The effects of colour coherence on the emission pattern of jets in e+e- collisions are well known and intuitive. However in hadron-hadron collisions the large number of possible colour flows involved in jet production complicates the identification of variables sensitive to coherence. Here, radiation patterns in gp collisions are studied by considering events where soft radiation is hard enough to form a jet. This reduces the effect of secondary interactions in resolved photoproduction.
The effects arising from different implementations of coherence were studied using 500 pb-1 of events generated with PYTHIA 5.7 [2] and HERWIG 5.8 [3]. Direct and resolved events were generated separately and combined according to their cross sections. Events were generated with a minimum pT of 20 GeV using the GRV proton and photon structure functions [4]. Two event samples were generated using PYTHIA: the PYTHIA Coherent sample and the PYTHIA Incoherent sample which was obtained by switching off the coherence in the parton shower and the initial-final state coherence. HERWIG represents an alternate implementation of coherent processes. Jets of particles were found using the KTCLUS [5] algorithm in covariant pT mode with radius equal to 1. Three jet events with at least two jets of transverse energy (Etjet) satisfying Etjet > 30 GeV and a third jet of Etjet > 3 GeV were selected. The jets are ordered by Etjet decreasing and referred to as ``first'', ``second'' and ``third'' jet acccordingly in the following. Two scenarios were considered, one to reflect the acceptance in jet pseudorapidity (hjet) of the present ZEUS detector, |hjet| < 2.5, and one to show the possibilities with an extended acceptance, |hjet| < 4. In addition the events satisfied 0.2 < y < 0.85 and P2 < 4 GeV2, where P2 is the negative of the four-momentum squared of the photon.
An overall drop in cross section is observed between incoherent and coherent event samples. For example, with a luminosity of 250 pb-1 and the standard detector acceptance, |hjet| < 2.5, 2600 multijet events are predicted by PYTHIA Incoherent, 1728 by PYTHIA Coherent and 1665 events by HERWIG. For comparison in the extended acceptance scenario, |hjet| < 4, 3012 multijet events are predicted by HERWIG.
The angular distribution of the third jet is also affected. Following [6] the angle a is defined as the azimuthal angle of the third jet about the second jet in the h- f plane. Here, however, we use centre-of-mass (c.m.) variables so a = arctan(DH / |Df|) where DH = sign(h2cm) (h3 - h2) and h2cm = h2 - 1/2 (h2 - h1) and Df = f3 - f2. h1, h2 and h3 refer to the pseudorapidities in the lab frame of the first, second and third jets respectively and positive h is in the direction of the incoming proton. Df is the difference in azimuth (f) between the second and third jets (in radians). The definition of a is illustrated for a typical event geometry in Fig. 2(c).
Canonical detector effects were simulated by smearing the HERWIG jet quantities with Gaussian distributions of varying widths. A resolution of 20% (10%) was used to smear the Etjet of jets with Etjet < 10 GeV (Etjet ³ 10 GeV). The width of the difference between generated and detected values of hjet and fjet was taken to be 0.1. As shown in Fig. 2(a) such detector effects should not seriously hinder the measurement of a distributions.
The coherent emission of soft radiation does not have a strong effect on the jet profiles of the first and second jets. For instance, in Fig. 3(a) the transverse energy profile of the second jet is shown.
One of the anticipated effects of colour coherence is that radiation from an incoming parton should be inhibited in regions far from the initial partons direction. Therefore in direct photoproduction events, where the single coloured parton in the initial state has positive h, the coherent emission pattern should be at relatively higher h than the incoherent emission. We have selected a subsample of events which is enriched in direct photon events by requiring xg > 0.8 where xg = (åjets Etjet e-hjet) / (2 Eg). The sum runs only over the two highest ETjet jets and Eg is the energy of the incoming photon. The h of the third jet in the c.m. frame, h3cm = h3 - 1/2 (h2 - h1), is shown for this selection in Fig. 4(a).
Resolved events, with incoming coloured partons from both the g and p directions, should show an effective enhancement of radiation in coherent processes both at higher positive and at more negative pseudorapidities in comparison to incoherent emission. This effect is evident as shown in Fig. 4(b). Note that the extended acceptance scenario must be employed in order to see the relative enhancement of radiation at high h in resolved events.
To summarize this section, a high integrated luminosity ( ~ 250pb-1) is desirable in order to accumulate statistics in multijet events at high Etjet. However luminosity upgrades which involve a significant reduction of forward acceptance are not worthwhile for this study. They destroy the sensitivity to colour coherence without significantly improving the statistical uncertainty.
The calculation at the generator level was done using the GRV proton structure function [4] and minimum pT equal to 2.0 GeV. The H1 detector simulation was taken into account as well. A jet-cone algorithm [7] with radius equal to 1 was used for the selection of two jets and gamma-jet events with Etjet or g>3 GeV and jet (or final g) emission angles 25-155o. This procedure corresponds to the selection of mainly direct processes. The calculated flow of charged particles with pt>0.2 GeV emitted at angles of less than 20o to the reaction plane is shown in Fig. 5(right) as a function of the scale angle W. W is defined [8] as the ratio of the particle angle qh to the angle between partons. W = 0 corresponds to the direction of the initial state photon; W = 1 - the final state quark; W = -1 - the final state g, gluon or antiquark for QEDC, QCDC or PGF respectively; W = -2 or 2 - the proton remnant.
It is seen that in the scale angle region between 1 and 2 (region II in Fig. 5) SF (solid histogram, generator level) and IF (dashed histogram, generator level) give different predictions for N. SF taking into account colour forces leads to a suppression of particle flow which is especially strong for QCDC process. The H1 detector simulation (dark circles, SF) weakly distorts the generator level N distribution except for directions close to remnant proton emission where detector acceptance is rather low. Thus colour coherence effects can be observed at the detector level.
It is interesting to consider ratios of particle flows N for different processes since the ratio is less sensitive to experimental errors. The ratios R = N(QCDC)/N(QEDC), R* = N(QCDC)/N(PGF) are shown in Fig. 6.
To observe colour coherence at the fragmentation stage of hadron production in direct processes it is necessary to distinguish these processes from resolved photoproduction and to separate QEDC, QCDC and PGF from each other. The jet selection procedure used here enriches the data sample with direct processes. Further enrichment can be achieved by going to larger Etjet or g and by choosing events with xg close to 1. Since the direct processes cross section is low we expect ~ 230 QEDC events at the detector level for an integrated luminosity of ~ 100 pb-1. So higher luminosity is needed to study interjet coherence.