- Email: [email protected]
Fermion pair production at LEP2
ELSEVIER
Nuclear Physics B (Proe. Suppl.) 66 (1998) 91-95
PROCEEDINGS SUPPLEMENTS
Fermion pair production at LEP2 A. Venturi a aINFN Sezione di Pisa, 1291 via Livornese, 1-56010 S.Piero a Grado, Pisa, Italy The results of the four LEP collaborations on the fermion pair production in e+e - collisions at the centre-ofmass energies above the Z resonance are presented. The (preliminary) results are in good agreement with the prediction of the Standard Model and limits on new phenomena are discussed.
1. I N T R O D U C T I O N After six years of running at the Z resonance (LEP1), since Fall 1995 the LEP collider has been operated at centre-of-mass energies above the mass of the Z bosom In 1995 about 2.8pb -1 were collected at 130GeV and 2.8pb -1 at 1 3 6 - 140 GeV (LEP1.5). In 1996 LEP went beyond the WW pair production threshold collecting about 11pb -1 at 161GeV and 10.3pb -1 at 170 - 172 GeV (LEP2). At these higher energies the physics content of the fermion pair production changes drastically. While at the Z peak this process is dominated by the huge, imaginary, amplitude of the Z resonance with a small contribution from the photon exchange diagram and an even smaller one from the interference term (_~ 10 -3 at x/~ _~ Mz 4-3 GeV), at higher energies, instead, these amplitudes, Z and photon exchange, are comparable in module and both real. Therefore it is possible to study the contribution of the interference between the Z and the photon (.~ 1/10 of the total cross section) or between the standard amplitudes and possible new physics amplitudes. The drawback is the much smaller available statistics since the cross sections are about 1/100 of those at the Z peak. This simple picture is complicated by the presence of the photonic initial state radiation (ISR). The emission of photon(s) can reduce the effective centre-of-mass energy of the fermion pair, v~ 7, to Mz and enhance the contribution of the resonating Z diagram (return to the Z); about 75% of the qq(7) events have v ~ - Mz. To preserve sensitivity of the cross sections and of the angular distributions to the interference terms, the V~7 value 0920-5632/98/$19.00 © 1998ElsevierScience PII S0920-5632(98)00017-6
B.V.
All rightsreserved.
of each event has to be measured and eventually only those events with v ~ 7 > sx/~c~t > Mz have to be considered [1]. This introduces additional both experimental and theoretical uncertainties and ambiguities, mainly due to the indirect measurement of the radiated energy, since about 85% of the photons escape undetected along the beam pipe, and to the separation of initial and final state radiation photons. 2. E X P E R I M E N T A L
RESULTS
Each of the four LEP experiments have analysed the data collected at the various centre-ofmass energies and have measured the hadronic and leptonic total cross sections and the leptonic forward-backward asymmetries, both without and with a cut on s' (inclusive and exclusive samples) [1-6] (only L3 and OPAL results can be regarded as final for all the final states and all the energies). A common feature of these results is that all the four experiments estimate systematics uncertainties due to detector calibration and simulation which are much higher than those at LEP 1 because of the small amount of data available, both at high energy and at the Z peak, collected during the short calibration runs. The systematics uncertainties of the luminosities measured by each experiment are about 0.55% for ALEPH, 0.6% for DELPHI and L3 and 0.25% for OPAL and a common theoretical uncertainty of about 0.25%. The uncertainty on the LEP centre-of-mass energies is about 60 MeV and its effect is totally negligible on these results.
A. Venturi/Nuclear Physics B (Proc. Suppl.) 66 (1998) 91-95
92
2.1. H a d r o n i c final s t a t e
The selection of the hadronic events (qq(7)) is very similar to the one used for the data at the Z peak. They have been selected requiring large charged track multiplicity and large visible energy or mass in order to reject the two-photon events which represent the most important background together with the WW pair events (when the energy is above their production threshold). The s ' / s ratio is reconstructed from the direction of the two hadronic jets, possible detected isolated photons and/or the expected photons radiated along the beam pipe and by imposing the energy/momentum conservation (see fig. 1). The cut applied to define the exclusive sample differs among the experiments: for ALEPH it is V / 7 / s > 0.9, DELPHI and L3 v/sv/sv/~> 0.85 and OPAL s ' / s > 0.8. The expected sensitivity on the interference term(s) does not depend critically on this cut if sv/~cut > Mz [1]. Typical
160 GeV
ALEPH PRELIMINARY
140 120 ~.. 100 {e
~ 80 60 4O 2O
°o 0:1 0'.2'o.~,"o.4'~o.50.6 0.7 0.8 ,~s'./s 0.9 Figure 1. (s'/s) 1/2 distribution for hadronic events at 161 GeV: real data (points), simulated events (solid line) and background events (gray area).
efticiencies for this selection are about 85 - 95% with a background of about 2 - 3% below the
WW threshold (two-photon events) and between
5% and 20% above the WW threshold depending if explicit cuts to reject WW events are applied or not. In the case of the exclusive sample an additional source of background comes from those events with a reconstructed # above the cut and a "true" value below the cut. In case of the hadronic events this contamination is between 5% and 13%. The uncertainties in the cross section measurements are dominated by the statistical errors which are, for each energy point, 2.6 - 3.7% for the inclusive sample and 6 - 7.8% for the exclusive sample. Typical systematics uncertainties are between 1% and 4% and are dominated by the detector simulations, the background estimation (two-photon events for the inclusive analysis) and, for the exclusive sample, the contamination from the l o w - # events. 2.2. L e p t o n i c final s t a t e
The di-lepton final states ( e, # and T) suffer from lower cross sections and higher statistical uncertainties: in the Standard Model the contribution of the Z - 7 interference term to the total cross sections is proportional to the vector couplings of the leptons to the Z, which are much better measured from the FB asymmetries at the Z peak. More interesting is the study of the fermion pair angular distributions, from which the measurement of the FB asymmetries can be extracted and which contribute largely to set limits to the parameters of the contact interactions. The e+e final state is dominated by the t-channel exchange diagram, especially for small production angle, therefore, since it contains different information with respect to the # + # - and T+r - final states, the cross sections and FB asymmetries are measured for various acceptances (cos 0, acollinearity and sl/s) and are compared to the SM prediction but not used in the fit to extract the Z - 7 interference term. Also for the leptonic final states the selection criteria are similar to those used at LEP1. Low charged track multiplicity, high track momenta (or mass) and particle identification are required for the it+it - and e+e - final states while for the 7-+v- final state the acollinearity cut is looser than at LEP1, especially for the inclusive sam-
A. Venturi/Nuclear Physics B (Proc. Suppl.) 66 (1998) 91-95 pie, and cuts on the missing transverse momentum and the visible mass are applied to reject the two-photon background. Typical efficiencies are: 65 - 90% for #+/1-, 35 - 60% (inclusive sample) and 50 - 75% (exclusive sample) for ~+T- and 95 - 98% (inside the acceptarme) for e+e - . Typical contaminations, mainly twophoton events and di-lepton events of different flavour, are: 2 - 10% for # + # - , 5 - 15% for T + T and less than 3% for e+e - (e+e - --4 -yy). For the exclusive analysis ( D E L P H I has a different cut of x / ~ > 0.9) the contamination from l o w - # events is typically 2 - 10% for p + p - and 5 - 15% for T + T - . The uncertainties are dominated by the statisti-
o(nb) .
.
ALEPH .
.
.
.
.
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.
,
60
,
?~............eI
8o
.
.
.
.
,
mo
,
~o
,
,
I
2.3. Rb OPAL, using the hadronic exclusive sample, has performed a determination of the bb/hadron ratio, Rb, at the various centre-of-mass energies. They used the same ]olded tag method used for the analysis of the LEP 1 data [7]: Rb is extracted from the difference between the number of events with large and positive and those with large and negative secondary vertex decay length significance. The results are [6]: 0.195 + 0.039 + 0.013 at 133 GeV, 0.162 4- 0.039 4- 0.011 at 161 GeV and 0.131 4- 0.046 :t: 0.010 at 172 GeV, in good agreement with the SM predictions (0.182, 0.169 and 0.165, respectively).
3. R E S U L T S I N T E R P R E T A T I O N
l o -1
o .-."
0.5 - 3% and < 0.03 for e+e - , mainly due to detector simulation, two-photon background and s' reconstruction for the exclusive sample.
' '
1 0
lo-I
93
,
1,0
,
,
160 E_(GeV)
,8o
Figure 2. Hadronic and leptonic cross sections as measured by A L E P H [2].
cal errors: 10 - 14% (15 - 20%) and 0.09 - 0.14 ( 0 . 1 2 - 0.17) f o r / z + # - inclusive (exclusive) cross sections (relative error) and FB asymmetries, respectively, 13 - 20% (18 - 28%) and 0.13 - 0.20 (0.14 - 0.25) for 7"+7 - - and 2.5 - 10% and 0.03 0.09 for e+e - . T h e systematic uncertainties for cross sections and asymmetries have been conservatively estimated to be 2 - 4% and < 0.05 f o r / ~ + # - , 3 - 7% and < 0.05 - 0.10 for T + r - ,
The results of the four experiments for the cross sections and the FB asymmetries (or angular distributions) are in good agreement with the Standard Model prediction, given the present statistical and systematic uncertainties (see, for example, figure 2). To extract quantitative information from those measurements two different approaches have been followed: a fit in the framework of the Standard Model to measure the fermion couplings and fits in the framework of extended models, like contact interactions or leptoquarks, to set limits on the parameters of these models. 3.1. S t a n d a r d M o d e l fit In the framework of the Standard Model those measurements above the Z resonance are useful to study the interference between the Z and the photon, especially in the hadronic sector. In the usual fit of the cross sections and asymmetries at the Z peak the contribution of the interference term has been kept fixed at the value predicted by the Standard Model. This assumption can be justified for the leptonic final states since the total cross section interference t e r m is linked to the vector couplings which are measured accurately by the FB asymmetries at the Z peak, but it can be regarded as too model dependent for
A. Venturi/Nuclear Physics B (Proc. Suppl.) 66 (1998) 91-95
94
the hadronic cross section. Moreover the odd-like behaviour of the interference term around the Z peak introduces a strong correlation between this term and the value of the Z mass and inflates the Mz uncertainty if the interference term is left free in the fit. The measurements of the cross sections at higher energies have the two-fold benefit of improving the precision on the interference term and reduce the correlation with Mz (see figure 3). Quantitatively the interference term is
¢
0.75
~
DEI.PItII~OO-IV~ '5 DELPHI1~0-1995+199511~6
0.5
-O.25
J~,~s~ 0.2 =
-0.5
(M~,p = 170-190 GcV)
-0.75 .1 zFrTTE'R 5.0
.i.251.17Y
,
t . . . . .
I
Mz (GeV)
measured by fitting the cross sections and the FB asymmetries using the S-matrix formalism [8,9]. The total and FB cross sections are parametrised
as (a = tot, fb): + .... = ~ - - ~--45-=-_-s (s-Uz) +/ZFZ]
3.2. N e w p h y s i c s The absence of a huge and imaginary resonance at these energies makes the fermion pair production sensitive to new production mechanisms through the appearance of new interference terms with the standard amplitudes. Two examples are given by the contact interactions studied by OPAL [11,6] and DELPHI [12] and the tchannel exchange of new particles investigated by OPAL [6]. T h e interest for these kind of phenomena has being increasing recently due to the results at the HERA ep collider [13]: the possible schannel resonance at HERA would show up as an additional t-channel contribution in e+e - -+ q~ at LEP2. The contact interactions are studied by adding an additional term to the interaction Lagrangian [14]: g2 V " rlij[~iT~ ei][f j % , f j] (2) ~cont (1 + a)A2 i,j=L,R _
Figure 3. 68% c.l. contour for -:tot / h a d and Mz from LEP1 data only and L E P I + L E P 2 data combined, as measured by DELPHI.
a ° (s) = 5
the fit for the interference term of the hadronic total cross section is ./tot dhad : 0.144-0.13 in agreement with the SM prediction (0.22):__ The correlation with Mz is - 7 2 % and Mz = M z ÷ 34.1 MeV = 91.18764-0.0031 GeV [9] (the present error on Mz from the standard fit with fixed interference term is 2.0MeV [10]). Without the high energy data the Mz - ./had:t°tcorrelation is --94%.
(1)
where 9~, r~ and j~ are the coefficient of the photon, Z and interference term, respectively. Using the LEP1, the high energy L E P data and the T O P A Z data, below the Z resonance, the result of
(5 --- 1 for e+e - -+ e+e - , = 0 otherwise). The parameter A can be considered or as the energy scale at which the fernfion compositeness shows up, or can be related to the mass of a possible particle exchanged in the t-channel and 17lijl _< 1 depend on the specific model taken into account. This new interaction adds a term proportional to 1 / A 2, due to the interference, and a term proportional to 1/A 4 to the fermion pair differential cross sections. By fitting the fermion cross sections and the leptonic angular distributions it is possible to set limits on e = [rhj(g2/4rr)]/A 2 or, equivalently, on A 2 with the assumption that g2/4rr = 1, for the various helicity configurations. OPAL has used the leptonic differential cross sections, the hadronic total cross sections and Rb, all from the exclusive analysis, to set the limits on A. T h e best limits for the combined results,
A. Venturi/Nuclear Physics B (Proc. Suppl.) 66 (1998) 91-95
4.7 - 7.7TeV, are for AA and VV models (A=LR, V = L + R ) while for the other models the limits generally lie in the range 2 - 5 TeV (see figure 4). DELPHI set the limits by fitting the p + # - and
OPAl.
A-
A+
95
of the Standard Model. At the time this contribution is being written LEP is running at higher energy (183GeV) and the preliminary results confirm this agreement. At the same time new analysis to set limits on new physics have been performed and the LEP experiments are working to set a procedure to combine these results as it was done for the LEP1 data. REFERENCES
10 IIJ,
I~R
5 Ilml,H I R L
0
5
l0 (TeV)
E2_IV'¢IIIAA ~ | . L R R :'.:L-IJRRI,~ ) 1 5
Figure 4. 95% confidence level limits on the energy scale A from OPAL contact interaction
fits [6].
T+7 - cross sections and FB asymmetries.
The combined limits are in the range 1.9 - 6.4 TeV. OPAL, in addition, set limits on the mass and on the coupling of a new (scalar) particle that couples to the eq current (lepto-quark or squark) assuming that it contributes with an additional t-channel amplitude to the e+e - --4 q~ process. Yukawa couplings larger than 0.5 - 0.6 are excluded for masses up to 400 GeV/c 2. Smaller couplings can be excluded only for smaller mass values (~ 0.3, 100 GeV/ca). 4. C O N C L U S I O N S The results on the fermion pair production obtained from the data collected above the Z resonance are in good agreement with the prediction
1. ALEPH Coll., Phys. Lett. B378 (1996) 373. 2. ALEPH Coll., Measurement of f e r m i o n pair production ..., submitted to 1997 EPS-HEP conference, Jerusalem, conf. pap. #602. 3. DELPHI Coll., D E L P H I results on the meas u r e m e n t of f e r m i o n - p a i r . . . , submitted to 1997 EPS-HEP conference, Jerusalem, conf. pap. #464 4. L3 Coll., M. Acciari et al., Phys. Lett. B370 (1996) 195; L3 Coll., CERN-PPE/97-52, accepted by Phys. Lett. B. 5. OPAL Coll., Phys. Lett. B376 (1996) 232; OPAL Coll., Phys. Lett. B391 (1997) 221. 6. OPAL Coll., CERN-PPE/97-101, submitted to Z. Phys. C. 7. OPAL Coll., Z. Phys, C74 (1997) 1 8. A. Borrelli, M. Consoli, L. Maiani, R. Sisto, Nucl. Phys. B333 (1990) 357; R. G. Stuart, Phys. Lett. B272 (1991) 353; A. Leike, T. Riemann, J. Rose, Phys. Lett., B273 (1991) 513; T.Riemann, Phys. Lett. B293 (1992) 451 9. LEP EW Working Group, S-matrix subgroup, LEPEWWG/LS/97-01 Internal note 10. G. Quast, talk at the 1997 EPS-HEP conference, Jerusalem. 11. OPAL Coll., Phys. Lett. B387 (1996) 432. 12. DELPHI Coll., Limits on contact interaction t e r m s . . . , submitted to 1997 EPS-HEP conference, Jerusalem, conf. pap. #467 13. H1 Coll., Z. Phys. C74 (1997) 191; ZEUS Coll., Z. Phys. C74 (1997) 207. 14. E. Eichten, K. Lane and M. Peskin, Phys. Rev. Lett. 50 (1983) 811
Nuclear Physics B (Proe. Suppl.) 66 (1998) 91-95
PROCEEDINGS SUPPLEMENTS
Fermion pair production at LEP2 A. Venturi a aINFN Sezione di Pisa, 1291 via Livornese, 1-56010 S.Piero a Grado, Pisa, Italy The results of the four LEP collaborations on the fermion pair production in e+e - collisions at the centre-ofmass energies above the Z resonance are presented. The (preliminary) results are in good agreement with the prediction of the Standard Model and limits on new phenomena are discussed.
1. I N T R O D U C T I O N After six years of running at the Z resonance (LEP1), since Fall 1995 the LEP collider has been operated at centre-of-mass energies above the mass of the Z bosom In 1995 about 2.8pb -1 were collected at 130GeV and 2.8pb -1 at 1 3 6 - 140 GeV (LEP1.5). In 1996 LEP went beyond the WW pair production threshold collecting about 11pb -1 at 161GeV and 10.3pb -1 at 170 - 172 GeV (LEP2). At these higher energies the physics content of the fermion pair production changes drastically. While at the Z peak this process is dominated by the huge, imaginary, amplitude of the Z resonance with a small contribution from the photon exchange diagram and an even smaller one from the interference term (_~ 10 -3 at x/~ _~ Mz 4-3 GeV), at higher energies, instead, these amplitudes, Z and photon exchange, are comparable in module and both real. Therefore it is possible to study the contribution of the interference between the Z and the photon (.~ 1/10 of the total cross section) or between the standard amplitudes and possible new physics amplitudes. The drawback is the much smaller available statistics since the cross sections are about 1/100 of those at the Z peak. This simple picture is complicated by the presence of the photonic initial state radiation (ISR). The emission of photon(s) can reduce the effective centre-of-mass energy of the fermion pair, v~ 7, to Mz and enhance the contribution of the resonating Z diagram (return to the Z); about 75% of the qq(7) events have v ~ - Mz. To preserve sensitivity of the cross sections and of the angular distributions to the interference terms, the V~7 value 0920-5632/98/$19.00 © 1998ElsevierScience PII S0920-5632(98)00017-6
B.V.
All rightsreserved.
of each event has to be measured and eventually only those events with v ~ 7 > sx/~c~t > Mz have to be considered [1]. This introduces additional both experimental and theoretical uncertainties and ambiguities, mainly due to the indirect measurement of the radiated energy, since about 85% of the photons escape undetected along the beam pipe, and to the separation of initial and final state radiation photons. 2. E X P E R I M E N T A L
RESULTS
Each of the four LEP experiments have analysed the data collected at the various centre-ofmass energies and have measured the hadronic and leptonic total cross sections and the leptonic forward-backward asymmetries, both without and with a cut on s' (inclusive and exclusive samples) [1-6] (only L3 and OPAL results can be regarded as final for all the final states and all the energies). A common feature of these results is that all the four experiments estimate systematics uncertainties due to detector calibration and simulation which are much higher than those at LEP 1 because of the small amount of data available, both at high energy and at the Z peak, collected during the short calibration runs. The systematics uncertainties of the luminosities measured by each experiment are about 0.55% for ALEPH, 0.6% for DELPHI and L3 and 0.25% for OPAL and a common theoretical uncertainty of about 0.25%. The uncertainty on the LEP centre-of-mass energies is about 60 MeV and its effect is totally negligible on these results.
A. Venturi/Nuclear Physics B (Proc. Suppl.) 66 (1998) 91-95
92
2.1. H a d r o n i c final s t a t e
The selection of the hadronic events (qq(7)) is very similar to the one used for the data at the Z peak. They have been selected requiring large charged track multiplicity and large visible energy or mass in order to reject the two-photon events which represent the most important background together with the WW pair events (when the energy is above their production threshold). The s ' / s ratio is reconstructed from the direction of the two hadronic jets, possible detected isolated photons and/or the expected photons radiated along the beam pipe and by imposing the energy/momentum conservation (see fig. 1). The cut applied to define the exclusive sample differs among the experiments: for ALEPH it is V / 7 / s > 0.9, DELPHI and L3 v/sv/sv/~> 0.85 and OPAL s ' / s > 0.8. The expected sensitivity on the interference term(s) does not depend critically on this cut if sv/~cut > Mz [1]. Typical
160 GeV
ALEPH PRELIMINARY
140 120 ~.. 100 {e
~ 80 60 4O 2O
°o 0:1 0'.2'o.~,"o.4'~o.50.6 0.7 0.8 ,~s'./s 0.9 Figure 1. (s'/s) 1/2 distribution for hadronic events at 161 GeV: real data (points), simulated events (solid line) and background events (gray area).
efticiencies for this selection are about 85 - 95% with a background of about 2 - 3% below the
WW threshold (two-photon events) and between
5% and 20% above the WW threshold depending if explicit cuts to reject WW events are applied or not. In the case of the exclusive sample an additional source of background comes from those events with a reconstructed # above the cut and a "true" value below the cut. In case of the hadronic events this contamination is between 5% and 13%. The uncertainties in the cross section measurements are dominated by the statistical errors which are, for each energy point, 2.6 - 3.7% for the inclusive sample and 6 - 7.8% for the exclusive sample. Typical systematics uncertainties are between 1% and 4% and are dominated by the detector simulations, the background estimation (two-photon events for the inclusive analysis) and, for the exclusive sample, the contamination from the l o w - # events. 2.2. L e p t o n i c final s t a t e
The di-lepton final states ( e, # and T) suffer from lower cross sections and higher statistical uncertainties: in the Standard Model the contribution of the Z - 7 interference term to the total cross sections is proportional to the vector couplings of the leptons to the Z, which are much better measured from the FB asymmetries at the Z peak. More interesting is the study of the fermion pair angular distributions, from which the measurement of the FB asymmetries can be extracted and which contribute largely to set limits to the parameters of the contact interactions. The e+e final state is dominated by the t-channel exchange diagram, especially for small production angle, therefore, since it contains different information with respect to the # + # - and T+r - final states, the cross sections and FB asymmetries are measured for various acceptances (cos 0, acollinearity and sl/s) and are compared to the SM prediction but not used in the fit to extract the Z - 7 interference term. Also for the leptonic final states the selection criteria are similar to those used at LEP1. Low charged track multiplicity, high track momenta (or mass) and particle identification are required for the it+it - and e+e - final states while for the 7-+v- final state the acollinearity cut is looser than at LEP1, especially for the inclusive sam-
A. Venturi/Nuclear Physics B (Proc. Suppl.) 66 (1998) 91-95 pie, and cuts on the missing transverse momentum and the visible mass are applied to reject the two-photon background. Typical efficiencies are: 65 - 90% for #+/1-, 35 - 60% (inclusive sample) and 50 - 75% (exclusive sample) for ~+T- and 95 - 98% (inside the acceptarme) for e+e - . Typical contaminations, mainly twophoton events and di-lepton events of different flavour, are: 2 - 10% for # + # - , 5 - 15% for T + T and less than 3% for e+e - (e+e - --4 -yy). For the exclusive analysis ( D E L P H I has a different cut of x / ~ > 0.9) the contamination from l o w - # events is typically 2 - 10% for p + p - and 5 - 15% for T + T - . The uncertainties are dominated by the statisti-
o(nb) .
.
ALEPH .
.
.
.
.
-<;./;):->o.,
.
,
60
,
?~............eI
8o
.
.
.
.
,
mo
,
~o
,
,
I
2.3. Rb OPAL, using the hadronic exclusive sample, has performed a determination of the bb/hadron ratio, Rb, at the various centre-of-mass energies. They used the same ]olded tag method used for the analysis of the LEP 1 data [7]: Rb is extracted from the difference between the number of events with large and positive and those with large and negative secondary vertex decay length significance. The results are [6]: 0.195 + 0.039 + 0.013 at 133 GeV, 0.162 4- 0.039 4- 0.011 at 161 GeV and 0.131 4- 0.046 :t: 0.010 at 172 GeV, in good agreement with the SM predictions (0.182, 0.169 and 0.165, respectively).
3. R E S U L T S I N T E R P R E T A T I O N
l o -1
o .-."
0.5 - 3% and < 0.03 for e+e - , mainly due to detector simulation, two-photon background and s' reconstruction for the exclusive sample.
' '
1 0
lo-I
93
,
1,0
,
,
160 E_(GeV)
,8o
Figure 2. Hadronic and leptonic cross sections as measured by A L E P H [2].
cal errors: 10 - 14% (15 - 20%) and 0.09 - 0.14 ( 0 . 1 2 - 0.17) f o r / z + # - inclusive (exclusive) cross sections (relative error) and FB asymmetries, respectively, 13 - 20% (18 - 28%) and 0.13 - 0.20 (0.14 - 0.25) for 7"+7 - - and 2.5 - 10% and 0.03 0.09 for e+e - . T h e systematic uncertainties for cross sections and asymmetries have been conservatively estimated to be 2 - 4% and < 0.05 f o r / ~ + # - , 3 - 7% and < 0.05 - 0.10 for T + r - ,
The results of the four experiments for the cross sections and the FB asymmetries (or angular distributions) are in good agreement with the Standard Model prediction, given the present statistical and systematic uncertainties (see, for example, figure 2). To extract quantitative information from those measurements two different approaches have been followed: a fit in the framework of the Standard Model to measure the fermion couplings and fits in the framework of extended models, like contact interactions or leptoquarks, to set limits on the parameters of these models. 3.1. S t a n d a r d M o d e l fit In the framework of the Standard Model those measurements above the Z resonance are useful to study the interference between the Z and the photon, especially in the hadronic sector. In the usual fit of the cross sections and asymmetries at the Z peak the contribution of the interference term has been kept fixed at the value predicted by the Standard Model. This assumption can be justified for the leptonic final states since the total cross section interference t e r m is linked to the vector couplings which are measured accurately by the FB asymmetries at the Z peak, but it can be regarded as too model dependent for
A. Venturi/Nuclear Physics B (Proc. Suppl.) 66 (1998) 91-95
94
the hadronic cross section. Moreover the odd-like behaviour of the interference term around the Z peak introduces a strong correlation between this term and the value of the Z mass and inflates the Mz uncertainty if the interference term is left free in the fit. The measurements of the cross sections at higher energies have the two-fold benefit of improving the precision on the interference term and reduce the correlation with Mz (see figure 3). Quantitatively the interference term is
¢
0.75
~
DEI.PItII~OO-IV~ '5 DELPHI1~0-1995+199511~6
0.5
-O.25
J~,~s~ 0.2 =
-0.5
(M~,p = 170-190 GcV)
-0.75 .1 zFrTTE'R 5.0
.i.251.17Y
,
t . . . . .
I
Mz (GeV)
measured by fitting the cross sections and the FB asymmetries using the S-matrix formalism [8,9]. The total and FB cross sections are parametrised
as (a = tot, fb): + .... = ~ - - ~--45-=-_-s (s-Uz) +/ZFZ]
3.2. N e w p h y s i c s The absence of a huge and imaginary resonance at these energies makes the fermion pair production sensitive to new production mechanisms through the appearance of new interference terms with the standard amplitudes. Two examples are given by the contact interactions studied by OPAL [11,6] and DELPHI [12] and the tchannel exchange of new particles investigated by OPAL [6]. T h e interest for these kind of phenomena has being increasing recently due to the results at the HERA ep collider [13]: the possible schannel resonance at HERA would show up as an additional t-channel contribution in e+e - -+ q~ at LEP2. The contact interactions are studied by adding an additional term to the interaction Lagrangian [14]: g2 V " rlij[~iT~ ei][f j % , f j] (2) ~cont (1 + a)A2 i,j=L,R _
Figure 3. 68% c.l. contour for -:tot / h a d and Mz from LEP1 data only and L E P I + L E P 2 data combined, as measured by DELPHI.
a ° (s) = 5
the fit for the interference term of the hadronic total cross section is ./tot dhad : 0.144-0.13 in agreement with the SM prediction (0.22):__ The correlation with Mz is - 7 2 % and Mz = M z ÷ 34.1 MeV = 91.18764-0.0031 GeV [9] (the present error on Mz from the standard fit with fixed interference term is 2.0MeV [10]). Without the high energy data the Mz - ./had:t°tcorrelation is --94%.
(1)
where 9~, r~ and j~ are the coefficient of the photon, Z and interference term, respectively. Using the LEP1, the high energy L E P data and the T O P A Z data, below the Z resonance, the result of
(5 --- 1 for e+e - -+ e+e - , = 0 otherwise). The parameter A can be considered or as the energy scale at which the fernfion compositeness shows up, or can be related to the mass of a possible particle exchanged in the t-channel and 17lijl _< 1 depend on the specific model taken into account. This new interaction adds a term proportional to 1 / A 2, due to the interference, and a term proportional to 1/A 4 to the fermion pair differential cross sections. By fitting the fermion cross sections and the leptonic angular distributions it is possible to set limits on e = [rhj(g2/4rr)]/A 2 or, equivalently, on A 2 with the assumption that g2/4rr = 1, for the various helicity configurations. OPAL has used the leptonic differential cross sections, the hadronic total cross sections and Rb, all from the exclusive analysis, to set the limits on A. T h e best limits for the combined results,
A. Venturi/Nuclear Physics B (Proc. Suppl.) 66 (1998) 91-95
4.7 - 7.7TeV, are for AA and VV models (A=LR, V = L + R ) while for the other models the limits generally lie in the range 2 - 5 TeV (see figure 4). DELPHI set the limits by fitting the p + # - and
OPAl.
A-
A+
95
of the Standard Model. At the time this contribution is being written LEP is running at higher energy (183GeV) and the preliminary results confirm this agreement. At the same time new analysis to set limits on new physics have been performed and the LEP experiments are working to set a procedure to combine these results as it was done for the LEP1 data. REFERENCES
10 IIJ,
I~R
5 Ilml,H I R L
0
5
l0 (TeV)
E2_IV'¢IIIAA ~ | . L R R :'.:L-IJRRI,~ ) 1 5
Figure 4. 95% confidence level limits on the energy scale A from OPAL contact interaction
fits [6].
T+7 - cross sections and FB asymmetries.
The combined limits are in the range 1.9 - 6.4 TeV. OPAL, in addition, set limits on the mass and on the coupling of a new (scalar) particle that couples to the eq current (lepto-quark or squark) assuming that it contributes with an additional t-channel amplitude to the e+e - --4 q~ process. Yukawa couplings larger than 0.5 - 0.6 are excluded for masses up to 400 GeV/c 2. Smaller couplings can be excluded only for smaller mass values (~ 0.3, 100 GeV/ca). 4. C O N C L U S I O N S The results on the fermion pair production obtained from the data collected above the Z resonance are in good agreement with the prediction
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