VI. Use of PFAs in SiD Development
1. Introduction
The SiD detector is designed to take advantage of jet reconstruction using the Particle
Flow Algorithm (PFA) approach. A PFA attempts to reconstruct all of the individual
particles in an event according to their detector signatures – tracks for charged particles
and calorimeter clusters for photons and neutral hadrons. Separation and identification of
calorimeter energy deposits is, therefore, crucial for the PFA approach to work. Charged
hadrons normally comprise ~65% of the typical jet energy, photons ~25%, and neutral
hadrons the remaining ~10%. By separating the calorimeter clusters made by these
particles, better jet energy resolution and also dijet mass resolution can be obtained by
optimal use of detector components – tracking detectors for charged particles, the ECAL
for photons, and the ECAL and HCAL for neutral hadrons. A PFA can be used to
optimize choices for detector components – mainly the ECAL and HCAL. The SiD will
take advantage of the PFA approach to optimize many of the detector parameters,
resulting in improved jet reconstruction performance over existing detector designs along
with optimized cost.
2. PFAs in Physics Processes
The goals for PFA performance have been expressed in many ways. For an ILC detector
based on PFA jet reconstruction, the goal is to be able to separate on an event-by-event
basis W and Z bosons using all decay modes including the dijet mode. For no loss in
luminosity, this means that the W and Z masses must be measured with a resolution of ~3
GeV, or to ~3-4%. Typical calorimeters designed without PFA optimization cannot
achieve this goal – even if they are perfectly compensating. Since the performance goal
depends on (QCD) jet reconstruction, the optimization of the detector will ultimately
depend on jets in simulation.
The PFA approach for the SiD detector has been studied with this goal in mind. The dijet
mass resolution performance of the SiD has been studied as a function of several
variables – notably the solenoidal B-field, the inner radius of the ECAL, jet energy, and
jet multiplicity. Our approach has been to start with the simulated process e+e- -> ZZ
where one Z -> 2 jets and the other Z -> nunu. This process produces jets of energy ~120
GeV – the typical jet energy of many 4-jet processes at e+e- annihilation at 500 GeV.
The dijet mass can be determined without any jet combinatoric ambiguity for these
events. Then, the all-hadronic decay mode is studied, where ZZ -> 4 jets. Thus, the
detector is filled with more 120 GeV jets. Another test is e+e- -> ttbar – 6 jets with
reduced jet energies. Finally, we can test the limitations of PFAs with e+e- -> qqbar at
500 GeV. With this analysis, we can investigate the jet energy dependence of the dijet
mass resolution. As the jet energy increases, confusion in the PFA eventually dominates
the mass resolution, degrading the PFA performance.
3. Tools for PFA Development
To develop the PFA, several tools are needed which are common to all detector models
and PFA implementations. A common basis for PFA applications is required – in
particular, a common standard detector calibration is needed along with a standard
Perfect PFA definition in order for useful comparisons to be made between PFA
algorithms and detector models.
Calorimeter Calibration
A method of calorimeter calibration has been developed which could be used in a real
test beam for a detector prototype. The PFA approach results in separated charged
hadrons, photons, and neutral hadrons. Therefore, a full calibration should include beams
of these species if possible. Neutral hadron beams are especially useful. In simulation,
pions (+-), photons, and a mixture of n, nbar, and Klong are used to calibrate the ECAL
and HCAL. The calibration method gives corrected energies for cheated (all hits)
clusters. Additional corrections are needed for the application of real cluster algorithms,
analysis techniques, etc. A standard calibration method exists and SiD variants all use
this method to provide standard calibrations for detector components.
Perfect PFA Definition
For PFA analysis, it is important to have a standard definition of the perfect application
of the PFA – no confusion in the identification of particle-cluster associations. It is
especially important for the useful cases in which perfect definitions are used – for
example, when perfect charged particle tracks are used to test the PFA performance in the
calorimeter only. When used with the standard detector calibration procedure,
resolutions of individual particle energy distributions match those of the particles used in
the calibration method. The Perfect PFA provides a check not only of the optimal PFA
performance, but also a check of the calorimeter calibration method.
Cluster Algorithms
Many cluster algorithms have been developed for use in PFAs. More importantly, most
of these have standardized inputs and outputs, so easy evaluation and comparison of
multiple cluster algorithms can be done. Procedures exist to illustrate purity and
efficiency of cluster algorithms, so that optimal choice can be made of algorithms to use
in various stages of the PFA. For example, when choosing a cluster algorithm for trackcluster matching, overall purity performance is preferred over efficiency, while for
photons, a more balanced performance is desired.
4. PFA Approaches for SiD
Several PFA approaches have been investigated for the ILC detector concepts. These can
be divided into basically 2 types – a modular approach designed to perform particle
identification and separation with methods optimized for each particle species, and
cluster algorithm approaches where a specific cluster algorithm is used to define all
particle clusters in the calorimeter.
One approach to PFA development is to use an optimized single cluster algorithm to try
to form clusters of all particles in the event. These cluster algorithms must be able to
reconstruct clusters of many varied types – mips, electromagnetic showers (photons and
electrons), and hadronic showers (both neutral and charged). Cluster algorithms based on
hit density, fragment distances, and shower shapes have been developed for this type of
PFA.
Another approach is to develop individual algorithms optimized for the particular particle
being tested. This type of PFA has a natural modular structure with each step consisting
of a cluster algorithm and topological evaluation algorithms optimized for a particular
particle species. The modular structure allows easy comparisons to be made at each stage
and for fast identification of PFA performance.
5. PFA Results
The following plots show results for application of a PFA on single particle species. The
ultimate performance limit of the PFA can be illustrated for each type of particle in this
way and estimates of the minimum confusion introduced by the PFA can be made. Plots
for charged hadrons (pions), photons, and neutral hadrons here.
Single Particle PFA Response
Charged Hadron/Cluster Association
Photon Algorithm Performance
Neutral Hadron Algorithms
Initially, PFAs were developed using simulated e+e- -> Z production at the Z pole (91.5
GeV). No jet algorithms were needed and the PFA performance could be shown as an
energy sum. Since there is no ambiguity in the choice of jets used in the dijet mass
calculation, the dijet mass resolution and the energy sum resolution are ~equal for these
events. Plots for ZPole performance of PFA if any.
PFA Results for Total Energy Sum at ZPole
The dijet mass is the most important result of PFA performance for the e+e- collider at
500 GeV CM. Dijet results are shown here for events with 2 jets, 4 jets, and 6 jets at 500
GeV CM. When plotted as a function of jet energy, the increasing contribution of
confusion in the real PFA is seen.
Dijet Results
@500 GeV
vs jet energy
6. Future SiD Optimization with PFAs
Based on the performance obtained so far, PFAs will be used to optimize several
parameters of the SiD detector, helping to choose these parameters for the final SiD
design. In particular, the PFA performance can be used to evaluate various choices of
inner radius (distance from IP to inner face of ECAL), and B-field (central solenoidal
field strength). Along with the cost parameters, the PFA can then be used to optimize the
size of the SiD detector. Also, various technologies for an optimized HCAL can be
tested with PFA applications. For example, the PFA performance of analog scintillator
designs can be compared to digital gas calorimeters. Some plots illustrating beginning
studies of these things here.
IR
B-Field
(H)CAL Technology