**KOPIO TN051 1 April 2003**

# TRIGGERING ALGORITHMS FOR THE KOPIO PROGRAM:

**Fast MC Studies**

By: Carol Scarlett

ABSTRACT: In the study that follows, several schemes for triggering at
KOPIO are investigated. While previous studies have focused on
maximizing the number of events having two gammas well into the
acceptance of both the pre-radiator and Calorimeter (canonical signal),
this study looks at ways of increasing the total signal through keeping
events with energy in the pre-radiator and Photon Barrel Vetos. Using a
high degree of subdivision of the Calorimeter, the K^0^~L~ background
can be well suppressed allowing events with one hit in the Photon Barrel
Veto to be kept at trigger level 0. The last two sections review the
potential increase in signal. Provided the tracks from both the
pre-radiator and Photon Barrel Vetos can be used in reconstructions, the
increase in signal is substantial.

**DETECTOR LAYOUT:**

As the detector design is still evolving, it is worthwhile to discuss
the geometry assumed in this study. To improve rejection of 3 π^0^
background events, the Photon Barrel Veto has been subdivided into 4
sections lining the fiducial volume and a wall at the entrance to the
volume. The upstream wall, part of the entrance, also forms part of the
vetoing system. The pre-radiator veto sits beyond the pre-radiator
volume at two meters from the geometrical beam center. Crystals line the
calorimeter and may be used to veto tracks entering directly from the
beam. Additionally, there are downstream vetos in both the Magnet and
the downstream beam pipe. Mike Zeller's downstream photon veto scheme
has been implemented entirely in this study.

![](media/image1.png) Figure 1: Detector layout showing the various
vetoing systems.

To avoid a high accidental rate, the timing windows for each of the veto
systems should be set as narrow as possible. In a studies performed on
the fastmc, it can be shown that the full width of the gates for the
photon barrel vetos can be as narrow as 5.5 ns. For this study,
triggering requires energy in both the pre-radiator and the Calorimeter.
Events with backward moving particles, shown to complicate setting of
the downstream veto timing windows when triggering on just the
pre-radiator, are completely rejected for the redesigned level zero
trigger now including the Calorimeter. The timing windows for both the
photon vetos in the Magnet and the downstream photon vetos can also be
kept narrow (5.5 ns). The offset of all veto systems has been chosen to
take advantage of an early "local" track from the 3 π^0^ decay, as these
decays constitute the highest level of background, as discussed in the
following section.

**VETO TIMING:**

For 3 π^0^ decays, a single steeped track hits the Photon Barrel Veto
within 1m of the parent (K^0^~L~) decay point. The timing for this track
occurs earliest in the timing distribution, when compared to the time
when the trigger occurs, for each section of this veto. Figure 2 shows
the time distributions for each section along with the proposed time
windows.

![](media/image2.png){width="5.125in" height="2.316666666666667in"}

![](media/image2.png){width="5.133333333333334in"
height="2.2465277777777777in"}

Figure 2: Time distributions for sections of the Photon Barrel veto
showing

the proposed time windows (vertical black lines). The sections are each
1m

long and are shown starting from the most upstream section (top left
panel)

to the most downstream (bottom right panel). This figure also shows the

upstream wall (bottom middle), which constitutes a separate veto, along

with a sum of all track times for tracks hitting the Photon Barrel veto.

With just 5.5ns windows, the expected background levels of 18-25kHz are
well within operation range for the experiment. Section 5, bottom middle
panel, shows tracks hitting the upstream wall of the decay tank. This
section has been gated separately from the upstream wall entering the
decay tank. More recent studies show that omitting this 5^th^ section
results in less than 1kHz increase of total K^0^~L~ background. When
accepting the canonical signal and events with one track in the
Pre-radiator Veto or a single track in the Photon Barrel Veto, this
increase places the overall background just out of range (26kHz) -- see
discussion of signal below.

**PRERADIATOR AND CALORIMETER DIVISIONS:**

To achieve a sufficient level of background trigger rejection it is
necessary to subdivide both the pre-radiator and Calorimeter. Both
devices are naturally divided into quadrants. The x and y-slats of the
pre-radiator make further division into sub-quadrants possible. For the
Calorimeter, the 24 x 24 modules forming each quadrant can easily be
divided into 4 x 4 sub-quadrants each of 6 x 6 modules. The figure below
shows the divisions used for this study. The blue lines, shown in the
section marked Calorimeter Divisions, represent border regions where
tracks can potentially trigger multiple sub-quadrants.

![](media/image3.png)

Figure 3: Diagram showing how the Calorimeter and

Pre-radiator are to be subdivided.

A counting algorithm has been employed to ensure that these overlap
regions do not cause unnecessary rejection of the canonical signal,
defined below. The algorithm used to count hits:

> Hits = ((Sub-quads + Corners)-Borders)

gives the total number of hits entering the calorimeter per event. By
constraining the number of sub-quadrants with energy for both the
pre-radiator and Calorimeter, and using the many veto systems, one can
effectively reduce the K^0^~L~ background rates without loss of signal.
A significant background contribution was shown to come from upstream
decay events, whose photons cluster around the edge of the pre-radiator
near the beampipe, in an earlier study by Ermanno. Interestingly enough,
accepting signals with one track in the pre-radiator headed for the
Calorimeter and a second track in either the pre-radiator or Photon
Barrel veto rejects much of this upstream background without further
need for vetoing events with tracks near the edge of the pre-radiator
and/or Calorimeter.

**CANONICAL SIGNAL:**

The canonical signal event consists of two gammas passing through the
pre-radiator and into the calorimeter. The gammas must be well contained
in the pre-radiator volume (figure 1) for a good directional measurement
and must deposit their remaining energy in the Calorimeter for a good
energy measurement. To achieve both of these requirements, only the
central ± 1.5 m of the ± 2.0 m pre-radiator entrance will be used as the
fiducial volume. Additionally, neutron background will hamper
reconstruction of events decaying near both the upstream wall and the
pre-radiator edge. This further reduces the useful decay volume along
the z-axis by 0.5 m at each end of the decay tank. Canonical events are
required to have a z(K^0^~L~)~decay~ position between 1025 to 1300 cm
relative to the target -- the pre-radiator begins at 1350 cm. Both
reductions have been taken into account in arriving at the estimated
number of signal events in Table 1. At this point, the significant
events with only one photon in the pre-radiator satisfy the canonical
selection. These events are called PR=1.

![](media/image4.png)

Figure 4: Detector layout showing a canonical signal event.

Only a small fraction of signal decays actually give triggers. In Table
1, the signal triggers fitting the canonical criteria are labeled with
PR=2 indicating that 2 hits were seen in the acceptable range of the
pre-radiator. Events with one track in the pre-radiator and one track in
the Photon Barrel Veto are labeled PBV=1. Out of the 20 k signal decays
only a couple hundred fit the canonical criteria.

Canonical Cuts

Signals: 278 / 20 K

(207 PR=2)

(71 PR=1)

3 π^0^ Bk: 67 Raw

(12.6 KHz)

Table 1: Canonical signal events with a requirement of

two sub-quadrants hit in the calorimeter.

The canonical signal for this sample of events has been established by
requiring no more than two sub-quadrants of the Calorimeter to have
tracks. The z(K^0^~L~)~decay~ distribution for the canonical signal
events appears in figure 4 below.

![](media/image5.png){width="3.3722222222222222in"
height="3.240972222222222in"}

Figure 5: Shows the canonical signal distribution

along Z.

All vetos have been gated and applied. Given the size of the background
for 3 π^0^ decays, it is not necessary to increase the width of the time
windows further.

![](media/image6.png){width="3.3722222222222222in"
height="3.2527777777777778in"}

Figure 6: Shows the background to the canonical

signal distribution.

**ENHANCING THE SIGNAL:**

Studies on the FastMC revealed that almost half of the signal events
with two tracks passing through the pre-radiator, have one track
printing towards the pre-radiator veto. Of course, accepting such events
would mean accepting events well beyond the reduced x and y-cut at ±1.5
m. For purposes of this study, two cases of signal enhancement are
considered: the first demands the reduced volume on at least one of the
tracks, while the second uses the entire pre-radiator volume for the
track not hitting the veto. The latter events will likely have lower
efficiency than both the canonical case and the case with one track in
the accepted volume. The triggering efficiency will be evaluated later
with the full Geant MC.

![](media/image7.png)

Figure 7: Detector layout showing signal event with track through the PR
veto.

To take advantage of the pre-radiator and Photon Barrel Vetos, the
following triggering conditions have been set:

1\. One hit in the PR veto IF only one Calo Sub-quad is hit

2\. One hit in the PBV IF only one Calo Sub-quad is hit

3\. Total count: PBV + PRV + Calo Sub-quad = 2

Table 2 gives the relative numbers of canonical signal events to events
with one track in the accepted region and a second track in the
pre-radiator veto and a listing for the case of just one track anywhere
in the pre-radiator and a second track in the pre-radiator veto. Notice,
applying the new algorithm to the sample of canonical events gave an
efficiency of 100%. The potential signal is further enhanced by the
numbers of Photon Barrel Veto events PBV=1.

Canonical Cuts 1 Accepted Vol 1 Accepted Vol

1 PR or PRV 1 PR or PRV or PBV

Signals: 278 / 20 K 394 / 20 K 583 / 20 K

(207 PR=2) (318 PR=2) (318 PR=2)

(71 PR=1) (76 PR=1) (77 PR=1)

> (0 PBV=1) (188 PBV=1)

3 π^0^ Bk: 65 / 100 K 96 / 100 K

π^+^π^--^π^0^ 5 / 100 K 35 / 100 K

2 π^0^ 366 / 100 K 625 / 100 K

(13.3 KHz) (23.0 KHz)

Table 2: Comparing the canonical signal to the enhancements

gained from including PR and single PBV hits.

The potential improvement for the first case, one track in the accepted
PR volume, is roughly 50% over the canonical case. The resulting signal,
provided these events are 100% reconstructable, is \~ 61 events. For the
second case, using the PR veto or the Photon Barrel veto, the potential
signal increases to \~ 98 events.

The potential signal events can be further increased, by adjusting the
time gates for the Photon Barrel Veto. Increasing the windows to 7.0ns
increases the number of events accepted with a single hit in the Photon
Barrel Veto, while simultaneously reducing the expected 3 π^0^
background. This larger window, however, does have the draw back of
increasing accidentals.