![](media/image1.png){width="1.1625in" height="0.7111111111111111in"}

# Run 2b Trigger Conceptual Design Proposal

#### **TTF Authorlist**

#### *September 5, 2001*

# Introduction

[Goals and Charge]{.underline}

-   Increase Instantaneous Luminosity by factor of 2.5

-   Improve Rejection of L1

-   Maintain Rejection Rate in L2 and L3

### Boundary Conditions

-   Installation Schedule

-   High Probability of Success Required

-   Assumed Running Conditions

### Document Outline

# Level 1 Tracking Trigger

[Goals]{.underline}

-   Electron and Muon Tagging

-   Support of b tagging

-   Constraints imposed by muon trigger requirements

-   Constraints imposed by STT requirements

### Description of Current Tracking Trigger 

-   Track triggers

-   Electron triggers

### Performance of Current Tracking Trigger

-   Efficiencies ?

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-   Rates for track triggers

-   Number of STT input tracks

-   Conclusions and implications for high luminosity

### Overview of Options 

-   Prescale and increase Pt threshold?

-   Fine tuning of current system (optimized axial equations)?

-   Reduce coincidence levels to improve efficiency?

-   Increase coincidence levels to reduce accidentals

-   Improve granularity to reduce accidentals

### Axial CPS as Ninth Layer

-   Concept and tradeoffs

-   Rates and Rejection Improvements

-   Efficiency/Acceptance

-   Implementation

-   Cost & Schedule

-   Recommendations

### Stereo Trigger 

-   Concept

-   Simulation

-   Rates and Rejection Improvements

-   Efficiency

-   Incorporating Axial CPS?

-   Implementation

-   Cost & Schedule

-   Recommendations

### Singlet Equations

-   Concept

-   Simulation

-   Rates and Rejection Improvements

-   Efficiency

-   Implementation

-   Cost & Schedule

-   Recommendations

### L1 Tracking Trigger Summary and Conclusions

# Level 1 Calorimeter Trigger

## Goals 

The primary focus of run 2b will be the search for the Higgs. The
increase in luminosity (and thus multiple interactions), and the
decreased bunch spacing (132ns) for Run 2b will impose heavy loads on
the L1 calorimeter trigger. The goal of the L1 calorimeter trigger
upgrade is to provide a number of performance improvements over the run
2a trigger system. It is the totality of these improvements that leads
us to propose this upgrade. In the following sections we describe how
the L1 calorimeter trigger upgrade will provide

-   An improved capability to correctly assign the calorimeter energy
    deposits to the correct bunch crossing via digital filtering

-   A significantly sharper turn-on for jet triggers, thus reducing the
    rates

-   The ability to make shape and isolation cuts on electromagnetic
    triggers, and thus reducing rates

-   The ability to match tracks to energy deposition in calorimeter
    trigger towers, leading to reduced rates

-   The ability to include the energy in the ICD when calculating jet
    energies and the missing ET

-   The ability to add topological triggers which will aid in triggering
    on specific Higgs final states.

The complete implementation of all these improvements will provide us
with the ability to trigger effectively with the calorimeter in the
challenging environment of Run 2b.

## Description of Calorimeter Electronics

### Overview

The charge from the calorimeter is integrated in the charge sensitive
preamplifiers located on the calorimeter. The preamplifier input
impedence is matched to the 30 Ω cable from the detector, and the
preamplifiers have been compensated to match the varying detector
capacitances, so as to provide signals that peak uniformly in time. The
fall time for the signals has been set to 15 μs. The signals are then
transmitted (single ended) on terminated twisted-pair cable to the
baseline subtractor cards (BLS) that shape the signal to an
approximately unipolar pulse with a risetime of 120 ns (see Figure 1 for
a simple overview). The signal on the trigger path is further
differentiated by the trigger pickoff to shorten the pulse width. The
signals from the different depths in the electromagnetic and hadronic
sections are then added with appropriate weights to form the analog
trigger tower sums. These analog sums are then output to the L1
calorimeter trigger after passing through the trigger sum drivers. The
signals are then transported differentially (on pairs of 80Ω coaxial
cable) 80m to the L1 calorimeter trigger. The key elements of the
calorimeter trigger path are described below.

![](media/image2.png){width="6.0in" height="4.135416666666667in"}

**Figure 1:** Functional diagram of the BLS system showing the precision
readout path and the location of the calorimeter trigger pickoff signal.

### Trigger pickoff

The trigger pickoff captures the signal before any shaping (a schematic
of the shaping and trigger pickoff in the upper left), as is shown in
Figure 2. The preamplifier signal is differentiated hard and passed
through an emitter follower to essentially restore the original charge
shape (a triangular pulse with a fast rise and a linear fall over 400
ns). This circuitry is located on a small hybrid that plugs into the BLS
motherboard. There are 48 such hybrids on a motherboard, and a total of
about 55,296 for the complete detector.

### ![](media/image3.wmf){width="5.583333333333333in" height="3.9166666666666665in"}

**Figure 2**: Schematic of the trigger shaper and trigger pickoff (upper
left of picture).

### Trigger summers

The trigger pickoff signals for EM and HAD sections in a trigger tower
are routed on the BLS board to another hybrid plug-in that forms the
analogue sums with the correct weighting factors for the different
radial depth signals that form a single tower. The weighting is
performed using appropriate input resistors to the summing junction of
the discrete amplifier. A schematic for this circuitry is shown in xxx.

A single 48 channel BLS board has 8 trigger summer hybrids (4 EM towers
and 4 HAD towers). There are a total of 9,216 hybrid trigger summers
made up of 75 species. Since they are relatively easy to replace,
changes to the weighting schemes can be considered. Recall however that
access to the BLS cards themselves requires access to the detector as
they are located in the area directly beneath the detector.

### Trigger sum driver

The outputs of the 4 EM trigger summers on a single BLS board are summed
once more by the trigger sum driver circuit (see the schematic in xxx)
where a final overall gain can be introduced. This circuit is also a
hybrid plug-in to the BLS board and is thus easily replaceable if
necessary (with the same access restrictions discussed for the trigger
summers). In addition the driver is capable of driving the coaxial lines
to the L1 Calorimeter trigger. There are a total of 2,304 such drivers
in 8 species (although most are of two types).

If finer (x2) EM granularity in φ is required for the calorimeter
trigger, these hybrids could be replaced to handle the finer
segmentation. We expect about 4 man months of work to modify and replace
these hybrids. If further simple shaping of the trigger signal is
required it could be implemented on this circuit or at the receiver end
on the L1 calorimeter trigger.

### Signal transmission, cable dispersion

The signals from the trigger driver circuits are transmitted
differentially on miniature coax (0.1"). The signal characteristics are
significantly better than standard RG174 cable. However first
indications are that the signal seen at the end of these cables at the
input to the L1 calorimeter trigger are somewhat slower than expected.
The cause of the deviation from expectations is not presently known and
is under investigation. It is possible that the signal dispersion in
these coaxial cables is worse than expected, and possible replacements
are under investigation.

## Description of Current L1 Calorimeter Trigger

### Overview

The DØ uranium-liquid argon calorimeter is constructed of projective
towers covering the full 2 π in the azimuthal angle, φ , and
approximately 8 units of pseudo-rapidity, η, with eight or nine depth
segments which provide convenient subdivision of the Calorimeter Towers
in electromagnetic (EM) and hadronic (H) sections. The Calorimeter Tower
segmentation in η,φ is 0.1 x 0.1, which results in towers whose
transverse size is larger than the expected sizes of EM showers but,
considerably smaller than typical sizes of jets.

As a compromise, for triggering purposes, we add four adjacent
Calorimeter Towers to form Trigger Towers with a segmentation of 0.2 x
0.2 in η x φ. This yields an array that is 40 in η and 32 in φ or a
total of 1,280 EM and 1,280 H tower energies as inputs to the
Calorimeter Trigger.

![](media/image4.wmf){width="4.277777777777778in"
height="2.4604166666666667in"}

**Figure 3:** Trigger Tower Formation.

The analog summation of the signals from the various calorimeter cells
in a Trigger Tower into the EM and H Trigger Tower signals takes place
in two steps. For both EM and H, first all the calorimeter cells in a
given Calorimeter Tower are added in the \"summer hybrid\". The summer
hybrids contain a resistor for each calorimeter cell to adjust the
relative contribution of that cell to the Calorimeter Tower sum. In the
second step, 4 signals, one from each of the Calorimeter Tower making up
the Trigger Tower, are summed on the \"driver hybrid\". The driver
hybrid also contains the circuits for driving the Trigger Tower signals
over coaxial cable to the Level 1 Calorimeter Trigger. This arrangement
for summing the calorimeter cells into Trigger Towers is shown in Figure
3.

Long ribbons of coaxial cable route the 1280 EM and H analog Trigger
Tower signals from the Detector Platform through the Shield Wall and
then into the first floor of the Moving Counting House where the Level 1
Calorimeter Trigger is located. The first step in the Level 1
Calorimeter Trigger is to scale these signals to represent the E~T~ of
the energy deposited in each Trigger Tower and then to digitize these
signals at the beam-crossing rate with fast analog to digital
converters. The digital output of these 2560 converters is used by the
subsequent trigger logic to form the Level 1 Calorimeter Trigger
decision for each beam crossing. The converter outputs are also buffered
and made available for readout to both the Level 2 Trigger System and
the Level 3 Trigger DAQ system.

The digital logic used in the Level 1 Calorimeter Trigger is arranged in
a \"pipe-lined\" design. Each step in the pipe-line is completed at the
beam crossing rate and the length of the pipe-line is less than the
maximum DØ Level 1 trigger latency for Run II which is 3.3 μsec. This
digital logic is used to calculate a number of quantities that are
useful in triggering on specific physics processes. Among these are
quantities such as the total transverse energy and the missing
transverse energy, which we will designate as \"global\" and information
relating to \"local\" or cluster aspects of the energy deposits in the
calorimeter. The latter would include the number of EM and H-like
clusters exceeding a set of programmable thresholds.

### Global Triggers 

Interesting global quantities include:

the total transverse energies:

Total E~T~EM = $\sum_{i = 1}^{\text{1280}}{E_{T}\text{EM}_{i}}$

Total E~T~H = $\sum_{i = 1}^{\text{1280}}{E_{T}H_{i}}$

and

Total E~T~ = Total E~T~EM + Total E~T~H

the missing transverse energy:

MP~T~ = $\sqrt{(E_{x}^{2} + E_{y}^{2}}$

where:

E~x~ =
$\sum_{i = 1}^{\text{1280}}{(E_{T}\text{EM}_{i} + E_{T}H_{i})\text{cos}(f_{i})}$

and

E~y~ =
$\sum_{i = 1}^{\text{1280}}{(E_{T}\text{EM}_{i} + E_{T}H_{i})\text{sin}(f_{i})}$

All of these global quantities can be used in constructing triggers.
Each quantity is compared to a number of thresholds and the result of
these comparisons is passed to the Trigger Framework where up to 128
different Level 1 triggers can be formed.

### Cluster Triggers 

The DØ detector was designed with the intent of optimizing the detection
of leptons, quarks and gluons. The charged leptons will manifest
themselves as localized EM energy deposits and the quarks and gluons as
hadron-like clusters.

Energy deposited in a Trigger Tower is called EM-like if it exceeds one
of the EM E~T~ thresholds and if it is not vetoed by the H energy behind
it. Up to four EM E~T~ thresholds and their associated H veto thresholds
may be programmed for each of the 1280 Trigger Towers. Hadronic energy
deposits are detected by calculating the EM E~T~ + H E~T~ of each
Trigger Tower and comparing each of these 1280 sums to four programmable
thresholds.

The number of Trigger Towers exceeding each of the four EM thresholds
(and not vetoed by the H energy behind it) is calculated and these four
counts are compared to a number of count thresholds. The same is done
for the four EM E~T~ + H E~T~ thresholds. The results of these count
comparisons on the number of Trigger Towers over each threshold is sent
to the Trigger Framework where they are used to construct the Level 1
Triggers.

### Hardware Implementation 

#### Front End Cards 

The analog signals from the calorimeter, representing energies, arrive
at the Calorimeter Trigger over coaxial differential signal cables and
are connected to the analog front end section of a Calorimeter Trigger
Front End Card (CTFE). A schematic diagram of one of the four cells of
this card is shown in Figure 4.

![](media/image5.wmf){width="5.999305555555556in"
height="4.634722222222222in"}

Figure 4: Calorimeter Trigger Front End Cell.

The front-end section contains a differential line receiver and scales
the energy signal to its transverse component using a programmable gain
stage. The front end also contains digital to analog circuitry for
adding a positive bias to the tower energies in accord with downloaded
values.

Immediately after the analog front end, the EM or H signal is turned
into an 8 bit number by fast (20 ns from input to output) FADC\'s. With
our current choice of 0.25 GeV least count this gives a maximum of 64
GeV for the single tower transverse energy contribution.

The data are synchronized at this point by being clocked into latches
and then follow three distinct parallel paths. One of these paths leads
to a pipeline register for digital storage to await the L1 trigger
decision and subsequent readout to the Level 2 Trigger system and the
Level 3 Trigger DAQ system.

On the other two paths, each 8-bit signal becomes the address to a look
up memory. The content of the memory at a specified address in one case
is the transverse energy with all necessary corrections such as lower
energy requirements etc. In the other case, the EM + H transverse
energies are first added and then subjected to two look-ups to return
the two Cartesian components of the transverse energy for use in
constructing MP~T~. The inherent flexibility of this scheme has a number
of advantages: any energy dependent quantity can be generated,
individual channels can be corrected or turned off at this level and
arbitrary individual tower efficiencies can be accommodated.

The CTFE card performs the function of adding the E~T~\'s of the four
individual cells for both the EM and H sections and passing the
resulting sums onto the Adder Trees. In addition it tests each of the EM
and EM+H tower transverse energies against the four discrete thresholds
and increments the appropriate counts. These counts are passed onto the
EM cluster counter trees and the total E~T~ counter trees, respectively.

#### Adder and Counter Trees 

The adder and counter trees are similar in that they both quickly add a
large number of items to form one sum. At the end of each tree the sum
is compared to a number of thresholds and the result this comparison is
passed to the Trigger Framework. A typical adder tree is shown in Figure
5.

Physical Layout ![](media/image6.wmf){width="5.999305555555556in"
height="3.388888888888889in"}

Ten racks are used to hold the Level 1 Calorimeter Trigger in the first
floor moving counting house. The lower section of each rack contains the
CTFE cards for 128 Trigger Towers (all 32 φ\'s for four consecutive
η\'s). The upper section of each rack contains a component of one of the
Adder or Counter Trees.

## Performance of Current Calorimeter Trigger

### Energy measurement and turn-on curves

The size of the 0.2 x 0.2 trigger towers is small compared to the
spatial extension of hadronic showers in inelastic events. This is
illustrated in Figure 6, which shows for simulated events the ratio of
the Et observed by the trigger to the generated Et. A Monte-Carlo sample
of QCD events is used here. A cone algorithm with a radius of 0.4 in η-Φ
is applied to the generated stable hadrons in order to find the
generated jets. The direction of each generated jet is extrapolated to
the calorimeter surface, leading to the "center TT" hit by the jet. The
highest Et TT in a 3 x 3 region around this center is then used to
define the "trigger Et" corresponding to the jet. It can be seen in
Figure 6 that this transverse energy is only 25 % of the jet Et on
average. Low thresholds are thus needed even to trigger on hard jets.
Moreover the trigger Et has a quite bad resolution. As a result, the
trigger efficiency (the efficiency for having at least one TT with Et
above a given threshold) rises only slowly with increasing jet Et, as
shown in Figure 7.

![](media/image7.wmf){width="3.9in" height="3.033333333333333in"}

**Figure 6** **:** Ratio of the trigger Et to the transverse energy of
the generated jet. Only jets with Et ≈ 40 GeV are used here.

![](media/image8.wmf){width="4.054166666666666in" height="3.29375in"}

**Figure 7:** Trigger efficiency as a function of the transverve energy
of the generated jet. The curves correspond to thresholds of 1.5, 2, 3,
4, 5 and 6 GeV.

### Trigger rates 

The trigger Et resolution, convoluted with the steeply falling pt
spectrum of QCD events, leads on average to migrations above the true Et
of such events. The number of QCD events which pass the L1 trigger is
thus larger than what it would be with an ideal trigger Et measurement.
Due to the huge cross-section of QCD processes, this results in large
trigger rates[^1]. For example, as shown in Figure 3, an inclusive
unprescaled high Et jet trigger, requiring at least one TT above a
threshold defined such that the efficiency on 40 GeV jets is 90 %, would
yield a rate of at least 10 kHz at 2 10^32^ cm^2^ s^-1^. Maintaining
this rate below 1 kHz would imply an efficiency on such high Et jets of
60 % only. Trigger rates increase faster than the luminosity due to the
increasing mean number of interactions per bunch crossing. Trigger rates
are shown in Figure 4 as a function of the mean number of minimum bias
events which overlay the hard interaction. These are shown for two
di-jets conditions: requiring at least two TT above 5 GeV, or at least
two TT above 5 GeV and at least one TT above 7 GeV. These correspond to
reasonable requirements for hard events as can be seen in Figure 2 since
a threshold of 5 GeV leads, for 40 GeV jets, to 80 % efficiency only.
The rates are shown for a luminosity of 2 10^32^ cm^2^ s^-1^ . For a
luminosity of 5 10^32^ cm^2^ s^-1^, the L1

![](media/image9.wmf){width="3.832638888888889in"
height="2.9069444444444446in"}

**Figure 8:** Efficiency to trigger on 40 GeV jets as a function of the
inclusive trigger rate, when one TT above a given threshold is required.
Each dot corresponds to a different threshold. The luminosity is 2 1032
cm2 s-1. *(figure to be remade with the lower (black) curve only...)*

bandwidth would be saturated by such dijet conditions alone, unless
large prescale factors are applied.

![](media/image10.wmf){width="5.307638888888889in"
height="2.854861111111111in"}

**Figure 4:** Inclusive trigger rate as a function of the number of
minimum bias events overlaid to the hard interaction. Rates are shown
for two di-jet conditions. The luminosity is taken to be 2 10^32^ cm^2^
s^-1^.

A more exhaustive study of the evolution of the L1 trigger rate with
increasing luminosity can be found in^1^. A possible trigger menu has
been considered, in which \~ 75 % of the L1 bandwidth is used by
multijet triggers. Results are shown in table 1. It can be seen that, at
the luminosity foreseen for Run 2b, the trigger rates should be reduced
by a factor at least 2 in order to keep a reasonnably small dead time.

  ----------------------- ----------------------- -----------------------
  Luminosity              Rate L1 High Pt (Hz)    Rate L1 total (Hz)

  1                       1700                    5000

  2                       4300                    9500

  5                       6500                    20 000
  ----------------------- ----------------------- -----------------------

**Table 1:** Evolution of the level 1 trigger rate as function of
luminosity expressed in units of 10^32^ cm^2^ s^-1^.

### Conclusions/implications for high luminosity

An obvious improvement is to select directly at level 1 complete
objects, electromagnetic showers and jets. Performing a "clustering" of
TT already at L1, as being currently done at L2, could reduce the
trigger rates by a factor 2 to 5 as will be shown later. The technical
justification for this gain comes from the improvement in the quality of
the energy cut, when applied to a cluster of trigger towers.
Transferring to level 1 some of the functions that currently belong to
level 2 could also permit the introduction of new selection algorithms
(topological selection ) at this level.

From a conceptual viewpoint, an important consequence of selecting
physics "objects" at level 1 is to allow a more « inclusive » and hence
less biased selection of signatures of complex physical phenomena. Thus
the trigger menus will become simpler and, above all, less sensitive to
biases arising from the combinatories of primary objects.

## Overview of Options for Improvement

### Global view of options considered

### Reducing pileup effects: digital filtering

The shape, especially the rise time, of the pick-up signal is not
compatible with 132ns beam crossing separation. There may be temporary
fixes to this problem, but the only long-term solution is to apply a
stronger shaping to this signal. This could be done by means of an
analog filter, but a digital filter is a better solution because it is
much more flexible for a similar cost.

### Improving jet efficiency turn on: sliding windows

### Improving electron efficiency turn on: sliding windows, segmentation, shape cuts

### Improving resolutions: adding ICD energies

### Reducing backgrounds: track matching

## Digital Filtering

### Concept & physics implications

The pick-up signal is the result of the electronic chain of the
calorimeter applied to the delta function shaped energy deposited in the
cells of the calorimeter at each beam crossing. This is characterized by
the transfer function of the electronics. The inverse transfer function
will transform the pick-up signal back to delta function. This inverse
function can be implemented by a FIR (Finite Impulse Response) filter.
In presence of noise, the digital filter offers an additional advantage:
one can use the theory of *optimal filtering* to minimize the noise
contribution.

In order to define the exact form of digital filter best suited to the
task, measurement of noise in pick-up signals would be needed. Studies
are expected to progress when such measurements become available.

### Pileup rejection

Two different "pile-up" effects arise with increasing luminosity, the
first being of physical origin, the second affecting the signal
measurement:

Underlying Events: For each triggered beam crossing there are several
minimum bias events in the same beam crossing, following a Poisson
distribution with a mean proportional to the luminosity. The energy
added by these events has a distribution close to a double exponential
(Laplacian). It is possible ^2^ to minimize the contribution of this
noise by using an appropriate digital filter (Matched Median Filter).

Pulses overlap: The width of the pick-up signal covers several beam
crossing (6 at 132ns and counting only the positive part of the signal).
When two such pulses are separated by less than these, there is some
overlap and the shape of the pick-up signal becomes complex. The inverse
filter, by definition, will extract from this signal the two initial
delta functions. Consequently, the overlap of pulses is not a concern if
one uses digital filtering.

### Simulation

Simulations of the FIR response await a better knowledge of the noise
contribution to the trigger signal. They will give insights of the
optimal number of filter coefficients and provide an estimate of the
resolution of the resulting energy measurement.

Coefficients Computation: The most reasonable way to compute
coefficients is to use the mean squared (LMS) optimization. This
proceeds by minimizing the sum of the square of the differences between
many input excitations and their filtered outputs; each input excitation
produces a pulse at the input of the ADC and contributes several terms
to the sum: one for each beam crossing where the pulse is non-zero. A
realistic simulation of the noise must be added to the theoretical pulse
(derived from the transfer function of the calorimeter).

### Implementation

#### Sampling rate and precision: 

An effective range of 8 bits for the transverse energy of each trigger
tower seems sufficient to meet the desired performance and is
technically practical. Because calorimeter signals are representative of
the energy deposited in the calorimeter while trigger algorithms deal
with transverse energy, a scaling from energy to transverse energy needs
to be done. Performing this scaling with a programmable analog circuit
placed before each ADC could be done but a digital solution is more
practical and flexible. In order to preserve a dynamic range of 8
effective bits for signals calibrated in transverse energy, using a 10
bit ADC to convert analog signals seems well adapted.

The conversion rate needs to be at least equal to the beam-crossing
rate, but it can be higher than that. Above a certain limit, over
sampling will not give any gain because of the relatively slow evolution
of the signal.

Actual 10 bits ADCs have a "pipelined" architecture. This implies that
the output data is available 4 to 6 cycles after the sampling. As the
level 1 trigger operates on a very tight latency budget, it is not
acceptable to choose a conversion rate equals to the beam-crossing rate
because the data conversion would consume too much latency. In order to
reduce the latency of the data conversion, the ADC must run at a
frequency higher than that of the beam crossing. ADCs in the 20-60 MHz
range are now common and inexpensive. If only a fraction of the samples
produced by each ADC is needed for filtering, decimation can be
envisaged. One should note that because the signal is over sampled, it
seems natural to use that data to improve the overall performance of the
digital filtering operation. Recalling Shannon's sampling theorem, it
can be stated that a FIR implementing the exact inverse transfer
function considered must have at least a sampling frequency that is
twice that of the beam crossing.

Possible solutions to implement the digital filter are discussed below.

### Cost & schedule

### Recommendations

## Sliding Trigger Tower Windows for Jets and Electrons

### Concept & physics implications

Various algorithms can be used to cluster the trigger towers and look
for "regions of interest" (RoI), i.e. for regions of fixed size S in (η,
Φ) in which the deposited Et shows a local maximum. To find those RoIs,
a window of size S is slided in both directions by steps of 0.2 in η and
Φ. By convention each window unambiguously correspond to one trigger
tower T and is labeled S(T). Examples are shown in Figure 4.

![](media/image11.wmf){width="3.779861111111111in"
height="1.3979166666666667in"}

**Figure 9:** Examples of sliding windows S(T) associated to a trigger
tower T. Each square represents a 0.2 x 0.2 trigger tower. The trigger
tower T is greyed.

Each window S(T~0~) such that :

For all trigger towers T in the neighborhood of T~0~ , the Et in S(T~0~)
is greater than that in S(T),

is called a region of interest. There is some freedom in the definition
of the neighborhood of trigger towers, resulting in different
algorithms. Due to the quantification of the Et of each trigger tower, a
prescription has to be chosen to unambiguously define those local
maxima. Figure 5 illustrates one possible choice, defining RoI's as
maxima in a 1.0 x 1.0 region. The RoI's can also be defined as being
local maxima in a 0.6 x 0.6 area.

![](media/image12.wmf){width="2.4583333333333335in"
height="2.067361111111111in"}

**Figure 10:** Possible prescription to define a local maximum.

A transverse energy is then associated to each RoI, and these Et
constitute the quantities used to issue the trigger decision. This Et
can be e.g. the transverse energy contained in the RoI itself, or in the
RoI and in its bordering TTs. It is called the trigger Et of the RoI in
the following and the region where it is deposited is called a "trigger
jet".

### Simulation

Several algorithms defining the regions of interest have been considered
and their performances have been compared using samples of simulated
events:

-   The RoI's size is 0.6 x 0.6 (Figure 4a) and the trigger Et is the Et
    contained in the RoI.

-   The RoI's size is 0.4 x 0.4 (Figure 4b) and the trigger Et is the Et
    contained in the 0.8 x 0.8 region around the RoI.

-   The RoI's size is 1.0 x 1.0 and the trigger Et is the Et contained
    in the RoI.

In each case, the prescription illustrated in Figure 5 is used to find
the local maxima RoIs.

For each algorithm, the transverse energy seen by the trigger for 40 GeV
jets is shown in Figure 6. This is to be compared with Figure 1 which
shows the Et seen by the current trigger. It can be seen that the
"sliding window" algorithms considerably improve the resolution of the
trigger Et.

  ---------------------------------------------------- --------------------------------------
  ![](media/image13.wmf){width="2.682638888888889in"   ![](media/image14.wmf){width="2.9in"
  height="2.2131944444444445in"}                       height="2.23125in"}

  ---------------------------------------------------- --------------------------------------

![](media/image15.wmf){width="2.6847222222222222in"
height="2.0868055555555554in"}

**Figure 11:** Ratio of the trigger Et to the transverse energy of the
generated jet, using three different algorithms to define the regions of
interest. Only jets with Et ≈ 40 GeV are used here. The ration of the
RMS to the mean of the distribution is written on each plot.

Moreover the relative resolution is similar in these three cases. The
choice of the RoI definition (i.e. of the algorithm) will thus be driven
either by more detailed studies, or by considerations relative to the
hardware implementation. As an example in the following, we consider the
algorithm b) .

### Efficiency

The simulated trigger efficiency for the algorithm b), with a threshold
set at 10 GeV, is shown as a function of the generated Et in Figure 7.
The rise of the efficiency with increasing Et is significantly faster
than that of the current trigger, also shown in Figure 7 for two values
of the threshold. With a 10 GeV threshold, an efficiency of 80 % is
obtained for jets with Et larger than 25 GeV.

The gain in efficiency which is specifically due to the sliding
procedure has been studied by considering an algorithm where the TT are
clustered 4 x 4, without any overlap in η, Φ. The comparison of the
"fixed" and "sliding" algorithms is shown in Figure 8. As shown in
Figure 8, using for the trigger decisions the Et deposited in 0.8 x 0.8
non-overlapping regions is much less powerfull.

![](media/image16.wmf){width="3.79375in" height="2.9381944444444446in"}

**Figure 12:** Trigger efficiency as a function of the transverse energy
of the generated jet, for the algorithm b) and for the current trigger.

![](media/image17.wmf){width="3.9291666666666667in"
height="2.923611111111111in"}

**Figure 13:** Trigger efficiencies when the trigger decision relies on
the Et deposited in regions of size 0.8 x 0.8 with (full curves) or
without (dashed curves) any overlap in η, Φ.

### Rates and rejection improvements

The performances of the sliding and current algorithms are studied here
by comparing both trigger efficiencies on a given class of processes and
inclusive rates as a function of the trigger threshold.

An inclusive jet condition is required here, i.e there should be at
least one RoI (one TT) whose trigger Et (whose Et) is above a given
threshold for the algorithm b) (for the current trigger). For different
threshold values varying by steps of 1 GeV, the inclusive trigger rate
and the efficiency for QCD events with pthat \> 20 GeV ( 40 GeV ) to
fulfill the trigger condition are shown in Figure 9, left (Figure 8,
right), for two values of the number of overlaid minimum bias events. On
each plot, the upper (lower) curve shows the performance of the sliding
(current) algorithm. It can be seen that the proposed algorithm can
reduce the inclusive rate by a factor of 2 to 4. The gain brought by the
sliding algorithm increases with the number of overlaid minimum bias
events.

A selective jet trigger is crucial to select "interesting" physical
events which do not contain any high pt lepton. Moreover, the
implementation of a "sliding" algorithm in logical devices allows
various quantities to be used in the L1 decision, not only the number of
towers above predefined thresholds. Two processes have been considered,
for which the selectivity of the current trigger will likely be not
optimal:

-   The production of a Higgs boson in association with a b-bbar pair.
    This process can have a significant cross-section in supersymmetric
    models with large tanbeta, where the Yukawa coupling of the b quark
    is enhanced. When the Higgs decays into two b quarks this leads to a
    4b signature. The final state contains two hard jets (from the Higgs
    decay) accompanied by two much softer jets. Such events could easily
    be separated from the QCD background in off-line analyses. with help
    of b-tagging. But it appears challenging to efficiently trigger on
    these events while retaining low inclusive trigger rates.

-   The associated production of a Higgs with a Z boson, followed by H →
    bb and Z →νν. With the current algorithm, these events could be
    triggered by a di-jet + missing energy requirement. The threshold on
    the missing energy could be lowered if a more selective jet trigger
    is used.

Figure 10 shows the efficiency versus inclusive rate for these two
processes. The performances of three trigger conditions are shown:

-   at least two fixed trigger towers of 0.2 x 0.2 above a given
    threshold.

-   at least one TT above 10 GeV and two TT above a given threshold.

-   at least two "trigger jets" whose summed trigger Et's is above a
    given threshold.

  ----------------------------------------------------- -----------------------------------------------------
  ![](media/image18.wmf){width="3.0548611111111112in"   ![](media/image19.wmf){width="3.0722222222222224in"
  height="2.3256944444444443in"}                        height="2.316666666666667in"}

  ![](media/image20.wmf){width="3.0548611111111112in"   ![](media/image21.wmf){width="3.0722222222222224in"
  height="2.2819444444444446in"}                        height="2.254166666666667in"}
  ----------------------------------------------------- -----------------------------------------------------

**Figure 14:** Trigger efficiency for events with p~t~ hat \> 20 GeV
(left) and p~t~ hat \> 40 GeV (right) as a function of the inclusive
trigger rate, for the algorithm b) (full curves) and the current
algorithm (dashed curves). Each dot on the curves corre spond to a
different trigger threshold. The luminosity is 2 10^32^ cm^2^ s^-^ and
the number of overlaid minimum bias events follows a Poisson
distribution of mean equal to 2.5 (upper plots) or to 5 (lower plots).

It can be seen that the third condition is the most selective.

### Implementation

These triggering algorithms can be implemented in Field Programmable
Gate Arrays on logical processing cards. Each of these cards has
responsibility for a region of the calorimeter. Necessarily, there are
overlapping areas of these regions as the algorithms must see data
belonging to neighboring towers to the tower being analyzed. We can
assume that for the processing of one tower, it is necessary to have
access to data from a region of maximum size (∆η x ∆φ) = 1.0 x 1.0
centered on the tower. This mandates overlap regions of size ∆η/∆φ = 1.6
or ∆η/∆φ = 0.8 between processing cards.

We estimate that the size of electronic circuits available in one year
will be large enough to contain the algorithms for a region (∆η x ∆φ) =
4.0 x 1.6. Choosing the largest possible elementary region has the
salutary consequence of minimizing the duplication of data among cards.
With this choice, the new trigger system will consist of only eight
logical processing cards (to be compared with the more than 400 cards in
the old system).

### Cost & schedule

### Recommendations

  ---------------------------------------- ----------------------------------------------------
  ![](media/image22.wmf){width="3.625in"   ![](media/image23.wmf){width="3.526388888888889in"
  height="2.7381944444444444in"}           height="2.676388888888889in"}

  ---------------------------------------- ----------------------------------------------------

**Figure 9:** Efficiency to trigger on bbh (left) and ZH (right) events
as a function of the inclusive rate. The three conditions shown require:
at least two TT above a threshold (black curves), at least one TT above
10 GeV and two TT above a threshold (blue curves), at least two trigger
jets such that the sum of their trigger Ets is above a given threshold
(red curves).

## Track Matching and Finer EM Segmentation

### Concept & physics implications

The capability to match tracks that are found in the central fiber
tracker (CFT) with trigger towers (TT) in the calorimeter is available
at a very coarse level in the Run2a detector. The matching of
calorimeter trigger towers to CFT tracks is limited to φ quadrants and
takes up valuable "and-or"in terms in the trigger framework (TFW). In
this section we explore the benefits of significantly increasing the CFT
φ granularity used in track matching to the much finer level of track
sectors. Such an upgrade is a significant augmentation of the
D∅ detector\'s triggering ability, which may provide a crucial handle to
some of the more difficult but desirable physics we wish to study in
Run2b.

### Simulation

The calorimeter trigger granularity is currently 2.5 times coarser in
φ than one tracking sector. For most of the results reported here, we
have matched all three of the sectors which at least partially overlap a
trigger tower. If there is at least one track with Pt\>1.5 GeV pointing
at the trigger tower, we consider there to be a match. In our studies
for this section, we have utilized five QCD samples. Four of these were
generated with QCD jets of Pt\> 2 GeV, 5 GeV, 20 GeV and 80 GeV,
respectively, and 0.7 min-bias interactions overlayed. One sample was a
20 GeV QCD sample with 5 interactions overlayed.

### Rates and rejection improvements

Since triggers will likely select jets of different inherent Pt\'s with
several different tower Et thresholds, we should understand what the
dependency of trigger tower track occupancy is on these parameters (see
Table 1). For instance, considering trigger towers with non-zero EM+HAD
Et, we find that towers in the 2 GeV QCD sample match tracks 2.4% of the
time, while 24.2% match in the 80 GeV sample. A more useful
understanding for the point-of-view of the trigger can be gotten by
looking at the dependence of this occupancy on tower Et within these
samples (for studies in the rest of this section, we match to EM
towers).

**Table 1** Trigger tower track occupancy for different tower Et
thresholds and jet Pt's, where the first line for every Et threshold
corresponds to the total number of towers (denominator) and the number
of track-matched towers (numerator). The second line gives the
fractional occupancy.

  -------- --------------- --------------- --------------- ----------------
  EM Et    Jet Pt \>2GeV   Jet Pt\>5GeV    Jet Pt\>20GeV   Jet Pt\>80GeV
  (GeV)                                                    

  \>0.5    9k/197k\        18k/240k\       42k/161k\       73k/147k\
           4.6%            7.5%            26.1%           49.7%

  \>2      69/297\         300/1147\       4k/7506\        16k/19k\
           23.2%           26.2%           53.3%           84.2%

  \>5      5/9\            27/63\          920/1587\       7800/9121\
           55%             42.9%           58%             85.5%

  \>10     \--\            3/7\            157/273\        4070/4579\
           \--             42.9%           57.5%           88.9%
  -------- --------------- --------------- --------------- ----------------

Where the first line for every Et threshold corresponds to the total
number of towers (denominator) and the number of track-matched towers
(numerator). The second line gives the fractional occupancy.

Since these results are based on samples corresponding to low-luminosity
conditions, it is important to ensure that these rejection factors are
robust against the additional interactions that we expect to typically
see. Using QCD events with parton threshold \~20 GeV, we compare two
samples with 0.7 and 5.0 minimum bias interactions, respectively. The
results are shown in Table 2

**Table 2**: Trigger tower track occupancy for 20 GeV jet Pt and
different tower Et thresholds and low (0.7 min bias) and high luminosity
(5 min bias) conditions, where the first line for every Et threshold
corresponds to the total number of towers (denominator) and the number
of track-matched towers (numerator). The second line gives the
fractional occupancy.

  ------------------ ------------------------ ---------------------------
  EM Et (GeV)        0.7 min bias             5 min bias

  \>0.5              42k/161k\                92k/291k\
                     26.1%                    32.6%

  \>2                4k/7506\                 2130/3482\
                     53.3%                    61.2%

  \>5                920/1587\                480/703\
                     58%                      68.3%

  \>10               157/273\                 96/125\
                     57.5%                    76.8%
  ------------------ ------------------------ ---------------------------

Given the significant rejection factors and robustness to multiple
interactions, we would like to know if there is a further way of
improving the rejection by segmenting the EM calorimeter towers more
finely to better match the CFT granularity. The simplest study one could
do divides each tower Et evenly in half between it\'s two phi halves. If
we only consider one of these halves for each tower, and match it to the
two sectors which overlap, we should obtain an unbiased estimate of what
is gained. Naively, this should be \~30% since we are matching 30% fewer
sectors. In practice, one finds the results shown in Table 3 for the QCD
Pt\>20 GeV sample (0.7mb overlay).

**Table 3:** Trigger tower track occupancy for 20 GeV jet Pt and
different tower Et thresholds for present ∆φ segmentation (0.2) and for
finer ∆φ segmentation (0.1), where the first line for every Et threshold
corresponds to the total number of towers (denominator) and the number
of track-matched towers (numerator). The second line gives the
fractional occupancy.

  ------------------ ------------------------ ---------------------------
  EM Et (GeV)        ∆φ = 0.2                 ∆φ = 0.1

  \>0.5              42k/161k\                31k/161k\
                     26.1%                    19.3%

  \>2                4k/7506\                 1160/2460\
                     53.3%                    47.2%

  \>5                920/1587\                130/273\
                     58%                      47.6%

  \>10               157/273\                 19/29\
                     57.5%                    65.5%
  ------------------ ------------------------ ---------------------------

It is likely in actual triggering that the track Pt threshold used will
be greater than 1.5 GeV, and more like 3 or 5 GeV, and maybe 10 GeV.
Since the number of fake high Pt tracks rises dramatically with multiple
interactions, we consider our 20 GeV sample with 5min-bias interactions.
This sample has 2147 events. We calculate the matching probabilities for
how many times a given TT overlaps sectors with tracks with Pt\>1.5 GeV,
\>3 GeV, \>5 GeV, and \>10 GeV. The results are shown in Table 4.

**Table 4:** Trigger tower track occupancy for 20 GeV jet Pt and
different tower Et thresholds and varying track Pt's, where the first
line for every Et threshold corresponds to the total number of towers
(denominator) and the number of track-matched towers (numerator). The
second line gives the fractional occupancy.

  -------- --------------- --------------- --------------- ----------------
  EM Et    Track Pt        Track Pt \>3GeV Track Pt \>5GeV Track Pt \>10GeV
  (GeV)    \>1.5GeV                                        

  \>0.5    92k/291k\       50k/291k\       25k/291k\       15k/291k\
           32.6%           17.2%           8.6%            5.2%

  \>2      2130/3482\      1630/3482\      1100/3482\      400/3482\
           61.2%           46.8%           31.6%           11.5%

  \>5      480/703\        380/703\        290/703\        140/703\
           68.3%           54.1%           41.3%           19.9%

  \>10     96/125\         80/125\         68/125\         37/125\
           76.8%           64%             54.4%           29.6%
  -------- --------------- --------------- --------------- ----------------

The first column in the table is from Table 2. The first column gives
the number of TTs matching tracks of the lowest Pt or greater divided by
the total number of TT\'s of that Et. Each of the other columns is
relative to the denominator in column 1. This shows, moving left to
right, that the tightening of the Pt cut does reduce the rate pretty
substantially, particularly for the lower Et towers.

### Efficiency

### Implementation

### Cost & schedule

### Recommendations

In summary, although the Et dependence of the rejection is large, the
gains from a calorimeter point-of-view are approximately a factor of 4
relative to no match for many of the backgrounds one will be triggering
on at level 1. The effect of multiple interactions on this result does
not appear to be large. If one were to contemplate further segmenting
the EM trigger towers in 0.1 in phi, there would a potential factor of 3
further improvement. Also, if one tightens the track Pt requirement
beyond 1.5GeV, then the rejection improves substantially again.

## Improving Missing Et Triggering using the Inter-Cryostat Energy at Level 1

### Concept & physics implications

Global tower Et sums such as missing Et or scalar Et, while very useful,
suffer from several significant problems at the L1 trigger. One
significant issue is that the ICR sampling layers are not available in
the calculation at Level 1. In addition, the imprecision of the tower
Et\'s gets compounded for global sums, resulting in signifantly degraded
effectiveness. This is particularly true in a multiple interaction
environment. There are two main possible solutions to these problems.
First we can take advantage of work done for Run2a to make the ICR
layers available at Level 2 and add these towers back into the global
sums at Level 1 in Run2b. Second, we can attempt to come up with a
scheme which descriminates towers which are from multiple interactions
and avoid adding them into the sum.

### Simulation

The region around 0.8\<\|eta\|\<1.5 encompasses the transition from
showers contained within the CC and showers contained within the EC.
There is a gap in EM coverage and a major thinning of FH coverage in
this area. Since these are the layers which comprise standard trigger
towers, there is a major degradation in Level 1 calorimeter response and
resolution in this region. This is exacerbated by the presence of
significant dead material in the solenoid in Run2. Simulations of single
pions and jets in this region indicate that the energy scale in this
region goes as low as 40% of the CC/EC scale, and the resolution is as
bad as 6 times worse than in the CC or EC. These results are very
consistent with findings from Run1 Level 1 missing Et analyses. One of
the major results of this deficiency is that the efficiency and
rejection of a Level 1 missing Et selection are noticeably degraded.
These simulations also indicate that adding ICD and MG cells into
trigger towers can improve the scale by a factor of 2, while optimizing
the resolution by a factor of 3.

In principle, it is straightforward to estimate the effect of the ICD
and MG to the missing Et calculation. Unfortunately, the Run2 software
currently suffers from three major problems in producing a trustworthy
study of this matter. The sampling weights valid for the trigger towers,
as opposed to the precision readout, are not applied to cell-level
energies when trigger towers are constructed for the trigger simulator.
Also, there has been no opportunity yet to determine whether the
detector simulation accurately reproduces the behavior in the ICR, and
this is especially important for the ICD which was substantially more
difficult to calibrate than the LAr gaps in Run1. Lastly, the mapping of
calorimeter cells has not been instituted into our standard Monte-Carlo
sample generation. The last of these problems is easily solved, but the
first two present a larger problem.

Until such time as we have resolved these problems, we will estimate the
expected improvement based on other studies.

### Rates and rejection improvements from ICR energies

To estimate the effect of adding the ICR detectors into the missing Et,
we consider the fact that in the region of 1.0\<\|eta\|\<1.4, the
sampling weight simulations indicate approximately half of the energy
will be deposited in the EM+FH, and the other half in the ICD+MG. As a
crude estimate of the magnitude of the effect of adding the ICR layers,
we will merely consider the missing Et measurement with and without the
EM+FH layers in this region and assume the ICR improvement will be
similar. Although the sample used for this calculation is a QCD sample
with jet Pt\>20 GeV and 0 min-bias events overlayed, for historical
reasons it is a different sample than that mentioned in the rest of this
document with the same specifications. The missing Et mean and RMS in
this sample behave as follows:

if remove all ICR TTs: μ/rms = 6.7 GeV / 4.8 GeV

if only use EM+FH TTs: μ/rms = 5.5 GeV / 3.9 GeV

The number of events passing various Level 1 missing Et cuts in this
sample are shown in Table 5.

**Table 5:** Events passing L1 missing Et cuts when the ICR energy is
included and when it is removed from the trigger towers.

  -------------------- ------------------------- -------------------------
  L1MET                Without ICR               With ICR

  \> 5GeV              948                       766

  \> 10 GeV            337                       185

  \>15 GeV             95                        40

  \> 20 GeV            37                        11

  \> 25 GeV            9                         4
  -------------------- ------------------------- -------------------------

Thus, the region is important to the missing Et calculation and the
rates of passing 15 or 20 GeV selection can change by factors of around
3. A proper treatment of the gains from adding in the ICD and MG,
however, will have to await a satisfactory treatment of the relative
weights of various layers.

### Improving Missing Et for Multiple interaction Events

Our experience in Run1 indicated the Level 1 missing Et to be very
sensitive to the number of multiple interactions. This results from
several factors, including the fact that the fundamental trigger tower
fractional energy resolution is poor, especially for very low Et towers,
and the numbers of these towers increases substantially with the number
of multiple interactions. As a result, we have explored a few ways in
which we might improve the Missing Et resolution to reduce this problem
in Run2b.

First, we varied the low threshold on the Et of towers going into the
global sum. In Run1, this threshold was 0.5 GeV and was apparently not
studied in the light of multiple interactions. Again, we\'ve used the
QCD Pt\>20 samples with 0mb and 5mb overlays for background, and the
ttbar sample with 2.5 mb overlays for signal. If we calculate the
missing Et mean and RMS in these samples for various Et thresholds, we
find the results shown in Table 6.

**Table 6:** Change in the means and rms for the missing Et for
background (QCD) and signal (ttbar) samples as a function of the trigger
tower (TT) threshold.

  ----------------- ------------------ ------------------ ------------------
  Met calc          QCD 0mb [(μ/rms)   QCD 5mb [μ/rms) in ttbar ([μ/rms) in
                    in                 GeV]{.underline}   GeV]{.underline}
                    GeV]{.underline}                      

  TT\>0.5GeV        5.1/3.8            6.5/4.2            35.9/25.4

  TT\>1GeV          5.2/3.9            5.8/4.0            35.4/24.7

  TT\>1.5GeV        5.3/4.1            5.6/4.0            35.0/24.1

  TT\>2GeV          5.2/4.2            5.4/4.2            34.6/23.6
  ----------------- ------------------ ------------------ ------------------

where the error on the mean and RMS for the QCD samples is approximately
0.1 GeV. So the cut of 2GeV reduces the mean of the QCD sample
noticeably. Although scalar Et is generally considered a poor variable
at Level 1 because of its sensitivity to multiple interactions, we have
studied its mean and rms (see Table 7) for the same thresholds to see
what is happening:

**Table 7:** Change in the means and rms for the Et scalar sum for
background (QCD) and signal (ttbar) samples as a function of the trigger
tower (TT) threshold.

  ----------------- ------------------ ------------------ ------------------
  Sum Et calc       QCD 0mb [(μ/rms)   QCD 5mb [μ/rms) in ttbar ([μ/rms) in
                    in                 GeV]{.underline}   GeV]{.underline}
                    GeV]{.underline}                      

  TT\>0.5GeV        23.5/13.0          179.7/68.8         57.7/39.3

  TT\>1GeV          17.9/11.9          26.6/15.8          161.1/66.4

  TT\>1.5GeV        14.7/11.4          18.0/12.5          151/64.9

  TT\>2GeV          12.5/11.1          14.2/11.6          143.6/63.8
  ----------------- ------------------ ------------------ ------------------

Comparison of the two QCD samples indicates that low thresholds let in
an enormous amount of energy which has nothing to do with the hard
scatter interaction.

Another promising variable is that of the TT eta, since the energy in
multiple interactions is often thought of as being deposited in the
forward region. As we did above for trigger tower thresholds, we apply
cuts on TT eta such that various detector ietas are left out of the sum.
We have left the TT Et cut at 0.5 GeV for this calculation. The results
are the following for missing Et:

**Table 8:** Change in the means and rms for the missing Et for
background (QCD) and signal (ttbar) samples as a function of the trigger
tower (TT) η range (using the detector η−index which is 10 x η).

  ----------------- ------------------ ------------------ ------------------
  MEt calc          QCD 0mb [(μ/rms)   QCD 5mb [μ/rms) in ttbar ([μ/rms) in
                    in                 GeV]{.underline}   GeV]{.underline}
                    GeV]{.underline}                      

  TT\<34            5.1/3.8            6.5/4.2            35.9/25.5

  TT\<32            5.3/3.9            6.7/4.3            36.0/25.4

  TT\<30            5.4/4.0            6.8/4.4            36.0/25.4

  TT\<28            5.6/4.1            6.9/4.5            36.0/25.4
  ----------------- ------------------ ------------------ ------------------

Which indicates a slight degradation in the missing Et behavior. The
scalar Et behaves as follows:

**Table 9:** Change in the means and rms for the scalar Et for
background (QCD) and signal (ttbar) samples as a function of the trigger
tower (TT) η range (using the detector η−index which is 10 x η).

  ----------------- ------------------ ------------------ ------------------
  Sum Et calc       QCD 0mb [(μ/rms)   QCD 5mb [μ/rms) in ttbar ([μ/rms) in
                    in                 GeV]{.underline}   GeV]{.underline}
                    GeV]{.underline}                      

  TT\<34            23.2/13.0          53.8/34.9          178.9/68.7

  TT\<32            22.6/13.0          51.2/32.7          178.2/68.7

  TT\<30            22.2/12.9          50.0/31.8          177.8/68.7

  TT\<28            21.7/12.9          48.3/30.6          177.3/68.7
  ----------------- ------------------ ------------------ ------------------

indicating that the total amount of Et at high eta is small, which is
why there is no effect.

Another concern for the missing Et measurement involves the truncation
of trigger tower Et\'s into 0.5 GeV bins. Since one to two hundred
towers are typically added into the Missing Et, this resolution loss can
start to be noticeable. Taking the QCD Pt\>20 sample with mb=0 and 1648
events, we can use the simulator described above in the ICR discussion
and toggle truncation.

  ----------------- ----------------- ----------------- -----------------
  MET\>             no trunc.         no trunc,         with truncation
                                      TT\>0.5GeV        

  5 GeV             947               868               766

  10 GeV            309               261               185

  15 GeV            76                51                40

  20 GeV            22                17                11

  25 GeV            7                 5                 4
  ----------------- ----------------- ----------------- -----------------

The first column indicates truncation turned off and no threshold
applied to trigger towers. The second column also has no truncation and
zeros out all towers with Et\<0.5. The third column employs the normal
0.5 GeV truncation. Since truncation lowers tower Et\'s only to the next
lowest 0.5 GeV increment, it effectively deweights all of the poorly
measured Et in low Et towers. In fact, if we consider the QCD Pt\>20 GeV
sample with 5mb already discussed, the missing Et mean and RMS are
mildly improved over the straight 1.5GeV threshold by a simple weighting
scheme. If we choose weights of 5%, 25%, and 75% for Et = 0.5, 1.0, and
1.5 GeV, respectively, we find the following

  ----------------------------------- -----------------------------------
  if TT Et\>1.5 GeV:                  μ/rms = 5.41 GeV / 4.20 GeV

  if weight TT:                       μ/rms = 5.41 GeV / 3.96 GeV
  ----------------------------------- -----------------------------------

If the capability exists in an FPGA to enforce a weighting scheme, then
one might devise a scheme which does better than this.

Because the trigger tower threshold seems to be the simplest solution
that shows progress, and the weighting also seems to help, one might ask
whether rejecting low Et towers unless they are near significant
neighbors might help. Looking again in the 5mb QCD sample at missing Et
means and sigmas, however, reveals the following:

  ----------------------------------- -----------------------------------
  no cut:                             μ/rms = 6.45 GeV / 4.17 GeV

  if NN Et \> 0.5 GeV:                μ/rms = 6.45 GeV / 4.37 GeV

  if NN Et \> 1.5 GeV:                μ/rms = 6.56 GeV / 4.37 GeV

  if NN Et \> 3.0 GeV:                μ/rms = 6.72 GeV / 4.86 GeV

  if NN Et \> 10 GeV:                 μ/rms = 5.62 GeV / 4.57 GeV

  if NN Et \> 1k GeV:                 μ/rms = 5.41 GeV / 4.20 GeV
  ----------------------------------- -----------------------------------

which indicates a significant degradation in missing Et mean and
resolution.

### Efficiency

### Implementation

### Cost & schedule

### Recommendations

In this section, we have explored several different ways to improve the
calorimeter missing Et measurement at Level 1. Studies leading to the
optimization of the Run2a trigger have indicated a large improvement in
the scale and resolution of jets in this region if the ICD and MG are
used. Although our current simulation samples do not have a proper
treatment of this region, a crude estimate indicates that this amount of
energy should have a noticeable improvement on the missing Et
resolution.

Several attempts were also made to improve the behavior of missing Et in
a multiple interaction environment. The most promising appears to be a
simple tightening of the Et threshold on a trigger tower to around 1.5
GeV which would reduce the background by around 20% in our QCD sample.
The actual degradation in the real data may be larger than we see here,
however, and the corresponding gain may also increase. We will be in a
better position to evaluate this when we have reliable data at various
luminosities. There is some evidence that a weighting scheme would
provide further benefits.

## Finer EM Tower Segmentation

### Concept & physics implications

### Simulation

Monte Carlo single electrons have been used to compare the performances
of the various options:

Fixed trigger towers of 0.2 x 0.2 (the current system)

Fixed trigger towers of 0.2 x 0.1

Trigger towers of size 0.2 x 0.2 which slide in either the η or Φ
direction by steps of 0.1.

The direction of the generated electron is extrapolated to the
calorimeter surface and trigger regions are looked for in the
neighborhood of the intersection point.

Figure 10 shows the transverse energy seen in the trigger region for
cases 2) and 3), normalized to that seen by the current trigger. It can
be sen that fixed trigger towers of size 0.2 x 0.1 will see \~ 5% less
Et than the current TTs. A slightly larger energy is deposited in
windows which are sliding in the η rather than in the Φ direction. This
is due to the fact that when the Zvertex is not zero, the calorimeter
geometry is not projective in η (while it is always projective in Φ).
Figure 11 shows that indeed, when electrons are emitted at Zvertex ≈ 0,
overlaps in η and overlaps in Φ yield similar energy deposits in the
trigger regions.

![](media/image24.wmf){width="4.30625in" height="3.1034722222222224in"}

**Figure 15:** Ratio of the Et measured in various possible trigger
regions to the Et seen by the trigger when using fixed 0.2 x 0.2 TTs.

![](media/image25.wmf){width="4.404861111111111in"
height="3.2395833333333335in"}

**Figure 16:** Ratio of the trigger Et seen by using sliding windows of
0.1 in η or in Φ to the Et seen in the current trigger towers, as a
function of the Zvertex.

### Rates and rejection improvements

### Efficiency

Efficiencies on single electron events are summarized in the following
table:

+---------+---------+---------+---------+---------+---------+---------+
| Et,e    | Trigger | 0.2 x   | 0.2 x   | 0.2 x   | 0.1 x   | 0.2 x   |
|         | th      | 0.2     | 0.2     | 0.2     | 0.2     | 0.1     |
| (GeV)   | reshold | (fixed) | sliding | sliding |         |         |
|         | (GeV)   |         | in η    | in Φ    |         |         |
+---------+---------+---------+---------+---------+---------+---------+
| 10      | 5       | 91.1    | 94.5    | 94.5    | 86.1    | 89.0    |
+---------+---------+---------+---------+---------+---------+---------+
| 10      | 7       | 69.6    | 78.0    | 76.4    | 57.4    | 59.1    |
+---------+---------+---------+---------+---------+---------+---------+
| 20      | 10      | 90.5    | 93.4    | 93.9    | 86.9    | 88.6    |
+---------+---------+---------+---------+---------+---------+---------+

### Implementation

### Cost & schedule

### Recommendations

## EM Trigger Tower Shape Cuts

### Concept & physics implications

### Simulation

### Rates and rejection improvements

### Efficiency

### Implementation

### Cost & schedule

### Recommendations

## Missing Et Filtering

### Concept & physics implications

### Simulation

### Rates and rejection improvements

### Efficiency

### Implementation

### Cost & schedule

### Recommendations

## Topological Considerations

### Concept & physics implications (acoplanar jets)

The search for Higgs boson is the central element of the Run IIb physics
program. The Run II Higgs workshop report \[1\] concluded that the
channel p pbar -\> HZ -\> b bbar nu nubar was critical. This final state
poses a difficult topology, two relatively soft jets (p_t \< M_h/2) with
modest missing Et. For a RunI style Di-jet plus ETmiss trigger, the
nominal calorimeter trigger tower and missing Et thresholds are such
that the efficiency for the b bbar nu nubar channel is compromised. The
trigger efficiency is driven by the allowable Level 1 rate. While
b-tagging can be used at Level2 to control the rate, it is important to
note that b tagging will not be possible at Level 1. Thus, it is clear
that this channel relies on alternative triggering techniques at Level
1.

To efficiently trigger on the HZ channel one can exploit the unique
topology: the higgs is recoiling off of a massive particle decaying
invisibly, thereby leading to an acoplanar jet topology. From Monte
Carlo based studies, it has been demonstrated that the L1CTT can be used
to identify acoplanar topologies using the fiber tracker. The algorithm
is based on identifying the 4.5 degree wide sector having the highest
track pt sum within the two 45 degree wide octants having the highest
track pt sum. In Figure 17, the opening angle between the leading
partons is shown, the binning reflects the CFT azimuthal segmentation.
The red histogram represents the true opening angle and the blue is the
corresponding angle reconstructed from charged tracks in the CFT using
the above algorithm. Note the QCD background is predominately
back-to-back (i.e. the most probable opening angle is 40 sectors or 180
degrees) whereas the Higgs signal has a substantial acoplanar component.
Figure 18 shows the correlation between delta phi and the ETmiss of the
event for signal and representative QCD backgrounds. The figures
demonstrate that combining an acoplanar toplogy cut (Nsector \< 35) with
a looser missing ET requirement can maintain good signal efficiency
while still suppressing most of the QCD background.

![](media/image26.wmf){width="5.992361111111111in"
height="5.992361111111111in"}

**Figure 17:** The opening angle between the leading partons.

![](media/image27.wmf){width="5.992361111111111in"
height="5.992361111111111in"}

**Figure 18**: The correlation between delta phi and the ETmiss of the
event for signal and representative QCD backgrounds

The use of the CFT phi correlations becomes compromised at high
instantaneous luminosity. as shown in Figure 19. Only for relatively
high pt jets does the correlation remain. At high luminosity one has to
rely on the calorimeter to confirm the CFT jets. Modest trigger
thresholds are able to reduce the rate from low pt scatters.

![](media/image28.wmf){width="5.992361111111111in"
height="5.992361111111111in"}

**Figure 19:** Correlation of ∆φ in high luminosity conditions (left
hand plots with 7 minimum bias events) and low luminosity (right hand
plots with zero additional minimum bias events).

With an improved Level 1 calorimeter trigger that allows correlating CFT
and calorimeter based jets these backgrounds can be further suppressed.

References

\-\-\-\-\-\-\-\-\--

\[1\] Report of the Higgs Working Group of the Tevatron Run 2 SUSY/Higgs
Workshop,

M. Carena et al, hep-ph/0010338

### 

### Simulation

### Rates and rejection improvements

### Efficiency

### Implementation

### Cost & schedule

### Recommendations

## L1 Calorimeter Trigger Implementation Issues

The physics imperatives that drive the need to build a new L1
calorimeter trigger raise a number of implementation issues that will
need to be resolved before construction can begin. In this section we
discuss the issues that have been raised to date regarding
implementation choices that need to be made.

### ADC/DFE Split

In the previous sections one has seen that several functions are needed
in the system. It is natural to split the system in an ADC part dealing
with the analogue signals and a DFE (Digital Front End) part purely
digital. These two parts being linked by LVDS links.The location of the
digital filter gives two options:

#### Option 1: "Dumb" ADC

The ADC part contains only the converter. This could be done since the
DFE should have enough power to perform both the digital filtering and
the physics algorithms. The ADC part produces output samples with 10
bits accuracy. It does not need slow controls. It is cheap, simple and
very easy (fast) to implement. However this is incompatible with a
sampling rate faster than the beam crossing because of output bandwidth
considerations.

#### Option 2: Filter in ADC

Here the digital filter is implemented in the ADC part. There are
several advantages to this option:

-   The output of the ADC consists of 8 bits words. This reduces the
    link bandwidth by 20%.

-   There are several special towers (at the boundary between central
    and end caps) needing an additional treatment. This treatment is
    needed anyway, but doing it in the ADC makes the DFE completely
    regular (i.e. easier).

-   The data at the output of the ADC is transferred to the level 2
    trigger and the read-out. Doing the filtering in the ADC avoids to
    redo it in level 2 and in off-line processing.

### Granularity

The current granularity of the trigger towers is 0.2 x 0.2. It is
possible with a modification of the summing mezzanine in the BLS to go
to a granularity of 0.1\*0.2 while keeping the current cable plant.
There are two options to this increase of granularity:

-   Cutting only the EM towers (mixed sizes)

-   Cutting both EM and Hadronic towers (0.1\*0.1).

The gains for physics have been shown previously; here we estimate the
cost of the three options, normalized to the cost of the 0.2\*0.2
option:

  ----------------- ----------------- ----------------- -----------------
                    0.2\*0.2          Mixed sizes       0.1\*0.1

  ADC               1                 1.5               2

  DFE               1                 2                 4
  ----------------- ----------------- ----------------- -----------------

The problems with the algorithms in the mixed size option have been
explained previously.

### 

### Overlap

The amount of data produced by the ADC is of the order of 20 Gbytes/s
(for 0.2 x 0.2 and twice that for 0.1\*0.2). This amount is too large
for a single DFE card: the digital processing must be done by tens of
DFE cards, each one processing a rectangular piece of the calorimeter.
The number and speed of the LVDS links feeding one DFE card determine
the number of DFE cards needed. Each DFE card is responsible for the
recognition of electrons and jets in its piece of the calorimeter.

In order to implement the algorithms, each DFE needs data from the
neighboring ones. The amount of sharing depends on the details of the
algorithms; the jet algorithm is the most demanding (because jets are
larger than electrons). The overlap must be lower or equal to two cells
in all directions to keep a reasonable size to the system. This limits
the choice of the jet algorithm. The first limitation comes from the
requirement to avoid double counting: the same jet should not be found
in two adjacent DFE. The second requirement is to avoid splitting a
single jet at the boundary of two DFE. Both limitations can be corrected
in the next processing stage, but this should be avoided if possible.
There are two options for the overlap:

#### 2 TT overlap in all directions:

#### This allows for jet algorithms up to 1.0\*1.0

> It is also needed in the 0.8\*0.8 algorithm if one requests separated
> jets.
>
> This symmetrical arrangement makes the cabling more systematic.

-   Alternating 2 TT and 1 TT:

> This is the minimum for the 0.8\*0.8 algorithm.
>
> This reduces the bandwidth between ADC and DFE by 8%.

### 

### 

### DFE design

#### Reuse of CTT's DFE

It has been proposed to reuse the DFE of the CTT for this application.
Initial studies on the logical mapping of DFE's to calorimeter sectors,
the physical cabling and the required capacity of the links tend to show
that an option based on DFEs seems viable. More detailed studies are
needed, especially on the implementation of trigger algorithms in
FPGA's, in order to draw a conclusion on the possibility to use DFE's.
We estimate that this solution would roughly divides by two the design
effort required, leading to several months of savings in manpower.

This solution mandates that the filter be implemented in the ADC cards
because carrying 10 bit samples over DFE links requires 25% more
bandwidth than dealing with 8 bit Et calibrated samples. In addition,
incorporating a series of digital filters and the trigger algorithm
logic may not fit in the FPGA of DFEs. The separation of the digital
filter and the trigger algorithm part would also facilitate development
and test, especially if these two units are developed at different
locations. A last argument in favor of the split is the limitation of
bandwidth for slow control on the DFEs that could make filter
coefficients loading and update a slow process.

There are however a number of concerns for a DFE based solution:

-   Some components of the DFE, especially connectors on the
    motherboard, may not be available anymore. It may not be possible to
    build a sufficient number of DFEs and spare cards.

-   FPGAs on the daughter card of a DFE are mature devices and will be
    obsolete when run 2b starts. Although a new daughter card with a
    more modern FPGA could be designed, the fact that the serial to
    parallel conversion for the input links is implemented on the
    motherboard of a DFE places a tight upper limit on link speed and
    imposes worrisome constraints on FPGA pin counts, printed circuit
    board design\...

-   The bandwidth of DFE links is marginally sufficient, even if these
    can be clocked at 61 MHz instead of the current 53 MHz. This
    limitation could exclude the possibi1ity to run algorithms that
    operate on a 1.0\*1.0 window in eta-phi space, though using 0.8\*0.8
    windows would probably fit.

-   There is no SCL links in the DFE system: the SCL link must be
    implemented in the ADC sub-system. This will obviously complicate
    the design of the ADC cards, offsetting the expected savings in
    manpower on the DFE side.

-   Because DFEs do not receive timing information and are purely data
    driven, the necessary timing signals must be imbedded in the
    dataflow by the ADC cards. This places additional constraints on the
    ADC cards and consumes a small fraction of the (precious) link
    bandwidth.

-   The logic capacity of the FPGA in the current DFE may not be
    sufficient. This point has not been studied yet. The FPGA
    manufacturer does not foresee much (\>2) larger devices because it
    has switched to a new footprint.

-   The bandwidth of the slow control is insufficient to keep all the
    functionalities of the current trigger software.

-   The mechanics of the front panel connectors has a delicate handling.

#### 

#### A dedicated DFE

In the study of a dedicated DFE a few points were decided:

-   Using much faster LVDS links. This is obtained by feeding the links
    directly into the FPGA, bypassing the slow serializer/deserializer
    used in the CTT DFE.

-   Using SCL data from the back plane for synchronization.

-   Using USB2 for slow control.

-   Using 12 input links and 6 output links.

-   Using latest generation FPGA. Using smaller footprint FPGA because
    of the reduced number of IO pins obtained by serial IO instead of
    parallel.

-   Placing all IO cables at the rear of the module.

#### Another possibility

It is possible to modify the previous dedicated DFE to make it
compatible with the current CTT DFE. One only needs the following
change:

-   Use the same LVDS cables.

-   Accept the slow control of the DFE crate as an alternate to the
    normal one.

-   Use software compatible FPGA.

This new DFE would provide ample improvement margin for possible CTT
upgrades.

## L1 Calorimeter Summary & Conclusions

# L1 Muon Trigger

### Goals

-   Efficient triggering on muons

-   Rejection of non-muon backgrounds

### Description of Current L1 Muon Trigger

-   Overview

-   Forward muon trigger

-   Central muon trigger

### Performance of Current L1 Muon Trigger

-   Simulation (data?)

-   Trigger rates and luminosity dependence

-   PDT aging

-   Conclusions and implications for high luminosity

### L1 Muon Trigger Improvements

-   Concept & physics implications

-   Simulation

-   Rates and rejection improvements

-   Efficiency

-   Implementation

-   Cost & schedule

-   Recommendations

### L1 Muon Summary and Conclusions

# Level 2 Triggers

### Goals

-   Maintain current rejection

### L2 Beta Upgrade

-   Concept & physics implications

-   Implementation

-   Performance scaling

-   Cost & schedule

-   Recommendations

### STT Upgrade

-   Concept & physics implications

-   Implementation

-   Performance scaling

-   Cost & schedule

-   Recommendations

### Other Level 2 Options

-   Concept & physics implications

-   Implementation

-   Performance scaling

-   Cost & schedule

-   Recommendations

### Level 2 Summary and Conclusions

# Level 3 Triggers

### Goals

-   Maintain existing rejection

### Level 3 Farm Upgrade

-   Concept & physics implications

-   Implementation

-   Performance scaling

-   Cost & schedule

-   Recommendations

### Replacement DAQ Option

-   Concept

-   Implementation

-   Cost & schedule

-   Recommendations

### Level 3 Summary and Conclusions

# CDP Summary and Conclusions

Below are some templates:

This is an example[^2] of a reference.

### Second Level Heading

**Table 1.** Sample Table

  ------- --------------- -------- -------------- ----- ---- ---------- --------
  Layer   Radius (mm)     Axial/   Silicon Sensor \#    #Z   \# Sensors \# Chips
          (approximate)   Stereo   (#SVX4,        Phi                   
                                   length)                              

  0       16              A        1 or 2chip,    12    8    96         144
                                   8cm                                  

  1       35              A        2 chip, 8cm    18    8    144        288

  2       62              A+S      5 chip, 12cm   12    6    144        720

  3       95              A+S      5 chip, 12cm   18    8    288        1440

  4       127             A+S      5 chip, 12cm   24    8    384        1920

  5       160             A+S      5 chip, 12cm   30    10   600        3000

  Total                   6A, 4S   3 types                   1656       7512
  ------- --------------- -------- -------------- ----- ---- ---------- --------

![](media/image29.wmf){width="5.998611111111111in"
height="2.8201388888888888in"}

**Figure 1:** Sample figure.

.

# References

[^1]: These rates are estimated here from samples of Monte-Carlo QCD
    events, passed through a simulation of the trigger response.

[^2]: F. Borcherding, *"Tracking Triggers at High Luminosity,"* D∅ Run
    2b Workshop, FNAL, February 28, 2000.