HLT Trigger for Jets at E 100 GeV in PbPb

In this section we describe the application of a cone jet finder algorithm to derive an on-line HLT jet trigger from TPC inspection of central PbPb collisions at 200 Hz rate. It is our purpose to test the jet detection efficiency, the degree of suppression of accidental background looking like jets and the specific demand on CPU time placed by the trigger algorithms over and above the computing budget already expended in the preceding clustering-tracking stages.

**Figure 1:** A typical di-jet tracking event with E of 300 GeV observed by CDF in Tevatron $p \overline {p}$ collisions [1].
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The present study is restricted to 100 GeV inclusive jets (without consideration, at first, of its near back-to-back partner). In principle the domain of jet total transverse energies that may be analyzed with ALICE charged particle tracking at 200 Hz PbPb event rate ranges from 100 GeV (where the statistics is good in one ALICE run year of about

sec) up to about 200 GeV where the jet statistics has dropped by a factor of about 15 and is, thus, marginal. The focus at E $_T\:\ge$ 100 GeV represents a qualitative consideration of the following conditions:

**Figure 2:** Typical 100 GeV Di-jet event with granularity $\Delta \eta = 0.1$ and $\Delta \phi = 0.25$ .
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In Fig. 1 we illustrate a typical di-jet tracking event with E

of 300 GeV observed by CDF in Tevatron $p \overline {p}$ collisions [1]. The jet related topological features dominate, by far, the non-jet related track background. This will be similar in pp at ALICE. However, note that the jet cone algorithm [3] employed in $p \overline {p}$ is aiming at an exhaustive coverage of the jet track manifold, down to tracks at rather large angle relative to the jet axis (to reconstruct the full fragmentation function). One thus normally employs a jet cone radius of $\mid R\mid=0.7$ in the plane of pseudorapidity $\eta$ vs. azimuthal angle $\phi$ (ranging from zero to 2 $\pi$ ). In ALICE this would comprise almost the full rapidity acceptance, and 22% of the azimuthal range. This may be appropriate for ALICE pp jet study but is clearly not useful in a straight forward manner under LHC PbPb conditions, because every such cone near mid-rapidity would now contain charged tracks with a total of about 650 MeV transverse energy, with a fluctuation RMS of about 45 GeV. This follows from a HIJING simulation assuming a midrapidity charged particle density of 6000. As the average charged track total E

of a 100 GeV jet is 60 GeV [1], the jets can not be well disentangled. Let us emphasize, again, that the LHC task considered here is only to find the jet candidate events. This requires a narrow jet cone finder algorithm - to exploit the overall typological jet pattern. Off-line analysis will subsequently study the jet activities in any cone required.

We wish to stay with the cone algorithm for its relative computational efficiency (required, at least, in the on-line analysis) but consider a significant reduction of R, to 0.3 or 0.2, for the process of on-line trigger generation, which is merely jet finding. The triggered events will then be written to storage in full raw data format, for off-line jet analysis of any kind. The jet finding conditions are illustrated in Fig. 1. Here and in the following, we use the code Pythia version 6.161 to generate elementary pp events with a contained hard parton scattering creating scattered partons of 100 GeV transverse momentum. These elementary events are then analyzed with the cone algorithm to identify the highest energy jet in the event, representing the outcome of the initial parton scattering. The charged tracks found within the cone of this particular jet are then embedded into a central PbPb HIJING event, represented by the charged track distribution in $\eta$ and $\phi$ . Actually it turns out that the HIJING average track and energy density is flat within the entire ALICE TPC acceptance of $\mid \eta_{CM}\mid \le \:1$ . Fig 1 thus represents the image of a typical 100 GeV di-jet event in a Lego plot with granularity $\Delta \eta = 0.1$ and $\Delta \phi = 0.25$ . The distribution and fluctuation of charged track transverse energy, observed here, would be typical of calorimetric summative

analysis. In this picture the typical jet correlation of high E

tracks, closely packed in a narrow cone about the jet axis, creates a topologically distinct pattern that stands out well above the background.

In ALICE we have to base recognition of the topological jet signature on an appropriate analysis of jet cone correlation among high E

individual charged particle tracks. For $p \overline {p}$ collisions at the Tevatron the CDF Collaboration has recently published a comprehensive study of jet physics, based on charged particle tracking only [2]. They study the systematic evolution of jet fragmentation functions upon variation of cone jet-finder algorithm, downwards from R=0.7 to 0.2 and note, in particular, that at R=0.2 still 80% of the total charged particle

is contained in the jet cone. This finding encourages us to work with cone radii of 0.3 and 0.2, respectively, for on-line jet finding to result in a fast trigger, in PbPb central collisions where higher cone radii would meet with increasing background fluctuations.

Within an on-line HLT clustering-tracking procedure for the entire event each track emerges with a determined center of mass momentum vector. For CPU economy of the ensuing jet finder algorithm it is essential to select the relevant track candidates right then, rather than depositing all tracks in a register that the cone finder would have to re-read. We thus base the jet finder on a cone correlation of high

tracks which are handed, above a certain

cutoff, directly from tracking to the jet finder algorithm. Within the latter we then inspect the event in terms of requiring n charged tracks above a

or E

cutoff of m GeV, contained within a cone of radius R=0.2 or 0.3 in $\eta$ and $\phi$ .

**Figure 3:** Efficiency of cone jet finder trigger applied for different cone radii and thresholds. At least 4 charged particles over threshold are required to be inside the cone.
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In the simulation with elementary Pythia jet identified events of 100 GeV initial partonic transverse energy/momentum, imbedded into HIJING simulated events for central PbPb collisions, at ALICE energy and within the ALICE acceptance, we have studied the jet-detection efficiency and accidental background rate of various trigger-defining options, employed in the cone jet-finder algorithm. As an example Fig. 1 shows the resulting jet recognition efficiency requiring at least four charged tracks correlated within jet cone radii ranging from 0.1 to 0.7, for various track

cuts ranging from above 2 GeV/c to above 5 GeV/c. Fig. 1 illustrates the selectivity of these cone trigger options, in terms of accidental background being created by random $p_T, \: \phi$ fluctuations in average HIJING central PbPb simulated events. The finite ALICE transversal momentum resolution should not lead to significant changes.

**Figure 4:** Background suppression rate of cone jet finder trigger measured on Hijing background events. Parameters for the jet trigger are the same as in Fig. 1.
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At the level of this preliminary study an optimum of trigger efficiency vs. accidental trigger background rate may be accomplished in requiring 4 charged tracks above 4 GeV transverse momentum within a jet cone of R=0.2. The resulting jet efficiency, of about 0.72, coincides with a background suppression rate of 4 %. I.e. this trigger mode, as applied in HLT central PbPb collisions inspection at 200 Hz, created a jet candidate trigger rate of about 8 events per second that can easily be written to tape, for comprehensive off-line analysis. Furthermore, the events collected under this HLT trigger mode can be considered as almost bias free concerning any other physics observable of interest: more than 99% of the resulting HLT triggers are based on random event-by-event fluctuations in the high

sector, immaterial to many other ALICE physics observables.

We thus argue that an appropriate on-line HLT jet trigger based on charged track 3-momentum determination on-line, at the tracking stage, and on an optimized cone-type jet-finder algorithm, will offer the required jet recognition efficiency, within a selectivity above background that will reduce the 200 Hz rate of HLT inspected central PbPb TPC events, down to a candidate trigger rate of about 8 Hz (essentially bias free as concerns analysis of any other physics observables, except for high E

jets). This latter event rate fits well within the overall anticipated ALICE TPC to DAQ bandwidth, of 20 events per second. Thus it will be possible to record other trigger modes concurrently.

It remains to be shown that the HLT jet-cone trigger search algorithm, as implied in this section, does not inflict a significant additional budget concerning CPU time, in addition to the -already maximal- HLT task, to perform cluster and track analysis for central PbPb TPC events at 200 Hz rate. At present we estimate the jet cone algorithm to require less than 10 milli seconds in the mode illustrated above. Both this estimate, and also the accidental background should improve with a further, more comprehensive optimization of the detailed trigger conditions.

It may turn out that a higher jet recognition efficiency may actually result from exploiting the approximate back-to-back topology of dijet production (this trigger mode could also be more interesting, physics-wise!). One could thus search with a double cone algorithm, relaxing the charged high p

track number requirement in each cone from the above 4-5 down to 2-3. In a single cone this leads to jet recognition with up to 90% efficiency but creates too high a background accidental rate. The additional topological constraint implied by di-jet events should significantly reduce the background rate, yet leaving one with an overall dijet efficiency of about 80%.

HLT Trigger for Jets at E $_T\:\ge$ 100 GeV in PbPb

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