Six-jet production at e+e− linear colliders

The calculation of the tree-level QCD processes ee → qq̄gggg, qq̄qq̄gg and qq̄qq̄qq̄ has recently been accomplished. We highlight here the relevance of such reactions for some of the physics at future electron-positron linear accelerators. 1. Motivations for an exact calculation of e+e− → 6 partons As accelerator physics will enter the Linear Collider (LC) epoch [1, 2], one will encounter a long series of resonant processes ending up with six-jet signatures. One should recall top quark production and decay for a start, whose study will represent one of the main areas of activity at a future LC [3]. Top quarks will be produced in pairs, via ee → γ, Z → tt̄, followed most of the times by tt̄ → bb̄WW → 6 jets. Then one should not forget the new generation of gauge boson resonances, such as ee → ZWW and ZZZ, and their dominant six-jet decays. The interest in these reactions resides primarily in the possibility of an accurate study of the gauge structure of the electroweak (EW) model [4]. In the same respect, one could also add highly-virtual photonic processes, like ee → γWW, γZZ, γγZ and γγγ, in which the photons split into quark-antiquark pairs. In addition, of particular relevance are reactions involving the Higgs particle, φ, e.g., in the Standard Model (SM), such as ee → Zφ → ZWW and Zφ → ZZZ – as discovery channels of a heavy scalar boson [5] – or ee → Zφ → Zφφ – as a means to study the Higgs potential of a light scalar (the latter decaying to bb̄) [6]. Given such a wide scope offered by six-jet final states, it is of paramount importance to have a strong control on the backgrounds. The parton-shower (PS) event generators (e.g., HERWIG [7] and JETSET/PYTHIA [8]) represent a valuable instrument in this respect, as they are able to describe the full event, from the initial hard scattering down to the hadron level. However, Matrix Element (ME) models are acknowledged to describe the large angle distributions of the QCD radiation better than the former do (see, e.g., [9]), which are in fact superior in the small angle dynamics. As in the processes we just mentioned the final state jets are typically produced at large angle and are isolated (being the decay products of massive objects), the need of exact ME computations should be Talk given at the 2nd ECFA/DESY Study on Physics and Detectors for a Linear Electron-Positron Collider, Lund, Sweden, 28-30 June 1998. manifest. As for theoretical advances in this respect, studies of ee → 6-quark EW processes are well under way (see Ref. [11] for a review). However, a large fraction of the six-jet cross section comes from QCD interactions. The case of QCD six-jet production from WW decays was considered in Ref. [12]. In this note, we discuss the dominant, tree-level QCD contributions to six-jet final states through the order O(α s), i.e., the processes: ee → γ∗, Z∗ → qq̄gggg, qq̄q′q̄′gg, qq̄q′q̄′q′′q̄′′, (1) where q, q and q represent any possible flavours of quarks (massless and/or massive) and g is a gluon, whose computation has recently been tackled [13]. 2. Numerical results In order to select a six-‘jet’ sample we apply a jet clustering algorithm directly to the ‘quarks’ and ‘gluons’ in the final state of the processes (1). For illustrative purposes, we use the Cambridge (C) jet-finder [14, 15] only. This is based on the ‘measure’ yij = 2min(E i , E 2 j )(1− cos θij) see , (2) where Ei and Ej are the energies and θij the separation of any pair ij of particles in the final state, with i < j = 2, ...6, to be compared against a resolution parameter denoted by y. In our tree-level approximation, the selected rate is nothing else than the total partonic cross section with a cut yij > y on any possible ij combination. The summations over the three reactions (1) and over all possible ‘massless’ (see Ref. [13] for a dedicated study of mass effects) combinations of quark flavours in each of these have been performed here. As for numerical inputs, they can be found in [13]. The six-jet event rate induced by the O(α s) QCD events at √ see = 500 GeV – the value that we use here for the centre-of-mass (CM) energy of a LC – can be rather large. Adopting a yearly luminosity of, e.g., 100 fb and assuming a standard evolution of αs with increasing energy, at y = 0.001 one should expect some 2300 events per annum: see Fig. 1. However, these rates decrease rapidly as y gets larger. From Fig. 1, one can appreciated how the dominant component is due to two-quark-four gluon events, followed by the four-quark-two-gluon and six-quark ones, respectively. These relative rates are of particular relevance to a LC environment. In fact, the capability of the detectors of distinguishing between jets due to quarks (and among these, bottom flavours in particular: e.g., in selecting top and light Higgs decays) and gluons, is of crucial importance there, in order to perform dedicated searches for old and new particles. The concern about background effects at a LC due to six-jet events via O(α s) QCD comes about if one considers that they may naturally survive some of the top signal The matching of fixed-order (as well as resummed) multi-parton final states with the subsequent PS to finally reach the hadronisation stage is also a pressing matter, towards which some progress has recently been made [10].