8 -t- 0 . 0 3 8 6 -I- 0 . 0 3 6 6 4-

gAl. 0.0021 0.0051 0.0023 0.0013

-0.50093 ± 0.00064 -0:50164 -4- 0.00096 -0.5026 + 0.0010 - 0 . 5 0 1 2 8 + 0.00054

Table 12 Lepton couplings gvl and gAz extracted from leptonic asymmetries and ~- polarization, showing the validity of lepton universality.

5. A n a l y s i s o f E l e c t r o w e a k M e a s u r e m e n t s

5.1. L e p t o n U n i v e r s a l i t y The couplings of the leptons can be extracted from the measurements of F~, F~,, F~, .~(~)~FB,A ( ~ , A ~ ; APOl(r) PB and ~v. The results of the fit are shown on table 12. Lepton universality is well verified and will be assumed in the following.

A. Blondel/Precision Electroweak Physics at LEP

5.2. N e u t r i n o p a r t i a l w i d t h What the experiment really measures is the ratio of the invisible width to the leptonic width: Fin.

(~/ --

12~rRz M s _peak,O

Rt - 3)

LEP/SLC Glasgow 1994

0.235

(23)

STANDARDMODE~.

In SU(2)L × U(1) the ratio

rt/r~

can be written

M~p=174 + 16

0.234

._c

0.233

MHI0gs

t0

Fl 1. (gw s 3a ~ - ~ : 5 ( 1 + ~-~Al) ) ( 1 + ~ - ~ ) ( 1 + ~ , )

0.232

(24)

where ~ = -0.0027 ~ 0.0003 is a vertex correction with no dependence on heavy physics. The ratio (gvt/gAt) 2 -: 0.0053 ~= 0.0001 can be obtained from the measured asymmetries. This yields the prediction:

0.231

0.23

--

i~l[ predicted

r--~

: 0.5022 =k 0.0001. number

of neutrinos

0.229

(25) is

then:

Nv

99% C.L

83

83.5

:

assume that t~te number of neutrinos is 3 and determine the neutrino partial width, a sensitive test of

su(2h. × u(1): PL F~

-

-

:

5.3. D e t e r m i n a t i o n o f SU(2)L x U(1) R a d i a t i v e Effects

The LEP measurements contain enough information to extract Ap, $~b, and Asq defined in eqs. 11. The resulting values for Ap, 6~b, and Asq are shown in table 5.3, and compared with the SM predictions. One notes: i) the sensitivity of the determination of Asq on the input value of Ac~, as can be seen from t h e first one of eqs. 11; ii) the sensitivity of the determination of 6vb on a°; as pointed out in [16], this comes from the fact the RL is as powerful as determining 6~b as ~r h . d is. This point is illustrated on fig. 16 and 17. In the SM, 6~b depends on Mt only (quadratically), Ap depends on Mt (quadratically) and on MH (logarithmically), while A s q has a logarithmic dependence on both Mt and MH, and thus is relatively more sensitive to MH. The leading terms are: a ¢c M i

84.5

85

Figure 15. Contours o f constant X 2 for sin s 0~,~ versus Pz. The S M predictions as a function of Mr and MH are shown.

0 . 4 9 9 2 -4- 0.0038

in excellent agreement with the prediction of equation 25. In the following, the number of neutrinos will be fixed to three and the SU(2)L x U(1) structure assumed.

_

84

I"lepton (MeV)

I ' ~ ' m e a s u r e d P--A'predicted----2.988:t:0.023. One can also Pl "r

Ap

~

Z°had

as:

The

17

a M~ --~ln-~z

(26)

fit

param,

value

error due to SM variation Ac~ A s , value Mt MH T4

44

.t-15

A8q x 104 - - 3 9 =k 23 =£9

=k3

-60

-F1

-8

--2

+17

5rb × 104

T51

Ap X 104

33 =t= 19

- 9 7 - 4 - 67

-

-

--14

--29 -175 +27

--18

+8

--1

+1

Table 13 Radiative corrections determ/ned from L E P data. The S M va/ues are given for Mt : 174 -4- 16 G e V GeV. and MH : -ann+¢°° ~-24o

,-,_ M~I

6.b

--

-~-~

13

\M~ + --~-In~)

(28)

More complete expressions have been calculated and implemented in computer codes, see refs [93]. Assuming the SM variation of 6~b upon Mt [49], it can be used [9] to place a limit on the top quark mass Mt < 195GeV at 95% C. L. This limit is as

18

A. Blondel /Precision Electroweak Physics at LEP

L E P / S L C G l a s g o w 1994

o.225 [

L E P / S L C G l a s g o w 1994

0.225 Mtop=174 ::!:: 16

MSM .......

lo 68% C.L. 99% C.L. ~

~ 0.22 =

'

X

0.22

90Ge~

0.215

0.215

50. 200,

0.21

0.23

0.235 • 2

sin

0.21

~

_

1000 GeV

_

_ _ 0.23

,

• 2

eft

0w

sin

,

,

I 0.235

eft

0w

Figure 16. Comparison o f sin z O~r and _E.L and the rhad S M prediction• The constraint from Rt, assuming ~, = 0.123 ± 0.006, is an oblique band.

Figure 17. Same as fig. 16, resu/t o f a two parameter

good at present than what can be obtained in the minimal SM, from A p mostly, but less sensitive to cancellation with other new physics. Given the small range allowed for A s q in the SM, its measurement constitutes a 0.3% test at the oneloop level. This test comes mostly from the comparison between the measurements of Ft and of sin s 0~ff from the asymmetries, shown in figure 15. In nonminimal theories, Aaq provides a test of the Higgs sector. Such an scenario is discussed in [7] where the related quantity S ~_ --AsQ X 4sin 2 0~tr cos 20~ft/a is expected to be increased by 2.1 for one generation of technifermions in Arc = 4 technicolor. The corresponding change of A s q is -0.024 and is clearly ruled out by LEP experiments. In principle, the measurement of AsQ can be used to set limits on the Higgs boson mass, and or on whatever plays its role, in particular on supersymmetry: such an analysis has been performed by e.g. [8,95] It can be seen from figure 15, t h a t the experimental error is still of the same size as the variation of AsQ from the Higgs boson mass. The agreement of the determination of the radiative corrections with the SM predictions is striking, especially if one takes into account the first possible direct determination of Mt by C D F [103] Mt = 174 d: 16 GeV. This is shown in figs 15, 16, 17 where the three experimentally independent observables sin s O~v i~, -EL FL are plotted against each other.

The discovery of the top quark, if confirmed, is an event of considerable importance: First, it happened in the range of masses predicted by the SM from precision measurements. Furthermore the SM loses one more free parameter, the only one left being the Higgs mass!

~'~had ~

a t O f -r~hL= d ' rt'l~ • peakO O'had ' ~s i•n 2 ~ e j , r z

t o ~,b ~ r l d s i n 2 0 ~ ff

assumed independent.

5.4. D e t e r m i n a t i o n of the top quark and Higgs boson masses Having shown the consistency of the measurements with the SM, it is justified to consider all available measurements as measures of Mt and, possibly,

MH. The most precise measurements to date are: i)the measurement of the neutrino N C / C C ratio from the CDHS [100], CHARM [101] and C C F R [102] experiments, averaging to sin 2 0w = 0.2253 +0.0047; ii) the measurement of the W massMw = 80.23 ± 0.18 [96] from UA2 [98] CDF [97] and D0 [99]; iii) the LEP measurements of the line-shape parameters, l"h.d r~ and of sin s 0~~ from asymmetries. A fit to these 14 observables yields Mt : 159_11 +11

(MH : 60)

~2 = 13.3

Mt = 178_11 +it

(MH : 300)

X2 = 15.1

Mt

(MH

:

196+t~

:

I000)

X2 = 16.9

(29)

Although the light Higgs mass seems to be preferred, the difference between the light and heavy Higgs hypothesis is only AX2 = 3.6 and no significant limit

A. Blondel/Precision Electroweak Physics at LEP

10

4M~ I:L and LEP/SLC ........

no limits Glasgow ~4

1o 41'4. R,. and LE-PiSI.C

10 Mw R, end LEP/SLC

only imils Glasgow 1~4

~tl dire Glasgow 94

lo

-,~¢j_ ---,~ ¢.L

........ ~

,-,~ C.L. . . . . . . . . -.e~ c£.

CJL.

'°'r

lO

,o~

10

5 1o

,o/ ' , ~ ~ o

19

lO . . . . ,;o . . . . ,~o. . . . ,~o . . . . =o

',00

Figure 18. Contours of constant X 2 for the global fit to M t , M H ; electroweak measurements only.

"',~0

....

,~0 ....

M,~(Ge~

Mt~(GeV)

,~0 ....

,~o ....

2;0

"

Mtop(GeV)

Figure 19. Same as lig 18 with direct limits Mt > 131 GeV, MH > 63.5 GeV, included.

Figure 20. Same as fig 19 includ•ng also the possible measurement of Mr = 1744- 16.

0.004

can be placed. The constraints on Mr, MH placed by this fit are shown in figure 18. If the experimental lower limits on MH > 63 GeV and Mt > 131 GeV are included, the situation is not substantially modified, fig. 19. Even when the possible direct measurement is included, the upper limit on the Higgs mass improves slightly, but not dramatically. The X2 difference between MH = 60 and MH ----1000 GeV becomes 4.2... Of course this occurs because i) the values of Mt from precision measurement and the diIect one are so close; and ii) the error on the direct measurement is as large as the sensitivity on the Higgs mass of the top mass from precision measurements.

NN\I

\

I

-O.OO2-~~ 2OO

/ 1:

-0,004

-0.006

0.002

0.004

0.006

0.00~

0.01

Z¢

6. C o n c l u s i o n s a n d O u t l o o k The advent of LEP accelerator and experiments has allowed a new and precise tests of the SM to be performed. Electroweak measurements have shown no deviation from the minimal picture at the 10 - a levd. This is confirmed by the lack of obserwtion of new particles within the range kinematically reachable, and of the Higgs boson up to 63 GeV. The top quark mass was predicted fight where it has possibly been found. So, is there a future for LEP precision experiments? The first, obvious missing piece is a precision measurement of Mr. It seems possible that its mass will be measured with a precision of 4. 5 GeV. Secondly, improvements in Electroweak measurements are stillto come: i)the measurement of the W mass from the energy upgrade of LEP, with a precision of about 30 M e V or better, ii) it is expected that the statistics of L E P experiments will have increased

Figure 21. A possible scenario for the ultimate precision of Electroweak measurements at LEP. S M predictions in the (Ap, Asq) plane. S M predictions: dash-dotted line: Mt free, MH= 50 GeV; full line: Mt free, MH= 200 GeV; dotted//he: Mt free, MR= 1000 GeV; Experimental constraints: vertical band: A r z = 4-0.07 M e V (from A r z : 4-2 MeV). 25 ° band: A M w : + 30 MeV. 45 ° band: Asin20~~ = 4. 0.0001. The S M prediction for Mt = 165 4. 5 G e V as expected from a future measurement o f the top mass is also indicated. by a factor 2-5 by the end of 1995. The measurement of the Z mass and width should improve significantly by steady scanning of the Z resonance, together with precise energy calibration of the beam energy by the resonant depolarization method. An error of + 2 MeV on I'z seems reachable. Asymmetry measurements should Mso improve, resulting in a

20

A. B l o n d e l / P r e c i s i o n E l e c t r o w e a k P h y s i c s at L E P

combined measurement error on sin 2 O~v ff of +0.0003. More speculatively, longitudinal polarization experiments at LEP [104,105]. could lead to much improved measurement of sin ~ 0~fr, down to +0.0001. In order to make full use of the future precision measurements of sin2O~~r, the present estimate of a(M~) should be improved. The present error corresponds to an uncertainty in predicting sin ~ 0~fr from Mz of ± 0.0003. The improvement of a(M~) requires better measurements of e + e - - ~ h a d r o n s in the energy region 1-10 GeV. It is hoped that the precision on electroweak measurements will be improved to the level of sensitivity that would make its indirect determination through radiative corrections significant. Such an analysis was performed in [15], stressing the importance of very accurate measurements of sin 2 0~fr at LEP, see fig. 21. Clearly, if the Higgs is found, these same measurements may be precise enough to reveal physics beyond the SM. Of course the best thing to do is to find the Higgs. The high energy programme of LEP offers a good chance of finding it up to a mass limit of MH=2.Ebe~ -- 100 GeV. Here the maximal energy that can be reached by LEP is the critical parameter. If this fails, we will have to wait for the LHC to give us s o m e answer to the mysteries of spontaneous symmetry breaking.

7. A c k n o w l e d g e m e n t s I am grateful to my colleages from the LEP collaborations for giving me access to their preliminary data, especially R. Clare, A. Kounine, P. Renton, M. Roney, D. Schaile, P. Wells, J. Wenninger, M.Winter. Useful discussions with many colleagues theorists are gratefully acknowledged. The LEP Electroweak working group has performed with great care the averaging of the experimental results. Manel Martinez and Bolek Pietrzyk deserve special credit for several discussions and graphs. I personally owe a lot to my colleagues of ALEPH and of the Polarization Collaboration for enjoyable company and support during these measurements.

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