## C. EMCal Trigger

### C.I Trigger Requirements 

The output bandwidth limitation from the ALICE detector drives the
ultimate need for a trigger to pre-select events that have high p~T~
jets within the EMCal acceptance. The final bandwidth to the long term
data storage media sets a limit on the amount of data that can be
permanently recorded for offline analysis. Thus, in turn, the size of
the event buffers will govern the final rate at which events can be
recorded. The unbiased occurrence rates for jets with p~T~ below about
50 GeV/c in EMCal are sufficiently large that no dedicated EMCal trigger
is required. The important range for an EMCal jet trigger is for p~T~
well above 50 GeV/c, where the jets are rare compared to the global
event rate.

It must be emphasized here that the algorithms developed for the low
level triggers are simply designed to maximize the efficiency for
inclusion within the final data set, all events with jets that have a
p~T~ above 50 GeV/c that are within the EMCal acceptance, while
simultaneously minimizing the total fraction of the global trigger rate
that is usurped. This is not an exercise in either Jet finding (locating
the exact position of actual jets) or Jet Measuring (determining the
best estimate of an already located jet's energy), each of which is a
distinct task performed during the higher-level analyses.

The event buffer size varies from event to event and its size is
strongly correlated with the multiplicity of the hits recorded. The
major unknown in determining the average multiplicity of the events is a
fundamental uncertainty in the physics, which will only be resolved when
the first Pb+Pb events are recorded at LHC energies. Predictions for
values of dN/dη range from 2000 to 8000, but as a canonical policy
adopted by the ALICE experiment based on the RHIC results, we will use a
value of 4000. A second factor that can affect the average event buffer
size is the average centrality of the events recorded. Minimum bias
events contain a spectrum of multiplicity sizes due to the mixture of
lower multiplicities from peripheral events and higher multiplicities
from central events. Current plans call for a combination of minimum
bias triggers and central triggers to be recorded, and this choice will
affect the average buffer size and the total number of events that can
be recorded in a given running time.

Our goal is to provide inputs to the decision making process regarding
which events are selected to be included in the final recorded ensemble
so as to enhance the number that contain jets within the EMCal detector.

Assuming an average luminosity of 5\*10^26^ cm^-2^ s^-1^ at ALICE during
a canonical 10^6^ seconds per year of PbPb running, we can anticipate
reaching integrated fluxes of \~ 0.5 nb^-1^ per year. That luminosity
will yield a rate of about 4 kHz of minimum bias triggers[^1], within
which approximately 10% will be events satisfying the central event
trigger. About 6.5 μs will be available after each minimum bias trigger
for the Level 1 (L1) trigger decision, which is needed to trigger the
TPC gating. This L1 discrimination must reduce the acceptance rate by a
factor of roughly 4 to the maximum TPC gating rate of 1 kHz. At that
point, an additional 100 μs will be available before the TPC readout
must be initiated by the Level 2 (L2) trigger. The acceptance rate must
be reduced by an additional factor of approximately 1.25 by that L2
trigger to reach the maximum data transfer rate of 800 Hz (this assumes
half minimum bias events and half central events in the canonical case
where dN/dη \~ 4000).

These L2 output buffers are transferred to the High Level Trigger (HLT)
processors where the final storage decision is made, further reducing
the number of permanently recorded events to \~100 Hz (assuming that
nominally \~50 minimum bias and \~50 central events will be stored per
second).

In summary, the combined L1 and L2 triggers will pass only \~20% of the
raw minimum bias triggers to the HLT, which in turn will again accept
only \~12.5% of those events for permanent storage and off-line
analysis. The integrated effect of *all* triggers is a 2.5% acceptance
rate from the raw minimum bias trigger (i.e. 2.5% \* 4 kHz = 100 Hz).

The L1 and L2 trigger decisions must be made by each individual detector
component separately, with only minimal inputs from other detectors. A
value for the overall event multiplicity will be available to the
individual triggers for each detector from the centrality detector about
100 ns after the event. The HLT will be able to make use of and combine
more detailed information from all of the detector systems, including
tracking information from the TPC.

Our discussion here will be focused on the steps we can take regarding
inputs to the L1 and L2 trigger decisions to enhance the likelihood that
we include events with high (well above 50 GeV/c) p~T~ jets in EMCal
while minimizing our impact on the fraction of the total trigger rate
that we employ. Based on discussions with ALICE management, our nominal
goal would be to achieve a L1 rejection factor of 40 for the minimum
bias events. That would be sufficient to reduce the number of EMCal jet
triggers to 100 Hz, or 10% of the total 1 kHz L1 acceptance rate. We
have been told by ALICE management that any further reduction below a
10% net EMCal rate would be inconsequential, and that at the other end
of the spectrum, our minimum acceptable performance must be an L1
rejection factor of 16, which implies that we could be responsible for
as much as 25% of the L1 acceptance rate.

We are ultimately concerned with the combined L1 \* L2 rate, and so long
as we meet the L1 requirement; we need only satisfy their product
requirement. The point is that if we were to achieve a better than
needed performance in the EMCal L1 trigger, we would have the
correspondingly smaller requirement on our L2 trigger. On the other
hand, the converse is not generally true. An underperformance of our L1
trigger cannot be compensated for by an over performance in our L2
trigger to obtain the same overall impact on the data.

In summary, taking the L1 and L2 rejection factors together, for the
nominal rejection factor, our goals become 40 x 1.25 \~50 yielding a net
1.25% acceptance rate for the EMCal high p~T~ jet trigger, which is the
desired 10% of the global 12.5% rate. The additional factor of 8
reduction that must be obtained in the HLT will involve actual analysis
jet-finding algorithms that will make use of the reconstructed TPC data,
and as such are not considered further here.

**C.II EMCal Trigger Performance**

The construction of a trigger strategy includes three steps. The first
is to identify selection criteria that will flag the rare events of
interest that we are seeking with high efficiency when they do occur.
Second, one must evaluate those same criteria on the events that do not
contain the properties of interest to get a sense of the "background"
that will also be admitted by the selection criteria. The third step
involves the evaluation of any bias that the chosen criteria may impose
on the selected sample. This latter concern for trigger bias will be
discussed in a following section.

Because the total event rate for the p~T~ well above 50 GeV/c jets in
EMCal is so small, the EMCal jet trigger is a rare-event trigger. Our
major concern is the need to minimize the *absolute rate* of triggers we
issue, essentially *all* of which are "background" events in the sense
that they will be otherwise useful triggers, but will *not* contain the
high p~T~ events in EMCal for which this trigger is intended. We will
not see any practical effect in the trigger rate as the result of
efficiency changes in the (first-step) jet tagging itself. As such, the
absolute limits on our selection criteria will be determined by their
effect on this "background" rate alone. The results presented here are
not intended to represent the final trigger design, but rather to guide
the overall detector design, and to demonstrate the feasibility of
employing at least one strategy that will satisfy the trigger needs
outlined.

Experimentally, jets are geometrically concentrated fluxes of particles,
nominally funneled in cone-like flows with the energy and momentum
peaking towards the center. When superimposed on a more or less
isotropic background, jets should reveal themselves when that background
is subtracted. In practice, fluctuations (including the far more
abundant lower energy jets) in that background can cause false triggers
in the absence of any real high p~T~ jets of interest.

Our current hardware readout design will sum the outputs from the
individual tower elements into fundamental square 2 tower x 2 tower
*Trigger Elements*. These in turn can be formed into contiguous square
"patches" of multiples of these Trigger Elements to search for jets. In
the analysis presented here, square patches of varying numbers of these
2 x 2 Trigger Elements were used, and every possible unique patch was
evaluated as part of the trigger decision. The total number of possible
patches is a function of the size of the patches chosen, with the
maximum possibility occurring for the minimum size patch (i.e. where a
single 2 x 2 Trigger Element constitutes a patch by itself).

As a first selection criterion, we impose the simple requirement that
for the patch size chosen, the 2 x 2 Trigger Element with the highest
individual value in EMCal and not on the edge of the EMCal reside inside
the patch with the highest total energy measured as the simple sum of
all of its elements. This requirement alone is satisfied by only \~1/5
of the background events. Once this criterion is satisfied, one can then
impose a further minimum threshold level cut on the total energy in each
patch, and that threshold can be a function of the average energy in the
Trigger Elements in the entire EMCal for that specific event.

Figure C.1 shows plots of this global energy (at the ADC's) in GeV
(y-axis) required for a trigger as a function of the size (x-axis) in
individual tower elements of each square patch. Note that the y-axis is
the actual sum of the ADC's, and should be multiplied by the sampling
fraction in the calorimeter (nominally \~11.8) to get the total energy
deposited. The events analyzed to obtain these plots were assembled from
pure central HIJING events, as this represents the worst-case
"background" condition, and the collection time was 30 ns, because
collecting for longer times allows splash from other ALICE detectors to
enter the EMCal. Figure C.1 (a) shows the results for the case where a
rejection factor of 20 in the "background" rate is attained from this
requirement in central event Triggers, and figure C.1 (b) shows the
values when a rejection factor of 5 is achieved. Note that this
evaluation is accomplished only for patches that satisfied the first
criterion of having the highest Trigger Element contained within the
patch with the highest original total energy, and these factors are in
addition to the factor of \~5 previously obtained from the imposition of
that requirement.

When taken together, the combined rejection factors attained are between
25 and 100, both of which are acceptable for our L1 trigger needs, and
could be easily implemented within the 6.5 μs L1 time constraint.

![](media/image1.png){width="2.4472222222222224in"
height="2.745833333333333in"}
![](media/image2.pct){width="2.4472222222222224in" height="2.7375in"}

\(a\) (b)

Figure C.1. Patch trigger energy vs. various trigger patch sizes.

Figure C.2 shows the effect of these same trigger choices on the
efficiency for finding jets in EMCal as a function of the total jet
energy. This evaluation was done using PYTHIA p-p jets superimposed on
central HIJING Pb+Pb events. Plots are shown for various patch sizes
with figure C.2 (a) presenting the results for the background rejection
factor of 20 in central event triggers, and figure C.2 (b) showing the
corresponding values when the rejection factor of 5 is achieved.

![](media/image3.png){width="2.2493055555555554in"
height="2.5236111111111112in"}![](media/image4.png){width="2.234027777777778in"
height="2.5236111111111112in"}

\(a\) (b)

Figure C.2. Efficiency for triggering on jets in EMCal vs. total jet
energy.

Again, our purpose here is not to propose the final detailed trigger
design, but rather to demonstrate that a fairly simple approach to the
trigger logic easily attains the level of rejection required for the L1
and L2 triggers, and that this is done while preserving efficiencies at
the 90% level for 100 GeV jets in EMCal for example with patch sizes of
12 towers x 12 towers (blue triangles). At lower jet energies around 50
GeV, the achievable efficiency is closer to 70%, which is acceptable due
to the substantially enhanced projected jet rates at these lower
energies over those anticipated at 100 GeV. Indeed, even at 50% at 50
GeV, we may be reaching the level where the genuine jet events become
sufficiently numerous to visibly affect our net trigger rate.

**C.III EMCal Trigger Bias**

The EMCal trigger is most efficient at detecting jets with leading
π^0^'s and photons. Jets with leading charged particles will tend to
produce jets in the TPC that are dominated by charged particles that
will be diffused over the EMCal detector and as such will be less
susceptible to being identified by our proposed trigger logic. This
trigger bias is not by itself problematic, if it can be characterized
accurately. Furthermore, the accuracy of the characterization needed is
a function of the amount of the bias. The lower the efficiency for a
particular type of event, the greater the requirement on the accuracy
that is needed in the characterization of that bias.

Figure C.3 shows the number of events (in black) and the number of
triggers (in red) as a function of the energy of the leading particle
for 104 GeV embedded PYTHIA jets in the upper plots and for 50 GeV
embedded PYTHIA jets in the lower plots. The left hand plots are for
neutral leading particles (π^0^'s and gammas) and the right hand plots
are for charged leading particles. These plots are all for the more
constraining trigger conditions that admit only a 5% "background"
acceptance rate. The most important observations are that there are no
holes in the trigger coverage, and that the efficiencies are reasonable.

As expected, the worst case is for the 50 GeV jets with a charged
leading particle. There the efficiency is only about 50%. However, as
one approaches 104 GeV in jet energy, this value increases to greater
than 90%.

Also as expected the performance for jets with neutral leading particles
is quite good. For 104 GeV jets, using the more stringent 5%
"background" acceptance rate, the efficiency is close to 100% and
remains to above 90% for 50 GeV jets.

![](media/image5.png){width="2.2416666666666667in"
height="2.515277777777778in"} ![](media/image6.png){width="2.21875in"
height="2.4895833333333335in"}

![](media/image7.png){width="2.2111111111111112in"
height="2.463888888888889in"}
![](media/image8.png){width="2.1729166666666666in"
height="2.4291666666666667in"}

Figure C.3. Comparison of trigger rates for neutral and charged leading
particles from 104 and 50 GeV jets.

![](media/image9.png){width="2.1881944444444446in"
height="2.463888888888889in"}
![](media/image10.png){width="2.203472222222222in"
height="2.463888888888889in"}

\(a\) (b)

Figure C.4. Fragmentation function vs. the ratio of p~T~ of the charged
hadrons in the jet divided by the p~T~ of the entire jet.

Figure C.4 displays the same simulated events that are included in the
plots in the previous figure, but with the fragmentation function
plotted against the p~T~ of the charged hadrons in the jet divided by
the p~T~ of the entire jet. To obtain such data represents one of the
primary objectives of EMCal, and as figure C.5 shows, the efficiency as
a function of p~T~ of the charged hadrons in the jet divided by the p~T~
of the entire jet remains relatively constant over the entire range, an
indication that there should not be any dramatic bias in our suggested
trigger scheme for the determination of the fragmentation function. The
overall efficiencies are comparable as a function of jet energy for
these most stringent "background" reduction conditions to those
indicated in figure C.3. Namely an average efficiency of \> 90% is
obtained for 104 GeV jets and for 50 GeV jets it is generally at or
above 70% across the spectrum of the fragmentation function values.

![](media/image11.png){width="2.782638888888889in"
height="3.1222222222222222in"}
![](media/image12.png){width="2.713888888888889in"
height="3.0541666666666667in"}

\(a\) (b)

Figure C.5. Ratio of raw data to triggered data as a function of the
ratio of the p~T~ of the charged particles in the jet to the total p~T~
of the jet for (a) 104 GeV and (b) 50 GeV jets.

Figure C.5 displays the relative ratio of raw data to triggered data as
a function of the ratio of the p~T~ of the charged particles in the jet
to the total p~T~ of the jet for (a) 104 GeV and (b) 50 GeV jets. As
expected from the prior plots the ratio is somewhat flatter for the 104
GeV jets than it is for the 50 GeV jets, and in fact the sensitivity of
the trigger appears substantially lower for those 50GeV events that are
dominated by high p~T~ charged particles. It should be noted, however,
that relative to the absolute numbers in the 104 GeV plot, the raw to
triggered ratios for the higher values of p~T~^ch^/p~T~^Jet^ in the 50
GeV plot are still well above the comparable values in the 104 GeV plot.
This behavior is reasonable because such events at lower p~T~ would not
be expected to have as much energy deposition in the jet cone region in
the EMCal due to the showering before EMCal and the dispersion of the
charged tracks in the magnetic field. However, such events will be
readily detectable in the final data analysis, which will include
information from the TPCs and Central Tracker. So the issue is really
one of insuring that there is a large well-understood sample in the
recorded data to allow their recovery in the final analysis, and to
enable the calculation of a trigger bias correction factor with
sufficient accuracy. These plots give us confidence that such
corrections will be reasonable and attainable.

Furthermore, the EMCal is designed to augment the detection of
electromagnetic showers and in particular to enhance the detection and
characterization of jets in the greater than 100 GeV regime. It is clear
that the trigger scheme proposed here is capable of insuring not only
the efficient triggering on all jets that are sufficiently rare so as to
require enhancement in the normal trigger sample, but to provide a
significant trigger rate for the lower energy jets that may not be
sufficiently enhanced in the broader acceptance of the entire ALICE
detector. Those events for which this trigger is least efficient, namely
the high charged particle fraction lower energy jets (\~ 50GeV), will
still be well represented in the EMCal trigger in the absolute sense.
Furthermore, they will be represented in the global triggers at a level
as high or higher than those jets visible to EMCal both because of their
substantially greater numbers compared with 100 GeV, and because of the
ability of the TPC analysis to find jets with a predominance of high
p~T~ in charged particles. Then, as the rate of jet occurrence drops at
higher p~T~ nearing 100 GeV, the efficiency of our proposed trigger is
sufficient to obtain the needed statistics for the entire breadth of the
fragmentation function with very small bias. In addition this proposed
trigger scheme results in an estimated trigger rate of 40 Hz, which is a
factor of 2 lower than our nominal goal of 80 Hz (i.e. 10% of the
combined 800 Hz from the L2 trigger)

In conclusion, our goal has been to demonstrate the feasibility of
implementing a trigger for the EMCal detector that will satisfy the
constraints imposed on us by the overall ALICE trigger and data
acquisition infrastructure and to provide a reasonably high efficiency
for detecting high energy jets within the acceptance of the EMCal
detector. Given the predictions for the performance of the simple
trigger schemes outlined here, it is clear that the implementation of an
acceptable trigger is immanently achievable.

[^1]: These are average rates. Peak rates in a given store will be
    higher. See ALICE PPR