The implementation of the four-jet matrix elements in HERWIG and elsewhere

The new version [1] of the HERWIG event generator [2] allows one to simulate hadronic final states in electron-positron annihilations using the O(αs) partonic matrix elements (MEs) for ee → qq̄gg and ee → qq̄QQ̄. The consequent phenomenology is discussed in the case of four-jet signatures of particular relevance to future electron-positron Linear Colliders (LCs), such as in Higgs boson searches. The new approach adopted in HERWIG is compared to the standard O(αs) description, as well as to other recently presented event generators also based on ee → 4 parton MEs. Four-jet events will play a crucial role at future LCs [3]. Just one example is sufficient to make this point. Such machines are an ideal laboratory where to pursue studies in the Higgs sector [4]. In this respect, it should be recalled that ee → 4 jet processes from QCD will represent a serious noise in the search for Higgs particles, both in the standard electroweak (EW) theory and in possible extensions. In particular, in the Standard Model (SM), the dominant Higgs production channel proceeds via the ‘bremsstrahlung’ process ee → HZ [5], followed by the hadronic decay H → bb̄ (in the intermediate MH regime), with the Z boson going into pairs of jets about 70% of the times. Thus, it is very important that four-jet events from QCD are correctly implemented in the Monte Carlo (MC) programs that are widely used in phenomenological studies of hadron production at ee colliders. In this connection, it has always been rather worrying that certain aspects of four-jet production were never well described by the standard ‘O(αs) ME + parton shower (PS)’ MC programs. As an illustration, one may recall the four-jet studies performed by the ALEPH Collaboration at LEP1 [6], which had revealed a significant disagreement between data and MCs in the typical four-jet angular variables (see Ref. [7] for the definition and the discussion of some of their properties): (i) the Bengtsson-Zerwas angle χBZ; (ii) the Körner-Schierholz-Willrodt angle ΦKSW; (iii) the (modified) Nachtmann-Reiter angle θ NR; (iv) the angle between the two least energetic jets θ34. Talk given at the 2nd ECFA/DESY Study on Physics and Detectors for a Linear Electron-Positron Collider, Padova, Italy, 4-8 May 2000. Figure 1: Differential distributions for the polar angle of the reconstructed Z. In Ref. [8], it was argued that the discrepancy was nothing but the evidence that the standard ‘O(αs) ME + PS’ MCs do not provide a correct description of the spin correlations among the various partons, particularly at large jet separations. In fact, the above angular quantities are defined in terms of the three-momenta of the particles in the final state and are precisely the spins of the latter that induce very peculiar orientations in (i)–(iv). Conversely, ‘O(α2 s) ME’ programs (for example, the ‘O(α2 s) ME + string fragmentation model’ as implemented in JETSET, i.e. with no parton shower) yielded a much better angular description of four-jet final states, see Refs. [6, 9]. In fact, all spin correlations are naturally included in a full O(α2 s ) ME calculation, but they are not necessarily present in a PS emulation based on the O(αs) scattering, although their availability (in the infrared limit, where soft and collinear correlations can be factorised in analytic form) is a feature of some of the above mentioned MC codes (for example, for the HERWIG implementation, see Ref. [10]). However, even an ‘O(α2 s) ME + fragmentation’ model, without the PS evolution, is inadequate to describe QCD four-jet production in ee collisions. The problem is that such ME models contain ‘ad-hoc’ hadronisation which is adjusted to produce a good agreement with some data [6, 11], but they cannot be extrapolated to other energies. Furthermore, their description of the sub-jet structure