Fermion pair production at LEP2 and interpretations
Abstract
Preliminary results on , , including all LEP2 data are discussed. Good agreement is found with the Standard Model up to the highest energies. Limits on possible new physics are extracted.
To appear in the Proceedings of the New Trends in HighEnergy Physics
Yalta, Ukraine, September 22  29, 2001.
Fermion pair production processes have been measured by the four LEP experiments up to GeV [1]. Above the peak radiation is very important, leading in particular to a high rate for the radiative return. Events can be classified according to the effective center of mass energy , which is measured in different ways. A typical inclusive selection requires , while events with only a low amount of radiation (exclusive) are defined by . Exclusive events are obviously more relevant to look for new physics. The signal definition is complicated by initialfinal state interference. Two theoretical definitions have been considered for in the combinations of LEP data:

channel propagator mass, with interference between initial and final state radiation subtracted (used by L3 and OPAL);

bare invariant mass of the dilepton pairs, or channel propagator mass for hadronic final states, with interference included (close to ALEPH and DELPHI definitions).
For pairs is not natural, as channel exchange diagram dominates: in this case nonradiative events are selected by a cut on the acollinearity angle of the final state electrons, typically . Another delicate point is the contribution from 4fermion processes which enter the pair selection, which has to be defined by a cut on the invariant mass of the extra pairs.
Theoretical uncertainties have been assessed during the LEP2 MC Workshop [2] and are presently well below the experimental errors for , and pairs. They amount respectively to for and for or cross sections. On the opposite side, the theoretical uncertainties on Bhabha cross sections are still large, in the barrel region and in the endcap regions: a sizeable reduction (factor ) is desired to exploit the experimental precision.
Preliminary combinations of LEP data exist for the exclusive cross sections and for and cross sections and forwardbackward asymmetries over the whole energy range ( GeV) [1], as shown in figure 1. Standard Model (SM) expectations are obtained with ZFITTER [3]. Correlations within/between experiments have been taken into account in the combinations. The combined errors are dominated by statistics and uncorrelated systematics. Moreover differential cross sections have been combined for and pairs for GeV. Available heavy flavour measurements of , , , have been combined at all LEP2 energies [1]. Bhabha measurements have not been combined yet, though each experiment has a complete set of measurements, see for example [4] or the references in [1]. All the LEP averages are in good agreement with the SM predictions, as each experiment’s results. Therefore such data have been used to set indirect limits on a number of new physics scenarios.
An alternative test of the Standard Model is possible in the matrix approach [5]. In this framework the only assumptions are the existence of a heavy neutral boson () in addition to the and validity of QED for photon exchange and radiation. In particular / interference is left free, while it is usually constrained by the SM itself in fits of the lineshape. LEP1 data have low sensitivity to exchange and  interference. An matrix fit restricted to LEP1 data shows a strong correlation between the fitted mass and the parameter related to  interference in the hadronic cross section. In a L3 analysis [6] such correlation brings about an additional MeV uncertainty to . LEP2 data strongly constrain  interference terms. L3 [7] fitted jointly all LEP1+LEP2 cross section and asymmetry measurements, either assuming lepton universality or not. The result is MeV ( MeV without lepton universality), in agreement with the SM lineshape fit. Here the correlation is reduced and contributes an error of MeV, already included in the quoted result. The fitted value of is , in agreement with the SM prediction of . Similar results have been obtained by OPAL [8].
A convenient way to describe any deviation from the SM in is the framework of fourfermion contact interactions [9], which is appropriate if the scale of new physics is much greater than . LEP averages of and cross sections and asymmetries have been used for such indirect search. They give at present the best lower limits on the scale for contact interactions, in the range of to TeV depending on the specific model ( C.L. limits assuming conventionally a strong coupling ) [1]. In detail the limits for each model and both signs of interference between the hypothetic new interaction and the SM are shown in Fig. 2 (left plot). Furthermore LEP combinations of heavy flavour measurements have been used to set lower limits on and contact interactions. Depending on the model they are in the range of  TeV for and  TeV for [1].
Limits on the masses of new heavy particles have been extracted also within specific extensions of the SM. This is actually appropriate when the mass of the new particle is of the same order of magnitude as the center of mass energy. New particles coupling to leptons and quarks could be leptoquarks [10] or squarks in supersymmetric theories with Rparity violation. Beyond the kinematic limit for direct production, they could be observed through a change of the total cross section and asymmetry in the process via a channel exchange diagram [11]. The best LEP limits come presently from ALEPH [12]. They have been extracted separately for leptoquarks/squarks of each of the three families, profiting of tagging and jetcharge techniques. It is assumed only one new particle contributing at a time, with coupling only to left or righthanded leptons. In particular the mass limit for coupling to first or second generation quarks (equivalent to or ) is about GeV, for coupling to third generation quarks (equivalent to ) is about GeV ( C.L. limits assuming electromagnetic strenght for the coupling ). They are complementary to limits obtained from HERA, Tevatron, and low energy data (atomic parity violation, rare decays).
Supersymmetric theories with Rparity violation have terms in the Lagrangian of the form , being L a lepton doublet superfield and E a lepton singlet superfield. The parameter is a Yukawa coupling and , , , , are generation indices. For dilepton final states, both and channel exchange of Rparity violating sneutrino can occur [13]. The strongest limits are obtained when channel resonant production of or is possible. This could be detected, depending on the non vanishing couplings, in the , or decay channels. Dilepton differential cross sections have been used by ALEPH to set upper limits on the couplings as a function of the sneutrino mass. / masses of a few hundreds GeV/c are probed and excluded for relatively small couplings [12]. Much weaker limits can be extracted for .
Additional heavy neutral bosons are predicted by many GUT models [14]. LEP data at the peak energy are sensitive to the mixing angle of the with a possible heavier , while LEP2 data are sensitive to its mass . Fits using all hadronic and leptonic cross sections and leptonic forwardbackward asymmetries are consistent with no extra . DELPHI results [15] are shown in Fig. 2 (right plot). The upper limits on the mixing angle are about mrads. Assuming the combined LEP data have been fitted to determine C.L. lower limits on the mass. The resulting limits are GeV respectively for model, GeV for model and GeV for [1].
Recently an idea has been proposed that Quantum Gravity scale could be as low as TeV if gravitons propagate in large compactified extra dimensions, while other particles are confined to the ordinary 3+1dimensional world [16]. Gravity would be modified at distances of the order of the size of the extra dimensions. This would solve the hierarchy problem, that is the striking difference between the electroweak scale ( GeV) and the Planck scale ( GeV). Existing gravity measurements stop at about mm, leaving room for new physics below this scale. New effects could be within the reach of present and future colliders. Virtual graviton exchange would modify the fermion pair cross sections through interference terms proportional to , where is a parameter of depending on the details of the theory and is a mass scale related to the Planck scale in the dimensional space [17]. Pure graviton exchange would lead to terms of order . Bhabha scattering has the maximum sensitivity to low scale gravity effects, due to interference with the dominant channel photon exchange. ALEPH [12], L3 [18] and OPAL [19] have analyzed all LEP2 Bhabha data and obtained lower limits on at about TeV. Such limits are derived by setting to account for positive or negative interference, with defined according to [17], and are shown in Table 1.
In the near future each experiment is expected to finalize its data analyses while the LEP working group should find a final agreement on exactly how to do the combinations (definitions, method, common uncertainties) and which results to combine. In particular Bhabha measurements are still in the waitinglist. They are the most sensitive ones for many indirect searches, but in this case theoretical uncertainties could be a serious limitation for the final results.
ALEPH  1.18  0.80 
L3  1.06  0.98 
OPAL  1.00  1.15 
Acknowledgment
I wish to thank all the organizers for the interesting conference
and the nice week we spent together.
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