Results on HIJING background studies


1. Introduction

An essiantial question for the jet finding in AA-collisions is the expected background from the underlying soft interactions. This sections contains some studies of this background.

2. Results

2.1  ET in cones (status 11/15/02)

HIJING 1.38 was used to generate 1000 Pb+Pb collisions at 5.5 TeV. The standard parameters were used, the impact parameter was set to be between 0-2fm. Only charged tracks were used.

Figure 1 shows the HIJING dn/deta distribution. The simulated dn/deta at midrapidity is ~6000. Figure 2 shows the track density in the eta-phi space. No structures in phi are visible and a plateau around midrapidity, which was already observed in figure 1. Since we are only interessted in the midrapidity region, this allows us to use a simple procedure to calculate the background in cones. A position within -0.3 < eta < 0.3 is randomly choosen (see figure 3) and then the Et in a cone with radius r is calculated for different radia.


Fig 1: dn/deta distribution of the HIJING events


Fig 2: track density in eta-phi space

Figure 3 shows the distribution of the randomly choosen cone centers in eta-phi space. For each of the 100 events, 20 cone positions were generated, resulting in 10,000 different cones for analysis.


Fig 3: Cone center positions

The ET in cones with different radia was calculated for each of the randomly choosen cone center positions. Figure 4 shows the ET distribution for the 14 different radia. For each ET distribution, the ET and the RMS were calculated. They are shown in figured 5 and 6. The expected quadratic dependence on the radius is observed.


Fig 4: ET in cones with different radia


Fig 5: mean ET in cone for different radia


Fig 6: RMS of the ET distributions for different radia


2.2 Estimates of trigger background rates (status 11/15/02)

The simple trigger is defined as nParticles with a transverse momentum larger than PtThreshold  (as in the ConeFinderSection 7.1.1). Five different PtThresholds were used (1, 2, 3, 4 and 5 GeV/c). All Results are from the same 1000 events which were used in the previous section 2.1.

Figure 7 shows the number of charged particles above PtThreshold for the different thresholds (red=1,green=2...). Please note the logarithmic x-axis. The acceptance was limited to -1<eta<1,0<phi<2*pi. Figure 8 shows the same on a linear scale for the lower nCharged part.

Figure 9 shows the mean number of charged particles per event as function of the PtThreshold, the error-bar shows the RMS of the distribution.

Using this information, one can try to make some simple calulations how many particles one would expect in a cone with radius R. The total area is given by 2 * 2 * pi, the area in the cone by pi*R^2. The number of particles in the cone can the be calcultaed as nCharged*area_Cone/area_total. This assumes of course independent particle production (which is wrong...) But this gives nevertheless a first estimate. Figure 10 shows the results, black is for 1 GeV/c PtThreshold, red=2...


Fig 7: Number of charged particles per event for different PtThresholds


Fig 8: Number of charged particles per event for different PtThresholds


Fig 9: Mean number of charged particles per event as function of PtThreshold


Fig 10: Estimated number of charged particles above PtThreshold in a cone with radius R.

Figure 11 shows the results for the mean number of charged particles above PtThreshold for the different cone radia as they can be observed in the HIJING events. There is a good agreement with theoretical estimate of figure 10 :-). To estimate the trigger background rate, we are more interested in the fluctuations of the number of particles above PtThreshold. Figure 12 shows the RMS of the nCharged above PtThreshold distributions.


Fig 11: Number of charged particles above PtThreshold in a cone with radius R


Fig 12: RMS of the number of charged particles above PtThreshold in a cone with radius R

Figures 13 to 16 show the trigger "efficiency" for background events as function of nParticles above PtTreshold. The different color indicate the different PtThreshold (black = 1GeV/c, red = 2, green =3, blue = 4, yellow = 5). Figure 13 uses a cone size of 0.7, figure 14 a cone size of 0.5, figure 15 a cone size of 0.3 and figure 16 a cone size of 0.1.

The efficiency is here defined as number of  cones with more than nParticles charged  particles above PtThreshold divided by the total number of cones. Is this correct? I'm not so sure... The plots show the probability to observe a cone with more than nParticles above PtThreshold in a HIJING event. The trigger algorithm would have to look for all possible eta-phi positions, so it looks into many cones per event. These cones are however highly correlated... And the probability to observe a cone with more than nParticles above PtThreshold in a HIJING event should be the same as the probability to trigger the event... I'm going to check this, maybe I'm just to confused now...

If I have 0 entries, I don't plot the bin. The error calculation is missing, the last blue and yellow bin in figure 16 has only one entry, which should give a large error.

But these plots give a first estimate of the background rate and where to set the trigger algorithm parameters. What is the background rate we would like to get? One can compare this to the trigger efficiency for signal (100 GeV jet) events (figure 16, section 7.1.1) There the jet radius dependence is unfortunaly missing...



Fig 13: Trigger "efficiency" for background events as function of nParticles above PtThreshold (cone radius = 0.7)


Fig 14: Trigger "efficiency" for background events as function of nParticles above PtThreshold (cone radius = 0.5)


Fig 15: Trigger "efficiency" for background events as function of nParticles above PtThreshold (cone radius = 0.3)


Fig 16: Trigger "efficiency" for background events as function of nParticles above PtThreshold (cone radius = 0.1)


Conclusions:
Thorsten Kollegger
Constantin Loizides
IKF - University of Frankfurt
Last updated: 11/15/2002 18:32pm EST