OPAL =0.08) (%) (y cut R 3. N events T ρ. L3 Data PYTHIA ARIADNE HERWIG. L3 Data PYTHIA ARIADNE HERWIG

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1 CR May 1996 QCD-RESULTS AND STUDIES OF FOUR FERMION PROCESSES AT THE INTERMEDIATE LEP ENERGY SCALE p s = 130{136 GEV Hans-Christian Schultz-Coulon Universitat Freiburg, Fakultat fur Physik Hermann-Herder-Strae 3, D Freiburg, Germany Abstract The upgrade of the LEP center-of-mass energy to 130 and 136 GeV (LEP 1.5) at the end of 1995 oered the possibility to test the Standard Model in this new energy regime. In this report we describe the LEP results on the properties of multihadronic events at p s = 130{136 GeV including measurements of s (133 GeV). In addition, studies of four fermion processes at this new energy scale are presented.

2 1 Introduction After the LEP energy upgrade in November 1995 (LEP 1.5) the rst step towards the LEP 2 operating phase e + e? center-of-mass energies of p s = 130{136 GeV have been reached for the rst time. With the available data sample of about 5 pb?1 integrated luminosity tests of the Standard Model at this new energy scale have become possible. The analysis of the properties of multihadronic nal states allows the investigation of the predictions of perturbative Quantum Chromodynamics (QCD) including the measurement of the strong coupling constant s. The results obtained by the four LEP experiments in this eld are described in Section 2. In addition, two studies of four fermion events concerning nal states with high and low multiplicity are presented in Section 3. The new energy regime of LEP 1.5 oers the rst opportunity to study these processes well above the Z peak, where the contribution from the various Standard Model diagrams is signicantly changed compared to lower center-of-mass energies. Four fermion processes, especially those containing a quark and a lepton pair in the nal state, are of particluar interest, since they form a sizeable background for Higgs searches. In addition, the good momentum resolution for lepton pairs can be used to search for new particles X in the process e + e?! /Z () X! ``f f (`=e,), where X or /Z () decay to `+`? and f f, respectively. 2 QCD Results Compared to events at the Z resonance, two main eects are expected to inuence QCD observables in multihadronic events at higher center-of-mass energies: the running of the strong coupling s, and the change of the quark avour composition. While the second eect is due to the increasing importance of the s-channel photon exchange and the dierent strengths of the qq- and Zqq-coupling to the dierent quark avours, the rst is a pure QCD eect. Even though the limited statistics of the available data sample leads to a statistical uncertainty of the same order as the predicted decrease relative to s (m Z ), the extraction of the strong coupling constant still provides an important test of QCD. In addition, a comprehensive study of QCD observables might show some unexpected eect in the data or deciencies in the Monte Carlo simulations. 2.1 Event shape and inclusive observables Hadronic events can be characterized by event shape distributions and inclusive observables such as jet rates, momentum spectra and charged particle multiplicities. Hadronic nal states at center-of-mass energies well above the Z resonance are characterized by a large probability for initial state photon radiation resulting in an hadronic system with an invariant mass of p s 0 m Z. In order to measure the various QCD observables at eective center-of-mass energies well above the Z peak, one has to select events with only little initial state radiation (ISR). This is done by estimating the radiated photon energy E using either a kinematic t or in case the ISR photon is seen in the detector the p measured photon energy in the electromagnetic calorimeter. With a typical cut on s 0 = s? 2E s around (110{120 GeV) 2, events with large p s 0 values are selected. All four LEP experiments have studied the distributions of various event-shape observables. Before comparing with QCD perturbation theory, the measured quantities are corrected for hadronisation and detector eects and residual eects due to the presence of radiative events using bin-by-bin correction factors derived from Monte Carlo simulation. The parameters of the dierent Monte Carlo models are set to values tuned at the Z peak. The global structure of multihadronic events characterized by the dierent event-shape distributions is well reproduced by the various Monte Carlo models used and no signicant deviation from the QCD predictions was found by any of the experiments. A retuning of the Monte Carlo parameters at the new center-of-mass energy was thus not necessary. As example Fig. 1 shows the thrust T and scaled heavy jet mass distributions measured by the L3 Collaboration [1].

3 N events 10 2 L3 Data PYTHIA ARIADNE HERWIG 10 1 R 3 (y cut =0.08) (%) Jade Tasso Mark II Amy Aleph Delphi L3 24 N events T L3 Data PYTHIA ARIADNE HERWIG QCD α s (M Z ) = (x µ =1) s (GeV) ρ Figure 1: Thrust T and scaled heavy jet mass distribution measured by L3. The data are compared with dierent QCD model predictions at particle level without ISR. The experimental errors are statistical only. Figure 2: Distribution of the 3-jet rate R 3 at y cut =0.08 for the JADE E0 algorithm as a function of energy. The energy evolution of the 3-jet rate, intimately linked to the magnitude of the strong coupling constant s, is shown in Fig. 2 [2]. The result measured by the collaboration is R 3 (y cut = 0:08) = 0:198 0:023(stat) 0:030(syst) : This value, obtained using the Jade E0 scheme with y cut = 0:08, is in agreement with results given by L3 [1] and a preliminary measurement presented by DELPHI [3]. The ALEPH collaboration reports compatible results using the Durham jet nding algorithm [4]. No discrepancy from QCD can be claimed within the statistical and systematic accuracy of all the experiments. In contrast to event-shape distributions calculable in the framework of perturbative QCD, the distribution of single hadrons in the actually observable nal state can only be described non-perturbatively taking coherence eects between subsequent gluon emissions into account. Theoretically this is described by the Modied Leading Logarithm Approximation (MLLA) used in combination with the assumption of Local Parton Hadron Duality (LPHD). Experimental evidence showing the existence of postulated coherence eects can be obtained from inclusive measurements of the momentum and charged multiplicity distribution [5]. Both have been measured by the LEP experiments [2, 6, 7]. In the framework of the MLLA the energy evolution of the mean charged multiplicity hn ch i and the peak value 0 of the fragmentation function = ln(1=x), where x = 2p= p s is the scaled particle momentum,

4 α s (Q) (133 GeV) L3 (133 GeV) ALEPH (133 GeV) NLO NNLO Lattice Deep Inelastic Scattering 0.3 e + e - Annihilation Hadron Collisions Heavy Quarkonia LEP LEP Q (GeV) Figure 3: Values of s at dierent energies. The curve shows the second order QCD prediction for s with s (m Z ) = are predicted. The combined results at p s = 133 GeV are 0 = 3:87 0:03(stat) 0:11(syst) hn ch i = 23:80 0:27(stat) 0:52(syst) : For the mean value we take the simple weighted average using only the statistic uncertainties as described in Ref. [8] and combine the resulting error with the largest systematic uncertainty quoted by a single experiment. There is no evidence for any deviation from MLLA-predictions. By tting the MLLA-prediction for the energy evolution of hn ch i to data taken at dierent center-of-mass energies, including their result at p s = 130 GeV, the DELPHI collaboration extracts a value of s (130 GeV) = 0:105 0:003(stat) 0:008(syst) [7]. 2.2 Determination of s (133 GeV) from event shape observables The measurement of the strong coupling constant s from event-shape variables is based on the idea, that to leading order the ratio of the 3-jet and the 2-jet cross section is proportional to s. At p s = 130{136 GeV L3 [1], [2] and ALEPH [6] have determined s from QCD ts to one or more of those event-shape observables that allow the use of combined O( 2 s)+nlla QCD calculations [9]. The observables used, are the thrust T [1, 2], the total and wide jet broadening B T and B W [1, 2], the heavy jet mass [1, 2] and the dierential 2-jet rate D 2 [2, 6]. The distributions are tted after correcting for detector eects, initial state radiation and the hadronisation process. Using the averaging procedure described above this leads to a combined value of s (133 GeV) = 0:113 0:003(stat) 0:009(syst) : It should be noticed that the dominant contribution of the systematic error comes from theoretical uncertainties, followed by uncertainties due to initial state radiation and hadronisation eects. Fig. 3 shows the strong coupling constant [1, 2, 6, 10] as a function of energy together with the second order QCD evolution for s using s (m Z ) = 0:120. All measurements of s (133 GeV) are consistent with the running of the coupling constant as predicted by QCD.

5 3 Four Fermion Processes The production of two fermion-antifermion pairs in e + e? collisions is described by the Standard Model without large theoretical uncertainties. To model the four fermion events the FERMISV [11] program is used, which includes all possible diagrams involving neutral boson (Z/ ) exchange and their interferences. The dierent diagrams can be categorized into four dierent gauge-invariant groups, called conversion, annihilation, bremsstrahlung and multiperipheral diagrams [11]. The contribution of certain diagrams is especially high if the Z boson is on mass shell. Therefore, depending on the center-of-mass energy, dierent diagrams dominate the four fermion cross section. 3.1 High multiplicity nal states The collaboration has searched for ``qq (`=e,) four fermion nal states at p s = 130{136 GeV selecting high multiplicity events with ``-jet-(jet) topology containing an isolated lepton pair [12]. They nd 6 ``qq events in the LEP 1.5 data sample, 5 in the qq channel and 1 in the eeqq channel. The total number of expected signal events was estimated to 1:18 0:07 0:17. This number includes higher order corrections to the photon propagator, the Z-qq, -qq and q-q vertices, which have not been included in the FERMISV program. The total background prediction from other four fermion channels and e + e?! ()f f is 0:16 +0:07?0:04 0:04 events. Tab. 1 summarizes the number of expected and observed events at p s = 130{136 GeV for various subclasses of events including the Poisson probability for observing at least the number of events in the data. In Fig. 4 the recoil mass m recoil versus the leptonic mass m`` for data and simulated signal events is shown, where m recoil = (1? 2E``= p s) s + m 2`` is the invariant mass of the hadronic system recoiling against the lepton pair. The events with large recoil masses cluster around the Z mass and no additional peak is seen in the data, as would be expected if the observed excess were due to a leptonic or hadronic resonance, not present in the Monte Carlo simulation. Furthermore, none of the events has missing energy. Several other kinematic variables have been studied and the properties of the 6 ``qq events seem very similar to the expectations from Monte Carlo simulation. Therefore, a reasonable explanation for the observed excess is a statistical uctuation. This statement is further supported by a preliminary result of the ALEPH collaboration [13]. Searching for ``qq events using similar cuts as, they nd 1 eeqq event, which is in perfect agreement with their expectation from signal and background Monte Carlo of 1:00 0:06 events in the eeqq and qq channel combined. 3.2 Low multiplicity nal states A preliminary study of four fermion events with low multiplicity performed by the ALEPH collaboration searching for f f and 4` nal states [13] leads to a total of 4 observed events, 3 in the neutrino channel, and one e + e? e + e? event. The signal and background expectation of 4:09 +0:20?0:17 estimated from Monte Carlo again is in good agreement with this observation. observed expected probability 0: % 0: % 0: % 0:07 1.0% 0:17 0.3% e + e? qq 1 0:72 +0:09?0:07 +? qq 5 0:62 +0:07?0:05 low recoil mass 2 0:53 +0:09?0:06 high recoil mass 4 0:81 +0:08?0:06 total 6 1:34 +0:10?0:08 Table 1: Number of expected and observed events at p s =130{136 GeV and the corresponding probabilities. As an alternative classication in rows 3 and 4 events with low recoil mass m recoil < m`` and with high recoil mass m recoil > m`` are grouped into sub-classes.

6 Recoil Mass (GeV) (a) Recoil Mass (GeV) (b) Leptonic Mass (GeV) Leptonic Mass (GeV) Figure 4: Recoil mass versus leptonic mass for four fermion events at p s =130{136 GeV for (a) eeqq, and (b) qq events; the small dots are the prediction estimated from a FERMISV Monte Carlo sample of 200 times larger size than the data; the stars represent the 6 data events. 4 Conclusion We have presented QCD-results and studies of four fermion events at center-of-mass energies p s = 130{136 GeV. No deviation from QCD expectations is found in multihadronic events at LEP 1.5 and the combined value of s (133 GeV) = 0:113 0:003(stat) 0:009(syst) is in good agreement with the predicted running of the strong coupling constant. In an analysis studying four fermion processes with ``-jet-(jet) topology the collaboration observed 6 ``qq (`=e,) events, where 1:3 0:2 events are expected from the e + e?! ``qq process including background. No signicant deviations in the shapes of the measured dierential distributions from those predicted is seen. A similar but more general analysis performed by the ALEPH collaboration nds no excess of four fermion events searching for f f, 4` and ``qq nal states. References [1] L3 Collaboration, CERN-PPE/95-192, submitted to Phys. Lett. B [2] Collaboration, CERN-PPE/96-047, submitted to Z. Phys. C [3] DELPHI Collaboration, DELPHI PHYS 602, internal note. [4] N. Brown and W.J. Stirling, Z. Phys. C53 (1992) 629. [5] For a review, see: M. Schmelling, Phys. Scripta 51 (1995) 683. [6] ALEPH Collaboration, CERN PPE/96-43, submitted to Z. Phys. C [7] DELPHI Collaboration, CERN-PPE/96-05, submitted to Phys. Lett. B [8] L. Montanet et al., Phys. Rev. D50 (1994) 1173n. [9] S. Catani et al., Phys. Lett. B295 (1992) 269. S. Catani et al., Nucl. Phys. B407 (1993) 3. G. Dissertori, M. Schmelling, Phys. Lett. B361 (1995) 167. [10] S. Bethke, Nucl. Phys. (Proc. Suppl.) 39B,C (1995) 198. [11] J. Hilgart, R. Kleiss and F. Le Diberder, Comp. Phys. Comm. 75 (1993) 191. [12] Collaboration, CERN-PPE/96-031, submitted to Phys. Lett. B [13] Saul Gonzales et al. (ALEPH Collaboration), private communication.