Jet Trigger Algorithm
1. Trigger algorithm
A very short description of the trigger algorithm: If there are >=
nParticles with pT>PtThreshold in a cone with radius R
, we accept the event. Cone are calculated around each trigger particle,
which is defined as a particle with pT>PtThreshold. A small comment: It
would be probably better to calculate the cones for many fixed positions in
the event. This is how it is done in the seedless cone jet finder. But please
note that the original UA1 cone jet finder uses also high-Et seeds to limit
the number of cone positions per event, so this is not so wrong.
2. Background rate from HIJING events
First results on the expected background trigger rate have been already
shown in section xx. I repeat some of them here to show how they are connected
with the trigger results presented here.
Figures 1a)-d) show the trigger efficiency for random cones in HIJING as
function of nParticles for different PtThresholds. The different color indicate
the different PtThreshold (black = 1GeV/c, red = 2, green =3, blue = 4,
yellow = 5). This shows the trigger efficiency for a random cone
in HIJING. Just to be sure: this is the trigger efficiency (or probablity)
for a random cone, not a HIJING event. (see below)
Fig1a: Trigger efficiency for HIJING background cones (cone radius =
0.7)
Fig 1b: Trigger efficiency for HIJING background cones (cone radius = 0.5)
Fig 1c: Trigger efficiency for HIJING background cones (cone radius = 0.3)
Fig 1d: Trigger efficiency for HIJING background cones (cone radius
= 0.1)
Why is this not the trigger efficiency or probabilty for a hijing event?
For the trigger algorithm, we look not only at one random cone. We rather
look on many cones. One should note that not all of these cones are independent,
therefore the trigger probablity for a HIJING event is not the number of
cones times the trigger efficiency from figures 1a)-d).
The only way to get trigger efficiency for HIJING events is to run
the trigger algorithm on them. I've done this for 1000 HIJING events, the
results are presented in figures 2a)-2... Unfortunaly I changed the meaning
of colors and the x-axis. Plotted here is the trigger efficiency as function
of the cone radius, the colors indicate different PtThresholds as in figures
1a)-d). As expected, the trigger efficiency (probablity) is much higher
than the ones shown in figures 1. Some comments to the plots: There are
no error bars :-(. That's simply because I don't know how to calculate it
correctly for this case. The minimal background trigger probablity I could
measure is 10^-4, since I used only 1000 HIJING events. 10^-4 probability
means one triggered event...
Fig 2a): Trigger efficiency for HIJING background events (nParticles
>= 1)
Fig 2b): Trigger efficiency for HIJING background events (nParticles
>= 2)
Fig 2c): Trigger efficiency for HIJING background events (nParticles
>= 3)
Fig 2d): Trigger efficiency for HIJING background events (nParticles
>= 4)
Fig 2e): Trigger efficiency for HIJING background events (nParticles
>= 5)
To summaries this part: Plots 2a)-e) show the results in which we are
interested. We are clearly limited in statistics, we must produce
~50.000 events for reasonable results and precision. But these plots allow
a first realistic view of the expected background rate.
3. Efficiency for PYTHIA events
3.1 Efficiency to trigger a 100 GeV jet
The results of the cone jet finder allow us to look directly at identified
jets (see section xx). Figure 3 shows again how these jets are defined:
the leading jet in the event with 85<Et<110 (blue area). Figure 4
shows the trigger efficiency as number of charged particles for one of these
100 GeV jets. The search radius of the jet-finder was 0.7, the actual jet
might be somewhat larger due to the merging/splitting step. To be sure:
this is the probablity to trigger one 100 GeV jet. Please
see section 3.2 why this doesn't tell the whole story. And section xx for
details of these plots.
Fig 3: Et distribution of leading jets from the cone finder, blue jets
are used for further analysis
Fig 4: trigger efficiency for a 100 GeV jet
3.2 Efficiency to trigger a 100 GeV jet pythia event
Figure 4 shows the trigger efficiency for a identified 100 GeV jet from
the cone finder. But in what we are more interested is the trigger efficiency
for events containing a 100 GeV jet. Why is this not the same: first of
all, most of the events (or all we are looking in the moment) are dijet-events,
there are two independent jets back-to-back in the event. Most of the time
the cone finder finds actualy both of them. Let's for the moment assume
they are completly independent. Then the trigger efficiency would be a factor
1-(1-P(jet))^2 higher, where (1-P(jet)) is the probability to not trigger
the jet. A second effect is the possibility to combine some of the particles
from one jet with background from the beam-remenants (the underlying event)
or the other jet. One would therefore expect that the trigger efficiency
for events is higher than the one for a single jet.
Figure 5a)-e) show the result: The color coding is the same as for figures
2a)-e) indicating the different PtThresholds. Again, there are no errors.
But the number of events in this case is 100.000, resulting in >>10.000
100 GeV jets. And the number of triggered events is also very large, one
could therefore use gaussian statistics to calculate the errors. We are in
this case not statistically limited. And we see the expected enhancement
compared to figure 4.
Fig 5a): Trigger efficiency for a PYTHIA event with a 100 GeV jet (nParticles
>= 1)
Fig 5b): Trigger efficiency for a PYTHIA event with a 100 GeV jet (nParticles
>= 2)
Fig 5c): Trigger efficiency for a PYTHIA event with a 100 GeV jet (nParticles
>= 3)
Fig 5d): Trigger efficiency for a PYTHIA event with a 100 GeV jet (nParticles
>= 4)
Fig 5e): Trigger efficiency for a PYTHIA event with a 100 GeV jet (nParticles
>= 5)
To summarize this section: Figures 5a)-e) show the trigger efficiency
for a PYTHIA event with a 100 GeV jet. Why this is only the lower limit
of the trigger efficiency in which we are interessted is explaint in section
4.
4. Efficiency for PYTHIA jet events embedded in HIJING background events
We've calculated in section 2.2 the trigger efficiency for a PYTHIA event
containing a 100 GeV jet. But in what we are really interested is the trigger
efficiency for a Pb+Pb event containing a 100 GeV jet. Why is this not the
same: In the heavy-ion reaction we have a mixture of many semi-hard and
hard parton collisions in the same event. We have seen in section 2.2 that
the trigger efficiency for a 100 GeV event is not the factor 1-(1-P(jet))^2
higher as the one for a single jet, as one would expect from momentum conservation
leading to dijet-events. The rest of the increase of the trigger efficiency
is believed to come from random combinations with the underlying event. Since
in a heavy ion collision, I have much more particles in the underlying event,
the probabilty of such combinations is much higher, leading to an increased
efficiency.
How to calculate this effect: embed the particles from PYTHIA events
where we identified a 100 GeV jet with the cone finder into the hijing background
events and then run the jet trigger algorithm. First some technical details
of the embedding. We run the cone jet finder on a PYTHIA event. If he finds
a 100 GeV jet (85 GeV<Et<110GeV), then all particles from the event
are embedded into a HIJING background event. This is not completly right,
in principle we simulate a Bi+Bi collisions. And we assume that each binary
collisions is independet of all others, that no color strings are formed
to other participating nucleons and that there is no stopping... But I don't
know another possibility to simulate it right now...
Prediction before analysing the events:
But: I'm convinced that the trigger efficiency is
again higher than the one for a PYTHIA event. And more important,
that this is the trigger efficiency in which we are interested and which
should be compared with the background rate from figures 2.
Please look into figures 6a)-e). As expected we can observe a significant
increase of the efficiency compared to PYTHIA events. This is the efficiency
in which we are interested. These results can be directly compared
to figures 2a)-e).
Fig 6a): Trigger efficiency for a HIJING event with a 100 GeV jet (nParticles
>= 1)
Fig 6b): Trigger efficiency for a HIJING event with a 100 GeV jet (nParticles
>= 2)
Fig 6c): Trigger efficiency for a HIJING event with a 100 GeV jet (nParticles
>= 3)
Fig 6d): Trigger efficiency for a HIJING event with a 100 GeV jet (nParticles
>= 4)
Fig 6e): Trigger efficiency for a HIJING event with a 100 GeV jet (nParticles
>= 5)
I guess we have now everything we need for the trigger efficiencies. The
question where to set the cuts on nParticles,PtThreshold and ConeSize
depends on the allowed background rate and the efficiency. The trigger algorithm
depends strongly on the underlying event, which causes some stange properties.
The trigger efficiency will go down for min-bias events... But given the
definition of a jet as topology of particles in the event, I don't know a
way to avoid this...
5. Some last thoughts why this is not completly correct:
I believe we still underestimate our trigger efficiency: We
are in first order not interested in trigger efficiency compared to an ideal
jet but in the one compared to the ones found by the offline software. So
far we have only looked into ideal/perfect jets, using also the information
on neutral and EM particles. As we know, this can not be done in the experiment.
The jets which offline will find are not the same jet's we've used so far.
It would be easy to fix this in p+p by rerunning the cone jet finder using
only the charged particles, but this doesn't help: We still don't have an
algorithm for heavy ion collisions... Therefore I believe that's this is
all what can be done in the moment, one might however argue that the real
efficiency is higher...
So far, we have not included a simulation of ALICE and it's reconstruction/HLT
software. This is critical to get the efficiencies right, but impossible
in the moment. The only thing so far we have done is to restrict the phasespace
to -1<eta<1. Let's assume that the single track tracking efficiency
is 90% and the acceptance in this eta-region is also 90% (sector boundaries).
Then we reconstruct only 81% of the particles, which shift's the nParticles
threshold by ~20%. This means the nParticles threshold here is ~ real nParticles
threshold+1. But again, offline will have the same problems, therefore it
will be only a second order effect for the efficiency.
And of course we have not addressed the problem how to simulate the
jet energy loss... And how our trigger algorithm reacts on the change
of the the fragmentation function.
A last comment: So far we have only looked at the trigger efficiency
for 100 GeV jets. In reality, the trigger algorithm will also trigger e.g.
50 GeV jets with a lower efficiency. To really calculate the trigger rate,
one would have to simulate minimum bias PYTHIA collisions, embed them into
HIJING and then run the trigger algorithm. If one folds the resulting efficiency
distribution with the expected cross-section for jet production, one has
the trigger rate. This rate might be quite high...