ELECTROWEAK PHYSICS AT y's = Mz

S. MARCELLINI

INFN and Department of Physics Universita' di Bologna, Viale C. Berti Pichat 6/2

40127 - Bologna, Italy

A summary of the measurements performed at LEP and SLC at centre-of-mass energy around the Z-peak which test the Standard Model of particle physics is presented. The experimen­tal results are compared with theoretical expectations, and their implication in the indirect determination of the mass of the Standard Model Higgs boson is discussed.

"HI O

1 Introduction

The four LEP experiments, ALEPH, DELPHI, L3 and OPAL, al).d the SLD collaboration at SLC, study e+e- interactions at centre-of-mass energy y'S "'=' 9 1 GeV. This energy corresponds to the mass of the Z boson, which is resonantly produced, and decays into fermion-antifermion pair. The exper­imental observables which ·are relevant for electroweak measurements at this centre-of-mass energy are the total cross-section for inclusive hadronic decays of the Z boson and the cross-section for each of the three charged leptons, the leptonic forward-backward asymmetry, the tau polarization, and the Z to bb and cc decay partial widths and forward-backward asymmetries. Taking advantage of the longitudinal polarization of the electron beam at SLC, the SLD experiment can also measure the left-right. polarization asymmetry which is not measured at LEP. These quantities are determined by each experiment, and they are combined using the common framework decided within the LEP Electroweak Working Group 1 . In the averaging procedure the correlations among the quantities arc taken into account, a.s well as the correlated and uncorrelated systematic errorn. Several experimental results arc still preliminary, as some analyses are still undergoing. In Section 2 the experimental mea­surements related to the Z lineshape and the forward-backward asymmetries are presented. In Section 3 the electroweak meitSurements concerning the heavy flavour sector are reported . The consistency of tlw experimental results with the Standard Model is shown in Section 4, where the impact of the measurements on the indirect determination of the Higgs mass is also discussed.

2 Z Line shape and Forward-Backward Asymmetries

Each L EP experiment analyses the interactions e+e- -+ hadrons and c+e- -+ 1+1- with 1 = e, 11 or T iu the centre-of-mass energy r;mgc I y'S - Mz I < 4 Ge V. A set of 9 weakly correlated parameters describing the Z resonance is determined by each experiment 1 . The parameters arc corn�ct.ed for initial state radiation and for t-charrnel exchange contribution in the rnse of e+e- final st.ate.

They are:

• The mass of the Z boson Mz and its total decay width I'z , which define the parametrization of the cross-section around the Z rpass by a Breit-Wigner function.

• The hadronic pole cross-section for Z-exchange:

( 1 )

wlwre re and rh are the part.ial widtlrn o f the z fo r decays into electrons and hadrons.

• The ratios R1 = Rh/R1 where 1 = e, µ or T

• The pole asymmetry A�-·k for each type of charged lepton. The forward backward asymmetry can be expressed as:

being A1 related to the vector and axial-vector coupling constraints by the relation:

AJ = -�2_V J9AJ 2 'l rlv1 + 9Af

(2)

(3)

Au average value for each of these parameters is t.hcn computed following the procedure described in 1 . Table l reports the results. By a.�suming lepton universality a value for R1 and A�-·� is also comp u tcd .

�90

Table 1: Averages of the parameters measured by each experiment concerning the Z lineshape and the leptonic forward­backward asymmetries

I Parameter I Average Value I Relative Error I Mz (GeV) 91 .1867±0.0021 2.3 · 10 ·<> I'z (GeV) 2.4939±0.0024 9.6 . 10-4 crg(nb) 41.491±0.058 1 .4 . 10-3 R, 20. 783±0.052 2.5 . 10 ° Rµ 20. 789±0.034 1 .6 . 10-3 R,. 20. 764±0.045 2.2 . 10-3 Ri 20. 765±0.026 1.3 . 10 ·3 Av,e 0.0153±0.0025 1.6 . 10-1 Ab,N 0.0164±0.0013 1.9 '. 10-2 Ab,� 0.0183±0.0017 9.3 . 10-2 Ji' r> AU,l

FR 0.01683±0.00096 5.7 . 10-2

The uncertainty in the measurement of the LEP beam energy is the limitation in the determination of the mass and the width of the Z. It gives an error of .6.Mz :::::: l .7 MeV and .6.I'z :::::: l .3 MeV. The error on the hadronic pole cross-section is dominated by the theoretical uncertainty in the calculation of Bhabha scattering, which is 0.1 1 % and it directly affects the cross-section by the same error. An other theoretical uncertainty arise from O(a3 ) corrections which are not included, at the moment, in the fitting procedure to the data. These corrections modify the cross-section by about one per-mille, as well as the niass of the Z by 0.5 MeV and its width by 0.6 MeV. As these effects are still under study, the central value of the fit was not modified, but the difference when the corrections were included or excluded was used as a systematic error.

The quantity Ae can be determined at LEP by measuring the r longitudinal polarization 2. As­suming lepton universality the average Ai value at LEP is:

Ai = 0.1452 ± 0.0034 The SLD experiment can measure Ae directly, taking advantage of the very precisely measured

polarization of the electron beam of the SLC machine. The SLD measurement combined with with measurements of the lepton left-right-forward-backward asymmetry and earlier measurements of the hadronic polarised asymmetry is:

Ai = 0.1504 ± o.oq23 Combining LEP and SLD results it is obtained:

A1 (LEP + SLD) = 0.1486 ± 0.0023

3 Heavy Flavour Electroweak Measurements

The relevant quantities in the beauty and charm quark sector for what concerns electroweak measure­ments at LEP /SLC are:

• The ratio of b and c quark partial width of the Z to its total hadronic partial width: Rb = r bh/rh and Re = r cc/fh

• The forward-backward asymmetries.' A�� and A��

• The final state coupling parameters Ab and Ac measured at SLD from the left-right-forward­backward asymmetry.

Other quantities which are not electroweak parameters but which are important inputs in the determination of the above quantities are also the beauty and charm semileptonic decay branching ratios, the B0B0 inclusive mixing parameter x and the probability for a charm quark to fragment

0· 1 85 ����..---�,.......,,.......,Pr�el�im-in�a-ry�

0. 1 75

0. 1 65

0. 1 55 +-���..----,.......,-----1 0.2 1 4 0.2 1 6 0.2 1 8 0.22

Fig11re 1: Re versllS Rb experimental result , superimposed to the Standard Model expectation

into a given charmed hadron. These quantities are now determined with good precision by the LEP experiments at the LEP energy. In averaging the experimental electroweak quantities among the experiments, correlations within them have to be taken into account, as well as correlations with the non-electroweak quantities listed above.

Several new measurements were presented in the beauty and charm electroweak sector after the ICHEP 3 3 Conference held in Vancouver, in summer 1998. New measurements of Rb by the DELPHI 5 and OPAL 6 collaboration were published. Measurement of Re from DELPHI 7 and SLD 8 were also performed, as well as measurements of AiB and A�B again from DELPHI 9. The L3 collaboration published a new measurement of AiB 10• The SLD experiment also updated the measurements of Ab and Ac 8 . According to the new measurements, the LEP+SLC average value for Rb , corrected for the 'Y exchange is:

Rg = 0.21680 ± 0.00073 The average value of Re is:

Rg = 0.1694 ± 0.0038 The error on Rg before the new experimental results was ±0.044, and the considerable improvement

mainly comes from the very precise measurement of this quantity performed by the SLD experiment. In figure 1 it is shown the Rg versus Rg contour plot for different confidence level, compared with the Standard Model expectation. The error associated to the Rb and Re measurements mainly comes from systematics, as the overall uncertainty of each individual measurement contributing to the average has an almost equal share between statistical and systematic errors. This is not the case for AiB and A�B where the error of each measurement is still dominated by statistics. The average value of A�� at the common centre-of-mass energy of ,,/S = 91 .26 GeV is:

A�·� = 0.0991 ± 0.0020

while for A�� it is obtained: A�� = 0.0712 ± 0.0043

Informations on Ab are not directly accessible at LEP, as Ab is related to Ah by the relation:

(4)

and therefore an independent measurement of Ai is required. This is not the case at SLC, where due to the polarization of the electron beam the quantity Ab is directly measured by the SLD experiment.

10')

P eliminary

0.9

0.8

0. 7 -i-.��.,.......�--,-.��r"".,.............-i 0. 1 3 0.14 0.1 6 0.1 7

Figure 2 : Status o f the Ab measurement. See text for explanation of the content of the plot.

A previous possible discrepancy of this measurement with Standard Model prediction is now recovered by the new improved measurements performed by the SLD collaboration, 8 as it can be seen in figure 2. In this figure the horizontal band shows the SLD measurement, whereas the diagonal band shows the region allowed by the LEP measurement of A�B as a function of A1 . The vertical band shows the LEP+SLD average for this quantity. The Standard Model prediction is superimposed, where the lengths of the arrows show the uncertainty coming from the top and the Higgs mass.

4 Comparison with the Standard Model Predictions

The various asymmetry measurements from LEP and SLD each provide a measurement of the effective electroweak mixing angle, sin2B�ff which is defined in terms of the vector and axial-vector coupling constants as:

· 2 I 1 ( 9Vl ) sin Bel I = - 1 - -4 9Al (5)

Figure 3 shows the measurements of this quantity, as well as the LEP+SLD average. The two most precise single determinations of sin2B�11 come from the measurement of A�B at LEP and from the left-right asymmetry at SLD, and they differ by about 2.5 a . Although this has generated some debate in the past, it has to be pointed out that the discrepancy between the two measurement has decreased as their precision increased. The errors from each individual measurement is manly statistical.

The precise electroweak measurements performed at LEP and SLD can be used to check the validity of the Standard Model. The LEP and SLD measurements are summarised in figure 4 (left). In the same figure it is shown the pull of each measurement with respect to the prediction of the Standard Model. It can be seen that the consistency with the theory is very good, as there are no measurements which differ more than two standard deviations from the result of the Standard Model fit. The largest pull at the moment is given by the forward-backward asymmetry for bottom quarks. Within the framework of the Standard Model, by comparing the experimental measurements with the theoretical predictions it is possible to infer about its fundamental parameters and extract informations on the top and the Higgs mass, which enter the calculations in loop corrections. As the top mass dependence is quadratic, given the very good precision of the measurements, rather strong constraints can be placed on its mass. On the other hand the Higgs mass enter the calculations only in logarithms, and therefore the sensitivity to its value is rather weak. The best constraint on the Higgs

393

Preliminary A,,0,1 0.231 1 7 ± 0.00054

A,,o.b Ai.'·' <Oft.?" Average(LEP)

1\:;.s: .. u; Average(LEP+SLD)

10 '

::c E 10 '

0.23

-4- 0.23223 ± 0.00036

-- 0.2321 ± 0.0010

·-- 0.2321 ± 0.0010

-a-x�

;2.3,1 ��1 � 0.00024

0.231 57 ± 0.0001 8 ;t�ld.o.I.: 7.7/6

0.232 0.234 . 2 lept sin e.tt

Figure 3: Measurements of sin2tl�ff from the asymmetries.

mass mH are obtained when also measurements of the W boson mass from LEP and Tevatron, and the direct measurement of the top mass also at Tevatron are used in the fit. Figure 4 {right) shows the observed value of L'l.x2 = x2 - x;;,in of the fit to the data as a function of mH. The solid curve is the result of ZFITTER, whereas the shaded band represents the uncertainty due to higher-order corrections which are not calculated. The figure also shows the very strong sensitivity of the curve to different values of O'em which are used in the fit. The vertical band represents the limit imposed by direct search at LEP. From the plot it appears that the data are consistent with a rather "light" Higgs boson, possibly in the reach of the forthcoming LEP run. The most probable value for the Higgs mass according to this fit is mH = 71 :'.:�� GeV. It has to be pointed out that the result of the fit is not driven toward a light Higgs boson by any measured quantity in particular. The quantity which alone has the strongest weight toward low Higgs masses is the SLD left-right polarization asymmetry, whose central value would. prefer a very light Higgs. This can also be argued from figure 3. It is interesting to note that even removing this quantity from the global fit, the result of the fit does not blow out at very high values, but it still remains bounded below about 150 GeV.

Neglecting experimental errors, the main limitation on a more accurate prediction of the Higgs mass are the uncertainty on O-em , on mw and on mtop · A precise determination of mtop within ± 2 GeV at the Tevatron in the forthcoming high luminosity run would be required to reduce the error on the Higgs mass below ,,, 40 - 50 Ge V 1 1

5 Conclusion

Data taken at LEP and al SLC at ../S ,,, Mz represent a very powerful tool to test the Standard Model with high accuracy. Although the data taking at this centre-of-mass energy is completed, several experimental results are still preliminary, and they can possibly be improved in the forthcoming years. Results are very consistent with the Standard Model predictions, and there are no measurement which differ more than two standard deviations from the correspondent result of the Standard Model fit. From these precision measurements it is also possible to extract informations on the unknown mass of the Higgs boson, which enter the theoretical calculations in the radiative corrections. Data indicate a rather light Higgs boson, possibly within the reach of LEP2.

394

Moriond 1 999 Measurament Pull Pull

mz lGe\ll 91.1867 ± 0.0021 .08 rz[GeVJ 2.4939 ± 0.0024 -.83

o�[nbJ 41 .491 ± 0.058 .29

A. 20. 765 ± 0.026 .70

�· 0.01683 ± 0.00096 .67

A .• 0.1479 ± 0.0051 20 A, 0.1431 -� 0 0045 - 84 4 sin� 0.2321 ± 0.0010 .56 ., ,-: iG(··�: �<:J_ .i :·:; ! (' ();;�} "2 Nl'< A, 0.21680 :r 0.00073 1.27 <l A, 0. 1694 ± o. 0038 ·.75

,,.;.�� 0.0991 ± 0.0020 -1 .94 �' 0.0712 .t 0.0043 -.55 2 A, 0.908 ± 0 027 -.99 A, 0.651 ± 0.030 -.56 sin�0:"1 0.23109 ± 0.00029 -1.54

-�in�i\<; �l.22f,::; t G.0021 l 08 m,, [GeV) 80.448 i 0,062 1 .1• m, [GeV) 174.3 ± 5.1 .50

Preliminary AaJ:.<m,) 0.02804 ± 0.00065 -.17

1 0 -3 -2 -1 0 1 2 3

Figure 4: Experimental measurements and correspondent pulls with respect to the Standard Model fit (left), and x2-x�in of the fit to the Standard Model as a function of the Higgs mass (right)

References

1 . The LEP Collab. et al., "A Combination of Preliminary Electroweak Measurements and Con­straints on the Standard Model" , CERN-EP /99-15, 8-Feb-1999. See also the LEP Electroweak Working Group page at: http://www.cern.ch/LEPEWWG/ and links therein.

2. H. Videau, "T Physics Review" , proceedings of this conference. 3. G. Borisov, "Measurements of Rb and Re and anomalous Z -+ b decay limit" , Proceedings of

the ICHEP99, Vancouver, Canada, July 1998, to be published. 4. A. W. Halley, _ "b and c Forward-backward asymmetries at LEPl" , Proceedings of the ICHEP99,

Vancouver, Canada, July 1998, to be published. 5. The DELPHI Collaboration, P. Abreu et al., CERN-EP /8-180, 6. The OPAL Collaboration, G. Abbiendi et al., Eur. Phys. J. CS (1999) 217. 7. The DELPHI Collaboration, P. Abreu et al., "'Measurements of the Z Partial Decay Width inco

coverlinec and Multiplicity of Charm Quarks per b Decay" , 99-43 MO RIO CONF 242,18-Mar-1999, http://delphiwww.cern.ch/ pubxx/www/delsec/conferences/moriond99/.

8. N. De Groot, "Electroweak Results from SLD" , Proceedings of this conference. 9. The DELPHI Collaboration, P Abreu et al., CERN-EP /99-07.

The DELPHI Collaboration, P. Abreu et al., CERN-EP /98-189. 10. The L3 Collaboration, M. Acciarri et al., Phys. Lett. B 448 (1999) 152. 1 1 . F. Teubert, "Precision tests of the Standard Model from Z physics" , Proceedings of RADCOR

98, Barcelona, Spain, September 1998.

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