Preprint March 30, 2022

Particle Flow Calorimetry

Randal Ruchti1, Katja Krüger2

1Department of Physics, University of Notre Dame, IN 46556, USA

2Deutsches Elektronen-Synchrotron DESY, Notkestr. 85, 22607 Hamburg, Germany

> ABSTRACT
>
>
>
>
> The motivation for PF calorimetry is to experimentally measure the energy of
> hadron jets with excellent resolution. In particle flow designs,
> $\sigma/E<5\%$ should be possible for a range of jet energies from $\sim
> 50\,{\rm GeV}$ to $\sim 250\,{\rm GeV}$, important particularly for
> experiments at electron-positron colliders (ILC, CLIC, FCCee, CEPC). The
> high granularity, which is essential for PF calorimetry, can also be very
> beneficial for removal of background from pile-up on an event-by-event basis
> making such calorimeters an attractive approach for hadron collider
> experiments, for example the HGCAL under construction for CMS at the CERN
> HL-LHC.

Submitted to the Proceedings of the US Community Study

on the Future of Particle Physics (Snowmass 2021)

##  1 Introduction

In the search for new physics at particle colliders, the understanding of jets
and jet reconstruction have been important tools for discovery. Jet
reconstruction has generally been the domain of calorimetry, where particle
energies are measured in an ensemble of instruments with separated
functionality: electromagnetic calorimeters for measurement of electron,
positron and photon energies, and hadron calorimeters for the measurement of
charged and neutral hadron energies. Because of sheer size and volume, the
hadron calorimetry designs involved coarse measurement elements, at the
expense of being able to measure hadron energies precisely. Nevertheless these
calorimeters provided exellent hermeticity, a functionality important for
triggering and for the measurement of missing transverse energy.

In recent years, there has been paradigm shift in design favoring high
granularity Particle Flow calorimetry, driven in part by the scientific
objectives of Higgs factories such as the International Linear Collider, where
a premium has been placed on clean separation of the hadronic decays of vector
bosons (W, Z) and for precision study of Higgs physics. Such calorimeters are
designed to serve as effective extensions of the tracking system with
granularity sufficient to associate energy depositions of individual incident
charged particles whose momenta have been measured independently in tracking,
revealing spatially identifiable energy clusters created by neutral hadrons.
By making the appropriate associations of this new information, jet
resolutions of $\sigma_{E}/E<30\%/\sqrt{(}E)$ have been demonstrated to be
achievable.

##  2 Motivations for Particle Flow Calorimetry

While there are commonalities in the choice of Particle Flow Calorimetry
designs across a variety of experiments, the motivations behind the choices
vary. In common are a sampling-layered structure with very high granularity of
readout channels, so that energy deposits recorded in the calorimetry can be
associated correctly with charged particles whose momenta are recorded in
tracking detectors. EM objects (e, $\gamma$) are identified and registered
primarily through energy deposits in the initial layers and charged hadrons
registered over a significantly greater range of layers in depth. Lastly,
unassociated energy deposits are then ascribed to neutral hadrons. In lepton
colliders (ILC, CLIC), the high granularity is used to emphasize separation
among the different objects and avoid confusion created by overlapping
information. At hadron colliders (HL-LHC/CMS), a major concern involves event
pileup created by the very high luminosity and the need to ameliorate such
effects. In both cases, extracting the physics performance from the wealth of
information depends upon complex pattern recognition analyses that ultimately
yield a list of reconstructed objects including particle type, energy and
momentum.

###  2.1 Scientific Motivation

The scientific goals of $e^{+}e^{-}$ colliders (linear or circular) are
directed toward reconstruction and precision measurement of specific physics
final states - for example, W, Z and Higgs - in a relatively clean initial
state environment. Variously for hadron colliders, emphasis is directed toward
searches for and discovery of new physics, generally in the face of
consequential event pileup and radiation fields. Interestingly, both can
benefit strongly from a new holistic view of tracking and calorimetry design
which are the domain of particle flow techniques.

####  2.1.1 Vector Bosons and Jet Reconstruction

For linear collider experiments, a performance benchmark is to distinguish W,
Z based on their (dominant) hadronic decays. To do so requires a hadronic mass
resolution comparable to the gauge boson widths, $\sigma_{\rm m}/{\rm
m}\approx 2.7\%$. That this is achievable has been demonstrated for the ILD
detector’s hadron calorimeter using software compensation [1], based on
simulation validated with CALICE testbeam data.

For hadron collider experiments, VB Fusion and VB scattering processes, top
quark physics, Higgs physics and searches for evidence of BSM physics will
continue to be prominent areas of investigation. The granularity of the CMS
HCAL should allow the ability to distinguish quark and gluon jets, important
for better understanding of VBF events [2].

####  2.1.2 Higgs Production and Event Reconstruction

At linear colliders, precision measurement of the Higgs boson and its various
decay channels are major priorities. The predominant production mechanisms of
Higgs bosons in the Standard Model (SM) are Higgsstrahlung at collision
energies below 450 GeV and WW fusion at higher energies [3, 4]. In the
Higgsstrahlung case, reconstruction of the Z is the crucial piece. Since the
kinematics are constrained, the recoil mass allows ”identifying” the Higgs
without selecting a decay channel or reconstructing it directly. Should the Z
decay hadronically, the challenge is to define a Z selection that has the same
efficiency for all Higgs decays, in the presence of an unknown number of
additional jets. In the case of WW fusion, the challenge is reconstruction of
Higgs pairs with missing energy.

At the HL-LHC, an important objective is the measurement of the Higgs self-
coupling. Given the expected rarity of this process, being able to combine as
many possible decay channels for the Higgs decay will be of significant
benefit. Additionally, hadron colliders are intrinsically discovery machines
due to their energy reach, and several BSM theories suggest that there may be
more Higgs-like particles than only the one in the SM. Discovery will place
strong demands on excellent jet reconstruction, jet resolution and angular
measurement.

####  2.1.3 Tau Reconstruction

Calorimetry plays a role in tau lepton detection and reconstruction primarily
through its hadronic decays, which consist of charged and neutral pions and an
associated (and undetected) neutrino. The granularity of PF calorimetry is
beneficial to the reconstruction of these narrow jets, including
identification and measurement of gamma energies, and, with timing timing
capability, to assist with pileup background rejection [2].

####  2.1.4 Long Lived Particles

The search for long lived particles can be facilitated with PF calorimeters
that are subsystems of multipurpose collider detectors such as those at hadron
or lepton machines, or in specialized designs (for example for forward
physics). The benefits of PF design include energy and timing measurement and
pointing, the ability to identify the source of the energy with a vertex
location that is significantly displaced from the source of primary
production. The actual effectiveness of any such approach will depend in part
upon the rest mass and lifetime of such hypothetical particles and the
effective available decay length in a given experiment.

###  2.2 Technical Motivation and Challenges

####  2.2.1 Channel Count and Calibration

Since the strength of PF calorimetry is its effective extension of particle
tracking into the energy measurement, the substantial channel count requires
special attention to calibration. For the hadron sections, calibration will be
effected in part by detection of mip signals (muons and charged hadrons) and
by electrons and positron detection in the EM sections. Critical issues are
aging due to radiation and thermal/mechanical issues affecting sensors and
associated electronics.

####  2.2.2 Event Timing, Pileup Subtraction and Vertex Location

In $e^{+}e^{-}$ linear colliders, beam collisions set the event timing, but
timing capability can also serve as an aid in rejecting beam-gas interactions.
In hadron colliders, the large number of collisions per beam crossing (140-200
at HL-LHC) leads to significant event pileup. The ability to measure timing of
particles as well as their energies becomes an important tool for event
reconstruction, association of particles to primary or secondary vertices and
for pileup background suppression.

##  3 Overview of PF Calorimeters currently under development or construction

Particle Flow calorimeters are under development for future collider
applications as well for upgrades of existing detectors. And numerous detector
technologies are under development to extend the reach of such
instrumentation. Several of these important efforts have been submitted and
described by the proponents in Letters of Interest to the Snowmass2021
Community Summer Study and are highlighted here.

###  3.1 Detector Upgrades/Concepts

####  3.1.1 CALICE

The CALICE collaboration is a dedicated detector R&D collaboration focusing on
the development of highly granular calorimeters optimized for the application
of particle flow algorithms. Originally founded for calorimeter development
for the International Linear Collider (ILC), the scope has been widened to
also integrate applications of highly granular calorimeters in other
environments. CALICE aims to provide a framework for the R&D activities,
ensuring common standards for beam tests and data analysis, as well as
organizing combined beam tests of full calorimeter systems consisting of ECAL,
HCAL and tail catcher/muon tracker. For the ECAL, small scintillator strips
and silicon sensors are investigated as active material. For the HCAL,
scintillator tiles and gaseous detectors (RPCs, GEMs and MicroMegas) are
studied. For the ECAL, tungsten is chosen as absorber due to its very small
Moliere radius. For the HCAL, the main absorber option is stainless steel for
its structural strength and machinability, while tungsten is considered as
alternative for very high center-of-mass interactions to limit the size of the
calorimeter while keeping sufficient thickness in interaction lengths.

Since the typical energy depositions in the cells are small, various readout
concepts have been developed: in addition to a “traditional” analog readout
with detailed information for each cell energy, a digital approach, recording
only if the energy crossed a fixed threshold, and a semi-digital approach,
recording hits with three thresholds, have been developed and tested. For
several of the concepts, large prototypes have been built. The first
generation of prototypes focused on demonstrating the performance reachable
with the corresponding concept. The second generation has focused on the
technical implementation of the concept scalable to a full collider detector,
which requires solutions adapted to a specific application and environment.
The requirement of scalability leads to the front-end electronics being
integrated into the active layers. One example of an adaptation to a specific
environment is power pulsing, which allows the building of calorimeters with
minimal-to-no active cooling in the active layers at linear $e^{+}e^{-}$
colliders. By adapting the front-end electronics to the beam structure of the
machine, the electronics is only switched on during the bunch train ($1\,{\rm
ms}$ at ILC), while it is off to save power in the long gaps between bunch
trains ($199\,{\rm ms}$).

The comparison of the test beam data with simulations forms an integral part
of the CALICE mission, both to provide a detailed realistic and validated
modeling of the concepts and to provide feedback to the simulation model
developers. Recently, dedicated efforts to measure the time development of
showers and to improve the resolution of the hit time measurements have been
initiated. Details of the individual technologies will be discussed in the
next section.

####  3.1.2 ILD

The ILD is a multipurpose detector and one of the two validated detector
designs for the future ILC. The particle flow paradigm was adopted as its
guiding principle since the start and the design has developed around it.

ILD has chosen a sampling calorimeter equipped with silicon diodes as one
option for the electromagnetic calorimeter. Diodes with pads of about $5\times
5\,{\rm mm}^{2}$ are used, to sample a shower up to $30$ times in the
electromagnetic section. A self-sustaining structure holding tungsten plates
with Carbon-Fiber-Reinforced-Polymer (CFRP) supports the detector elements
while minimizing non-instrumented spaces. As an alternative to the silicon
based system, sensitive layers made from thin scintillator strips are also
investigated. Orienting the strips perpendicular to each other has the
potential to realize an effective cell size of $5\times 5\,{\rm mm}^{2}$, with
the number of read-out channels reduced by an order of magnitude compared to
the all silicon case.

For the hadronic part of the calorimeter of the ILD detector, two technologies
are studied, based on either silicon photomultiplier (SiPM) on scintillator
tile technology or resistive plate chambers. The SiPM-on-tile option has a
moderate granularity, with $3\times 3\,{\rm cm}^{2}$ tiles, and provides an
analogue readout of the signal in each tile (AHCAL). The RPC technology has a
higher granularity, of $1\times 1\,{\rm cm}^{2}$, but provides only 2-bit
amplitude information (SDHCAL).

The conceptual and technological development of this particle flow calorimeter
have been largely done by the CALICE collaboration.

####  3.1.3 SiD

The SiD Detector (Snowmass2021 LoI [5]) is the other of the two validated
detector designs for the future ILC. SiD features a compact, cost-constrained
design for precision Higgs and other measurements, and sensitivity to a wide
range of possible new phenomena. A robust silicon vertex and tracking system,
combined with a $5\,{\rm T}$ central solenoidal field, provides excellent
momentum resolution. The highly granular calorimeter system is optimized for
Particle Flow to achieve excellent jet energy resolution over a wide range of
energies.

The SiD ECAL design employs thirty silicon longitudinal layers, the first
twenty each with a $2.50\,{\rm mm}$ tungsten alloy absorber thickness and
$1.25\,{\rm mm}$ readout gaps, and the last ten with $5.00\,{\rm mm}$ tungsten
alloy. The total depth is $26$ radiation lengths, providing good containment
of electromagnetic showers. The baseline design employs tiled, large,
commercially produced silicon sensors. The sensors are segmented into pixels
that are individually read out over the full range of charge depositions. The
complete electronics for the pixels is contained in a single chip, the KPiX
ASIC, which is bump bonded to the wafer. The low beam-crossing duty cycle
allows reducing the heat load using power pulsing, thus allowing passive
thermal management within the ECAL modules. Results have been obtained from an
initial 9-layer prototype and further R&D is foreseen on a full-depth stack.

The SiD HCAL has a depth of $4.5$ nuclear interaction lengths, consisting of
alternating steel plates and active layers. The baseline choice for the active
layers is scintillator tiles read out via silicon photomultipliers. For this
approach SiD is closely following the developments within the CALICE
collaboration. An initial, conceptual mechanical design has been developed,
and further work is needed on all aspects of the design.

####  3.1.4 CLICdet and CLD

CLIC is a proposed linear electron-positron collider with center-of-mass
energies up to $3\,{\rm TeV}$, while the proposed circular electron-positron
collider FCC-ee reaches only lower energies, but offers unprecedented
luminosities at the Z mass. Both can operate at energies close to the highest
Higgsstrahlung and top-antitop production cross sections, and are proposed for
construction in Europe (at CERN). The CLICdp collaboration has developed the
CLICdet detector concept and is actively engaged in the corresponding detector
technology development. In recent years, members of the CLICdp collaboration
and the FCC collaboration have adapted the CLIC detector concept for operation
at FCC-ee, resulting in the CLD concept, optimized in view of the FCC-ee Higgs
and top physics energy stages.

Both CLICdet and CLD (Snowmass2021 LoI [6]) are general purpose $e^{+}e^{-}$
detector concepts. Their design was driven by jet energy resolution (through
PFA), together with high-performance tracking in view of precision
measurements of single particles and jet flavor identification. The
reconstruction of individual particles in a dense environment through PFA is
also essential for the suppression of particles from beam-induced background
in $e^{+}e^{-}$ colliders, which is especially relevant in the forward
direction. For the ECAL, a sampling calorimeter with tungsten absorbers and
silicon active layers of $5\times 5\,{\rm mm}^{2}$ cell size is foreseen,
comprising $40$ layers. For the HCAL, a sampling calorimeter with steel
absorbers and scintillator active layers with SiPM readout is planned, with a
cell size of $3\times 3\,{\rm cm}^{2}$. While the CLICdet HCAL has $60$ layers
to ensure a good containment of very high energetic jets, the CLD HCAL has
only $44$ layers. In the domain of calorimetry, the technology development is
carried out in the framework of the CALICE and FCAL collaborations. A notable
distinction to these detector developments compared to those for ILC
applications is the nature of the beam structure, which does not allow for
power pulsing (FCCee) or requires adaptations to it (CLIC).

####  3.1.5 CEPC

The Circular Electron Positron Collider (CEPC) is proposed for construction in
China as a Higgs factory to study the Higgs boson with an unprecedented
precision. It also serves as a Z-factory when operating at the Z pole. The
CEPC baseline detector concept includes a PFA calorimetry system (Snowmass2021
LoI [7]). The design implements concepts developed within the CALICE
collaboration. There are still various detector technology options that need
to be further explored to address challenges from the stringent performance
requirements for the CEPC detector design.

  * •

ECAL: A highly granular calorimeter with a scintillator-tungsten sandwich
structure is one option for the PFA ECAL in the CEPC baseline detector
conceptual design. The design largely follows that of the ILD Sci-W ECAL, and
realizes a very high effective granularity with less channels by using
scintillator strips arranged in a way that strips in adjacent layers are
orthogonal to each other.

  * •

HCAL: The Sci-Fe HCAL concept is adopted as one PFA HCAL option. There are
significant similarities between the Sci-Fe HCAL and Sci-W ECAL detector
options in that both use the technology of scintillator directly coupled to
SiPM. A major difference is the different scintillator cell size and geometry.
While the Sci-W ECAL uses small scintillator strips, the Sci-Fe HCAL uses
large scintillator tiles.

  * •

Active cooling system: Due to the high granularity design of PFA calorimeters,
the number of readout channels of the calorimetry system is extremely large.
Because CEPC operates in continuous mode, the power dissipation produced by
the embedded readout system could reach about 100kW. It is therefore crucial
to design an active cooling system to bring the heat out of the CEPC PFA
calorimeters.

####  3.1.6 CMS HGCAL

The Phase 2 upgrades of the Compact Muon Solenoid (CMS) detector will enable
the detector to function in the environment of the High Luminosity Large
Hadron Collider (HL-LHC). Slated to begin operations in 2027, the HL-LHC will
have an instantaneous luminosity of ${\cal L}=5-7.5\times 10^{34}\,{\rm
cm}^{-2}{\rm s}^{-1}$, a projected total integrated luminosity of $3-4.5\,{\rm
ab}^{-1}$, and 140 - 200 pileup interactions per bunch crossing. These
benchmarks significantly exceed those of the LHC, for which the current CMS
detector was designed. The Phase 2 upgrade program largely encompasses
improvements to the data acquisition (DAQ) system to increase the Level-1
trigger accept rate from 100 to 750 kHz and replacements of aging front end
materials with new ones expected to withstand the HL-LHC total ionizing dose
and 1-MeV-equivalent neutron fluence in the CMS interaction region.

Central to the Phase 2 upgrades is the replacement of the current endcap
($1.5\leq|\eta|\leq 3.0$) calorimeter, consisting of a total absorption
scintillating crystal electromagnetic section followed by a brass and plastic
scintillator sampling hadronic section, with the High Granularity Calorimeter
(HGCAL) (Snowmass2021 LoI [8]), which is a 6M channel particle flow sampling
calorimeter. The HGCAL is a $47$-layer sampling calorimeter with 26 layers
constituting a front electromagnetic section (CE-E) of 27.7 radiation lengths
($X_{0}$) followed by $21$ layers composing a rear hadronic section (CE-H).
The total calorimeter depth is $9.97$ hadronic interaction lengths
($\lambda_{I}$). Copper, tungsten, and lead are used as absorber materials in
the CE-E, while stainless steel is used in the CE-H. Detector planes equipped
with either silicon sensors or scintillator tiles with SiPM readout are used.
The silicon sensors will account for $\sim 55\%$ of the total active area,
which is $1100\,{\rm m}^{2}$. The silicon is divided into $\sim 6$ million
channels with an area of either $\sim 0.5$ or $\sim 1\,{\rm cm}^{2}$. The CE-H
design foresees $\sim$400,000 scintillator+SiPM channels. The longitudinal
cross section of one half of one endcap of the HGCAL design is shown in Figure
1.

Figure 1: layer structure of the HGCAL

After the final phases of sensor prototyping, major construction is planned to
begin in 2022. Drawing on years of R&D pioneered by the linear $e^{+}e^{-}$
collider community, the HGCAL will be the largest PF calorimeter ever built,
and the first to operate at a hadron collider. Throughout the next decade, the
lessons of the HGCAL project – how to construct high quality, highly segmented
calorimeters on a budget; and the utility of PF design at high luminosity
hadron colliders especially in pileup rejection and radiation tolerance – will
be instrumental in efforts to adapt the PF technology to ambitious new
experiments. The HGCAL Collaboration supports continued investment in PF
calorimetry, both in direct support of HL-LHC construction and operations and
at the R&D level. Active communication continues between the $e^{+}e^{-}$ and
hadron collider calorimetry communities, to the benefit of both.

###  3.2 Technologies

####  3.2.1 Scintillator Strip ECAL

A calorimeter based on scintillator strips with SiPM readout (Sci-ECAL)
(Snowmass2021 LoI [9]) is one of the promising technology options for a highly
granular ECAL being developed within the CALICE collaboration. The detection
layers with scintillator strips ($45\times 5\times 2\,{\rm mm}^{3}$ each)
coupled to SiPMs are stacked alternately in an orthogonal orientation to
achieve an effective transverse segmentation of $5\times 5\,{\rm mm}^{2}$,
allowing to significantly reduce the number of readout channels. The same
performance as the real segmentation of $5\times 5\,{\rm mm}^{2}$ is
achievable with an appropriate reconstruction algorithm. The detection layers
are interleaved by tungsten absorber layers. The Sci-ECAL with the compact and
cost-effective design is proposed for ILC-ILD and CEPC-ECAL.

Important progress has recently been made on the SiPMs for Sci-ECAL. MPPCs
with a smaller pixel pitch of $10$ or $15\,{\rm\mu m}$ have been developed,
which can provide a larger dynamic range required for Sci-ECAL. Further
improvements have been made for the most recent small-pixel MPPCs, including
reduced optical cross-talk by a trench structure between pixels, lower dark
noise and higher photon detection efficiency, which have been confirmed by lab
tests. In earlier studies, the SiPM was attached to the side edge of the
strip. New designs of the SiPM readout at the bottom side of the strip are
being developed for more uniform response and a better compatibility with
future large-scale production.

A full-size Sci-W ECAL prototype with readout electronics embedded in the
detector has been constructed as a joint effort of the CEPC calorimeter group
and some ILC-ILD detector R&D groups from Japan. The key parameters for this
technological Sci-W ECAL prototype are $22\times 22\,{\rm cm}^{2}$ for
transverse area, 24 $X_{0}$ for thickness, and $5\times 5\,{\rm mm}^{2}$ for
effective cell size. The scintillator strips are read out using SiPMs with a
small pixel size of $10$ or $15\,{\rm\mu m}$ to provide a large dynamic range
for measurement of high energy EM showers. The prototype has been fully
assembled and integrated with readout electronics and DAQ. A LED-based SiPM
monitoring and calibration system has also been developed and integrated into
the readout electronics. The prototype is now being commissioned with cosmic
rays and is ready for test beams in the coming years.

The remaining challenges include the development of a detector assembly system
for the large-scale production, testing the power pulsing operation of the
integrated electronics for the ILC Sci-ECAL and optimizing the cooling system
for the integrated electronics for the CEPC Sci-ECAL, where a continuous
operation is required unlike the ILC Sci-ECAL.

####  3.2.2 Silicon Tungsten ECAL

A highly granular ECAL based on silicon sensors and tungsten absorber combines
the advantages of a very compact design and a possibly radiation hard
technology. Silicon-tungsten ECALs are under development for detectors at
$e^{+}e^{-}$ colliders as well as hadron colliders. The CALICE collaboration
is developing one of the concepts (Snowmass2021 LoI [10]), described in more
detail here. For other developments see section 3.1.3 (SiD) and 3.1.6 (CMS
HGCAL).

After the realization of a physics prototype (2005–2011) as a proof of
concept, CALICE has constructed a technological prototype of a highly granular
silicon tungsten electromagnetic calorimeter (SiW-ECAL), taking into account
the many constraints of a large scale detector, using ILD as a baseline. The
most critical part is the so-called Active Sensor Unit (ASU), the base element
of detection, including a PCB, glued Si sensors, and ASICs. A calorimeter
stack with around $20$ layers, each composed of a single ASU, of size
$18\times 18\times 0.5\,{\rm cm}^{3}$ with a total depth of about one
interaction length is available. The ASUs are subdivided into 1024 readout
cells of around $5\times 5\,{\rm mm}^{2}$. Their embedded front-end readout
electronics records the energy deposit and the time at which a cell is hit,
with $12$-bit resolution on a large dynamic range ($1-3000$ MIPs) and a time
precision of $\sim 1.5\,{\rm ns}$ for a MIP.

In the coming years, beam tests in conditions compatible with the ILC (power
pulsing) will be used to fully characterize the prototype in terms of
linearity uniformity, noise, and cross talk, for MIPs, and electromagnetic and
hadronic showers. Detailed characterization of the spatial shape of
electromagnetic and hadronic cascades in tungsten, will be complemented by the
timing information. Combined beam tests are foreseen with already existing
prototypes of hadronic calorimeters. With an overall depth of about $6$
interaction lengths, starting with the much higher segmentation of the ECAL,
where $55\%$ of hadrons interact, these setups are an important validation of
PFA performance with realistic devices.

Future R&D for the SiW-ECAL will address several aspects: (1) System issues to
integrate ASUs into long cassettes of up-to twelve chained ASUs; (2) Large
sensors to profit from the use of 8” wafers pioneered by the CMS HGCAL; (3)
Thin design by moving from BGA packaged ASICs (overall ASU thickness of $\sim
3\,{\rm mm}$) to ultra-thin ASU, $1.2\,{\rm mm}$ thick, where the ASICs are
mounted in recessed cavities; and (4) Reliability to ensure that all
components of the detector (connectors, flat capacitors, …) work reliably in
an experiment for more than twenty years, possibly operated in a pulsed mode
in a strong magnetic field.

####  3.2.3 Digital Silicon ECAL

Within the ALICE collaboration there is a proposal to develop and build a
forward calorimeter, FoCal, including a SiW electromagnetic part with several
layers of extremely high granularity. In the context of the R&D for this
calorimeter, and as part of the general R&D effort in the CALICE
collaboration, a SiW calorimeter based on monolithic active pixel sensors with
a pixel pitch of $30\,{\rm\mu m}$ is being developed (Snowmass2021 LoI [11]).
A first prototype with $\sim 40$ million pixels has been constructed using
MIMOSA sensors and has successfully been tested in beam, showing good energy
linearity and resolution and extremely high position resolution and two-shower
separation capabilities. This provided a proof of principle of digital pixel
calorimetry only, because the MIMOSA sensors are too slow to use in a collider
experiment.

Very recently a second full pixel prototype has been constructed using ALPIDE
sensors, which have been developed at CERN for the ALICE ITS upgrade. These
sensors are fast enough to be used in the ALICE FoCal upgrade, and first tests
show excellent calorimetric performance. It is planned to go further with this
development to explore the possibilities of still faster sensors for
calorimetric purposes that could be used in a standard modern collider
experiment. This would be of interest for detectors at future hadron and
electron-positron colliders, and also for EIC. Further development could be
based on a next generation of the ALPIDE technology, but also other pixel
sensors could be suitable. The detector concept in development for FoCal has
been shown to have excellent performance for direct photon measurement,
requiring in particular the separation of close-by EM showers. The performance
for other applications of the detector have not really been explored so far.
In parallel to the technological R&D, the possible performance of such a
technology for jet measurements will be studied, in particular with suitably
adapted particle flow algorithms. A very similar detector concept using the
same technology is the basis for a development of a proton CT scanner for
medical applications.

####  3.2.4 Gaseous HCALs

To cover the large areas of the detection layers in a highly granular hadron
calorimeter, gas-based detectors like Resistive Plate Chambers (RPCs), gas
electron multipliers (GEMs) or Micromegas provide a cost-effective solution.
For gaseous detectors operated in avalanche mode, the measured charge is only
weakly correlated with the primary deposited energy in a given cell, such that
the detailed readout of individual hit charges is not expected to improve the
hadron energy resolution. Therefore, dedicated readout concepts with digital
or semi-digital hit information have been developed.

##### Resistive Plate Chambers

Within the CALICE collaboration two large prototypes with RPCs as active media
have been built. The CALICE Digital Hadron Calorimeter (DHCAL) (Snowmass2021
LoI [12]) uses RPCs as active media and has a 1-bit resolution (digital)
readout of $1\times 1\,{\rm cm}^{2}$ pads. A prototype has been built and
tested with steel and tungsten absorber structures, as well as with no
absorber structure. A single layer of the DHCAL prototype measures roughly
$1\times 1\,{\rm m}^{2}$ and consists of $96\times 96$ pads, with the readout
electronics embedded in the active layer. In addition to the absorber plates,
each layer of RPCs was contained in a cassette with a $2\,{\rm mm}$ thick
Copper front plate and a $2\,{\rm mm}$ thick steel back plate. In order to
obtain a unique dataset of electromagnetic and hadronic interactions with
unprecedented spatial resolution, the DHCAL went through a broad test beam
program. For test with steel absorber, up to $52$ layers were installed. The
calorimeter consisted of a $38$-layer main stack with $1.75\,{\rm cm}$ thick
steel absorber plates and a $14$-layer tail catcher. The tungsten DHCAL
consisted of $54$ active layers, where the first $39$ of these layers were
inserted into a tungsten absorber structure featuring $1\,{\rm cm}$ thick
tungsten plates. The remaining $15$ layers were inserted into a steel tail
catcher. The total thickness of the $54$-layer W-DHCAL (main stack and tail
catcher) corresponded to approximately $183$ radiation lengths or $11.1$
nuclear interaction lengths. In special tests, $50$ active layers of the DHCAL
were exposed to low energy particle beams, without being interleaved by
absorber plates. The high spatial segmentation of the imaging calorimeters
allows the application of corrections to the measured number of hits which
might result in an improved linearity of the response and energy resolution.
The DHCAL data can be corrected for leakage using the detailed shower
profiles, and the response can be linearized by assigning different weights to
hits based on their densities.

The CALICE Semi-Digital Hadron Calorimeter (SDHCAL) also uses RPCs as active
media, but has a 2-bit resolution (semi-digital) readout. A large prototype of
$1.3{\rm m}^{3}$ made of 48 units was designed and built. Each unit is built
of an active layer made of $1{\rm m}^{2}$ glass RPC detector placed inside a
cassette whose walls are made of stainless steel. The cassette contains also
the electronics used to read out the RPC detector, which support operation in
power pulsing mode. The lateral granularity of the active layer is provided by
the electronics pick-up pads of $1\,{\rm cm}^{2}$ each. The cassettes are
inserted into a self-supporting mechanical structure built also of stainless
steel plates which, with the cassettes walls, play the role of the absorber. A
dedicated acquisition system was developed to deal with the output of more
than 440,000 electronics channels in both trigger and triggerless modes. Since
2012, the prototype has been subject to a large scale test beam campaign. The
numbers of hits above the three thresholds can be used to reach a linear
response (within a few percent) and a good energy resolution for a large range
of hadron shower energies.

The CALICE collaboration has also performed tests of GEMs and Micromegas in
smaller prototypes, which have shown the general suitability of these
technologies for application in a digital or semi-digital hadron calorimeter.

##### Advanced GEM Detectors

Micro-Pattern Gaseous Detectors (MPGDs) (Snowmass2021 LoI [13]) are radiation
hard detectors, able to cope with rates of ${\rm MHz/cm}^{2}$, exhibiting good
spatial resolution ($\leq 50\,{\rm\mu m}$) and good time resolution of
$5-10\,{\rm ns}$. They have the potential of economically covering large
areas. Gas Electron Multiplier (GEM) detectors are the most consolidated
technology inside the MPGD family, and in the last decade they have been
considered as tracking devices for Muon Systems in LHC experiments.
Additionally, several technological solutions and optimization of the
operation parameters have been achieved in order to make the detector suitable
for operation at HL-LHC.

The challenge is now open for future colliders considering the high particle
rates, discharge probabilities and accumulated doses expected at Future
Colliders. Time resolutions of $30-100\,{\rm ps}$ per track are required to
distinguish pile-up collisions and high background conditions, while sub-ns
time resolutions are required for experiments at future colliders that will
work at $200\,{\rm MHz}$ bunch crossing frequency. Studies are planned that
will aim at achieving major advances in the development of a new generation of
MPGDs for several applications in HEP experiments at future colliders, such as
a pre-shower for an electromagnetic calorimeter, active readout layers in
sampling calorimeters, a muon tracking or tagging detector at FCC-ee/hh and
Muon Collider or as the readout layer of a Time Projection Chamber.

The main objectives of the R&D are: (1) stable and efficient operation with
incident particle flows up to $\sim 100\,{\rm MHz/cm}^{2}$; (2) radiation
hardness up to integrated charges of hundreds of ${\rm C/cm}^{2}$; (3) very
high granularity readout with dedicated electronics to operate efficiently at
high fluxes; (4) high timing resolution; and (5) manufacturing on an
industrial scale. The main technological solution explored to optimize the
operation of MPGD detectors in terms of speed and uniformity of response,
damping and eliminating gas discharges, spatial resolution and gain, under
particle flows expected at future accelerators, is the development of GEM
foils with resistive electrodes. Industrial partners are already involved in
the development of the new technology with two advantages: being at the
forefront in the mass production phase of the detectors to be installed at
future colliders and taking advantage of any spin-offs of these technologies
in application areas outside HEP such as X-ray and neutron imaging systems in
the industrial field, hadron therapy in the medical field, muon tomography in
geology and archaeology, and for national security systems.

####  3.2.5 Scintillator HCAL

The CALICE collaboration has pioneered the development of the SiPM-on-Tile
technology for highly granular calorimeters (Snowmass2021 LoI [14]). The
construction and operation of a Physics Prototype of the Analog Hadron
Calorimeter (AHCAL) established the performance, in terms of energy and
topology reconstruction, of the approach in principle, as well as the adequacy
of detailed simulations. An AHCAL Technological Prototype, which demonstrates
the viability of engineering solutions for a large collider detector, has been
built and successfully tested in beams at CERN in 2018. The prototype consists
of a steel absorber structure and active layers of small scintillator tiles
that are individually read out by directly coupled SiPMs. Each layer has an
active area of $72\times 72\,{\rm cm}^{2}$ and a tile size of $3\times 3\,{\rm
cm}^{2}$. With $38$ active layers, the prototype has nearly $22,000$ readout
channels, and its total thickness amounts to $4.4$ nuclear interaction
lengths. The dedicated readout electronics provide time stamping of each hit
with an expected resolution of about $1\,{\rm ns}$. The design has been guided
by the ILD detector concept for the ILC, but variations are being proposed for
SiD at the ILC, CLICdet at CLIC and CLD at FCCee as well. Moreover, it has
inspired the design chosen for the scintillator section of the upgrade of the
CMS endcap calorimeter (HGCAL) for the HL-LHC.

Further beam measurements are planned with the prototype to fully exploit the
ns timing capabilities of the technological prototype readout electronics, to
study hadron showers in an existing tungsten absorber structure and to study
the performance for energy and topology reconstruction in a realistic
configuration with a combined ECAL and HCAL system. In addition, the AHCAL
prototype can be used as a test bed for new types of scintillators, SiPMs,
front end electronics and back-end interfaces, providing a realistic
environment and, by virtue of the reconstruction of the shower start location,
enabling the test of components in different stages of the shower evolution.
Timing layer prototypes with tens of ps resolution could be integrated in the
prototype to study their interplay with the rest of the detector showing more
moderate resolution.

To validate the AHCAL technology option for its application to the CEPC
experiment, a large-scale technological prototype is being developed by the
CEPC calorimeter group. It consists of 40 longitudinal sampling layers with a
transverse plane size of $\rm 72\times 72~{}cm^{2}$ and a total depth of
around $4.8\lambda_{I}$. There are 12,960 SiPM-on-Tile readout channels and
the total weight is around 4.5 tons. The dimension of a scintillator tile is
$\rm{40\times 40\times 3~{}mm^{3}}$ and the cavity inside the tile for
coupling is optimized for the NDL-SiPM package to improve the response
uniformity. The prototype design optimization studies have been done for the
CEPC based on the Arbor PFA, including the cell size, the number of sampling
layers, total thickness of the absorber, the thickness of scintillator tiles,
etc. The ”CEPC-AHCAL” prototype has the major updates: (1) tile size is
optimized by PFA studies to $\rm 40\times 40\times 3~{}mm^{3}$ from $\rm
30\times 30\times 3~{}mm^{3}$, with coarser granularity but similar
performance expected; (2) to cover the same transverse size of $\rm 72\times
72~{}cm^{2}$, the dimensions of HBU PCBs has a different shape and
considerably larger i.e., $\rm 24\times 72~{}cm^{3}$ instead of $\rm 36\times
36~{}cm^{2}$; (3) besides the ones from HPK, SiPMs from another vendor ”NDL”
with a high pixel density and a large sensitive area have been instrumented to
achieve a better signal-to-noise ratio and a wider dynamic range; (4) the
CEPC-AHCAL DAQ system has been newly designed and optimized to be capable to
read out events with a much higher rate, up to around 3kHz (finally limited by
the SPIROC chip). A fully integrated system dedicated to SiPM calibration and
monitoring has been developed. The QA/QC system for scintillator tiles and
SiPMs have been established and successfully tested all needed components. The
construction of the technological prototype is expected to be completed in
2022. After finishing the commissioning with cosmic muons, the prototype will
then be tested with high energy hadron beams at CERN in late 2022 and/or early
2023.

####  3.2.6 Highly Granular Crystals

A highly granular crystal electromagnetic calorimeter (ECAL) (Snowmass2021 LoI
[15]) is newly proposed in the context of the PFA-oriented detector design for
future lepton colliders, with an aim to achieve an optimal electromagnetic
energy resolution (around $3\%/\sqrt{E(GeV)}\oplus 1\%$) using the homogeneous
design with scintillation crystals while maintaining the PFA capability for
precision measurements of jets with finely segmented crystal cells. The
electron momentum resolution can be improved with Bremsstrahlung corrections
to refine Higgs recoil mass measurements. With the capability to trigger on
single photons, crystal calorimetry can also play an essential role in the
rich flavour physics programs as well as searches for new physics. Dedicated
readout schemes to determine Cherenkov and scintillation photons in crystals
with the information of the wavelengths or timing are expected to
significantly improve the energy resolution of hadrons and jets.

To strengthen the joint efforts, software developments and design
optimizations are indispensable. Small-scale hardware prototypes and
measurements can also provide solid inputs to validate the simulations. An
inexhaustible list of key issues and critical R&D tasks have been initiated:
(1) Develop reliable software tools to validate the crystal calorimeter and
reconstruction algorithms optimized for different layouts; (2) Study the
electromagnetic showers with realistic detector layouts and calibration
schemes; (3) Evaluate the performance of hadronic showers with the crystal
ECAL and HCAL options; (4) Study how to utilize the timing information of
showers for the particle identification, shower separation, response
compensation, etc.; (4) Explore potential of detecting both Cherenkov and
scintillation photons with a crystal-SiPM detector unit and study the
performance with the dual-gated or dual-readout schemes.

####  3.2.7 RADiCAL – Ultra-compact, Radiation-hard, Precision-timing
Electromagnetic Calorimetry

RADiCAL (Snowmass2021 LoI [16]) is a collaborative conducting R&D on advanced
calorimetry techniques for FCC-hh experimental applications and based on
radiation-hard scintillator, waveshifter and photosensor technologies [17].
The emphasis is on ultra-compact, radiation hard EM calorimeters, based on
modular structures consisting of alternating layers of very dense absorber and
scintillating plates, read out via wavelength shifting solid fiber or
capillary elements to photosensors positioned either proximately or remotely,
depending upon their radiation tolerance. Initial versions of RADiCAL modules
consist of interleaved layers of 1.5mm thick LYSO:Ce tiles and 2.5mm thick
tungsten plates, stacked to a total depth of $114\,{\rm mm}$, corresponding to
$25\,{\rm X}_{0}$ and $0.9\,\lambda_{I}$. The modular cross section of
$14\times 14\,{\rm mm}^{2}$, set by the $13.7\,{\rm mm}$ Molière radius of the
structure, results in an ultra-compact module both transversely and
longitudinally. The shower energy is measured from the overall optical signal
detected in the module; timing and position are measured from the optical
signals detected in the region of EM shower max. R&D on rad hard materials is
central to the effort and includes: for scintillators: LYSO:Ce crystal plates,
LuAG:Ce and LuAG:Pr ceramic plates and ${\rm BaF}_{2}$:Y crystal plates; for
waveshifters: DSB1 organic filaments, LuAG:Ce ceramic filaments, flavenol
organic filaments, and quantum dot siloxane filaments; for photosensors: rad-
hardened SiPM, and large band-gap sensors based on GaInP, SiC, diamond and
other materials. The design goals for the modules include the simultaneous
measurement of shower energy, with resolution
$\sigma_{E}/E=10\%/\sqrt{E}\oplus 0.3/E\oplus 0.7\%$ [18], and shower timing,
with $\sigma_{t}<50\,{\rm ps}$, and shower position determined to within a few
mm.

####  3.2.8 High-rate Forward Calo (Direct Detection in PMTs)

A new idea for calorimetry which will survive in the forward region of future
colliders, high intensity experiments, and orbiting systems is the use of
Photomultipliers (PMTs) for the direct detection of shower particles
(Snowmass2021 LoI [19]) . The PMTs act as direct calorimeter sensors to detect
shower particles via Cerenkov light in the PMT window, and/or by direct
secondary emission from shower particles traversing the dynodes. The secondary
emission proportional to dE/dx provides compensating information.

Calorimeters in the Forward Region ($\eta\geq 3$) at future colliders will
need to measure in a very hostile environment at irradiation levels $\sim
1\,{\rm GigaGy}$ and $>10^{17}$ neutrons/${\rm cm}^{2}$, with an expected
number of pileup events of $100-1000$ per bunch crossing. Almost none of the
presently used calorimetry basic sensors can either survive the radiation
damage or operate at the required rate or both. It has been proposed to study
the capability of photomultiplier and dynode technologies as a potential
energy-flow calorimeter with multiple signal compensation. Previous experience
with dynodes in PMTs and with detectors in space and x-ray scanners show that
metal-oxides can survive many GRad exposures. Depending on the application,
PMTs could be manufactured with a metal “window” – no photocathode – for
dynode secondary emission as the shower particles sampling detector. A PMT
with a quartz or sapphire window and coupled to a quartz, sapphire,${\rm
MgF}_{2}$ or silica aerogel tile may prove to be quasi-compensating, by in
effect dual sampling. The Cerenkov light is more sensitive to EM showers,
while the dynode secondary emission is proportional to dE/dx for shower
particles traversing the PMT. Examination of the waveform may indicate
differences in the Cerenkov signal and the direct dynode signal in the shower.

####  3.2.9 Compact Readout Electronics

Compact high-performance readout techniques are essential for a successful
operation of particle flow calorimeters. Coordinated developments foster the
common data taking with different prototypes and facilitate the comparison of
the performance of different proposals.

Within the CALICE collaboration, R&D on a compact, homogeneous readout system
for all the prototypes is ongoing (Snowmass2021 LoI [20]). The most compact
implementation so far is the so-called SL-Board for the CALICE silicon
tungsten electromagnetic calorimeter (SiW ECAL), which has a length between 10
and 42mm and a width of 180mm and is conceived to serve up to 10k calorimeter
channels of a detector layer. The cards are connected to a data concentrator
system, able to serve up to 30 layers. It is envisaged to adapt the system of
the SiW ECAL to other calorimeters. This task is facilitated by the fact that
all calorimeters use a similar type of front-end ASIC. On the other hand
electromagnetic and hadronic calorimeters differ in size and layout. Moreover
additional functionality needs to be taken into account. The analogue hadronic
calorimeter and the scintillator electromagnetic calorimeter for example use a
LED system for the calibration of the scintillating tiles and the SiPMs, which
has to be driven by the interface card. Detailed design work is still needed
to understand how to transfer the concept in place for the SiW ECAL to for
example hadron calorimeters. A major difference is the typical size of the
prototypes and final systems which may require modifications in the way clock
and control signals have to be propagated within the individual systems.

The heat dissipation of the SL-Board will require the integration of cooling.
The SL-Board is designed for the integration of a cooling system, and cooling
systems do exist, but detailed integration work has to start in the near
future. In the coming years it is planned to investigate precision timing in
highly granular calorimeters. The digital readout systems will have to cope
with new requirements while at the same time keep the same level of
compactness.

###  3.3 Design Goals

Since all calorimeter designs optimized for particle flow reconstruction
algorithms feature small cells and a high channel count, they face a number of
common challenges. On the other hand, their (intended) use in different
environments as well as the characteristics of the employed detection
techniques lead to design differences.

####  3.3.1 Commonalities

The cell size of particle flow calorimeters is typically influenced by several
requirements:

  * •

in the ECAL, the cell should be small enough to allow the separation of close-
by showers and a reliable assignment of showers produced by charged particles
to the corresponding track in the tracking detector.

  * •

in order to distinguish electromagnetic and hadronic showers as well as to
identify electromagnetic sub-showers within hadron showers, the cell size
should be of the order of the Moliere radius and the radiation length $X_{0}$,
which are the typical scales of electromagnetic (sub-)showers

  * •

a very small cell size especially in the ECAL can be beneficial for the
reconstruction of $\tau$ decays

  * •

especially at hadron colliders, a small cell size allows a better rejection of
energy depositions from pile-up events.

Typical cell sizes are in the range of $0.5-1.0\,{\rm cm}^{2}$ for ECALs and
$1.0$ to $\sim 10\,{\rm cm}^{2}$ for HCALs. A notable exception is the digital
ECAL with a cell size of $30\times 30\,{\rm\mu m}^{2}$.

The large channel densities mean it is not practical to bring the analog
signals of all cells outside of the main calorimeter volume. In order to avoid
this, the first step of the data acquisition including zero-suppression or
some other means of data reduction is usually performed by front end
electronics fully embedded in the active layers. This has several implications
for the calorimeter design:

  * •

the fully embedded electronics is not accessible for repair, so has strong
requirements on quality tests before assembly and on longevity

  * •

complex readout elements such as ASICs will be situated in positions of
vulnerability to radiation and environmental issues

  * •

the amount of heat produced by the electronics needs to be minimized or
removed by cooling inside the active layers

  * •

the large area covered by PCB on the active area can contribute significantly
to the cost especially for HCALs.

####  3.3.2 Distinguishing characteristics

At future hadron colliders like HL-LHC and FCC-hh, the expected radiation
levels restricts the choice of the active material in the most affected areas.
Up to now, the most common materials are liquid Argon (or more general liquid
noble gases) and silicon. For the latter, cooling to $-30^{\circ}{\rm C}$ or
colder helps to keep the noise acceptable, but poses other practical problems.

For most PF calorimeter concepts, a ”classical” analog readout is foreseen.
The exceptions are the digital silicon ECAL and the (semi-)digital gaseous
HCALs. For the ECAL, the availability of Monolithic Active Pixel Sensors
(MAPS), which were originally developed for vertex and tracking detectors,
lead to the idea of a calorimeter with very small cell size and digital
readout, which can provide unrivaled position resolution and two-particle
separation. For the energy resolution, the small sampling fraction of thin
silicon sensors as well as saturation effects at high energies, when more than
one shower particle hits a pixel, play a role. For gaseous HCALs with
detectors operated in avalanche mode (e.g. RPCs), the measured hit energy is
strongly influenced by the depth at which the avalanche started, and therefore
is not really proportional to the energy deposition of the traversing shower
particles. This makes a simplification of the readout system by reading out
only digital or semi-digital hit information attractive.

The various materials and technologies discussed above have some
characteristics that lead to differences in the detector design:

Silicon:

Silicon sensors show very stable signals with very small channel-to-channel
variations, but they are expensive, and the signals are very small, which
means that special care has to be taken in the design of the readout system.

Crystals and Ceramics:

The high density, radiation hardness and intrinsic brightness of scintillation
crystals and inorganic ceramic scintillator plates make them attractive
choices in particular for the EM region of PF calorimetry. Detector designs
include their use as active layers in sampling calorimetry and optically
transparent blocks in homogeneous designs. A strength of the approach is the
prospect of good sampling fraction, to the benefit of both energy and timing
resolution. A challenge is the cost of scintillation crystal manufacture,
which has helped to drive the development of more cost-effective alternatives
based on ceramic scintillators.

Gaseous:

The signal of gaseous detectors like RPCs or MPGDs is sensitive to the gas
flow and to environmental conditions like temperature and humidity. This means
that special attention has to be paid to the monitoring of these conditions
and of the stability of the detector response. Many of the common gas mixtures
used in gaseous detectors have a strong negative impact on the environment, so
either the detector has to be built leak-tight or R&D on eco-friendly gas
mixtures is mandatory.

SiPM-on-tile:

The SiPM signal for a given number of photons depends on the overvoltage, the
difference between the bias voltage and the breakdown voltage. Since the
breakdown voltage is sensitive to the temperature, either the temperature
needs to be kept stable or the bias voltage should be adjusted to keep
overvoltage fixed. At large hit amplitudes, saturation effects due to the
limited number of pixels play a role, which can be corrected at analysis level
if they are known well enough.

Different active materials can also lead to different mechanical
considerations. Examples are the fragility of silicon sensors or the rigidity
of glass RPCs, which need very flat absorber plates and very well defined gaps
in the absorber.

###  3.4 How they are built

####  3.4.1 Structure and Sensors

An overview of the characteristics of the calorimeter concepts discussed in
the previous sections can be found in Table 1.

name | purpose | project | active | channel size | readout |  $\\#$ of layers
---|---|---|---|---|---|---
|  |  | material |  | (A/D/SD) | (depth)
CALICE SiW ECAL | ECAL |  ILC 111also for CLIC & FCC-ee | silicon | $5\times 5\,{\rm mm}^{2}$ | analog |  $30$ ($24X_{0}$)
SiD ECAL | ECAL | ILC | silicon | $13\,{\rm mm}^{2}$ | analog |  $30$ ($26X_{0}$)
HGCAL Si |  ECAL 222silicon also used in HCAL part | HL-LHC | silicon | $52-118\,{\rm mm}^{2}$ | analog |  $28$ ($25X_{0}$)
FoCal | ECAL | HL-LHC | silicon | $30\times 30\,{\rm\mu m}^{2}$ | digital |  $28$ ($25X_{0}$)
CALICE Sci-ECAL | ECAL |  ILC 333also for CEPC | SiPM-on-tile |  $5\times 5\,{\rm mm}^{2}$ 444effective size, strips have $5\times 45\,{\rm mm}^{2}$ | analog |  $30$ ($24X_{0}$)
RADiCAL | ECAL | FCC-hh | crystal + WLS |  $4\times 4\,{\rm mm}^{2}$ 555effective shower size at shower max; module cross section is $14\times 14\,{\rm mm}^{2}$ | analog |  $29$ ($25X_{0}$)
CALICE AHCAL | HCAL |  ILC 666also for CEPC, CLIC & FCC-ee | SiPM-on-tile | $3\times 3\,{\rm cm}^{2}$ | analog |  $40$ ($4\lambda_{I}$)
HGCAL Scint | HCAL | HL-LHC | SiPM-on-tile | $6-30\,{\rm cm}^{2}$ | analog |  $22$ ($7.8\lambda_{I}$) 777contains also pure silicon and mixed layers
CALICE DHCAL | HCAL | ILC | RPC | $1\times 1\,{\rm cm}^{2}$ | digital |  $40$ ($4\lambda_{I}$)
CALICE SDHCAL | HCAL | ILC | RPC | $1\times 1\,{\rm cm}^{2}$ | semi-digital |  $40$ ($4\lambda_{I}$)
Table 1: Overview of the characteristics of several particle flow calorimeter
concepts and technologies.

In addition to these calorimeter concepts, new active materials have been
proposed for particle flow calorimeters, for which quantities like channel
size and depth are not yet defined and could not be included in the table.
These comprise highly granular scintillator crystals, advanced MPGDs like
Micromegas and classical photomultipliers used directly for the detection of
shower particles.

####  3.4.2 Fabrication, Assembly, Factory-style methodology.

Due to the large channel count, scalable production and assembly technologies
are important for all PF calorimeter concepts. In order to reduce manual
assembly steps and the number of units that have to be handled manually, large
basic units, called modules in the following, are attractive. Some examples
are:

Silicon:

For silicon ECALs, the module size is related to the wafer size from which the
sensors are produced. In the case of the CALICE SiW ECAL, the sensors have a
square shape and are made from 6-inch wafers. The module is made from one PCB
equipped with 4 silicon sensors. For the CMS HGCAL, hexagonal sensors made
from 8-inch wafers have been chosen because they use a larger fraction of the
wafer area for the sensor. The module comprises one sensor. For both
calorimeters (semi-)automatic module assembly stations for the gluing of the
sensor(s) to the PCB, and in the case of the HGCAL for the wire bonding, have
been built.

RPC:

In the CALICE SDHCAL prototype, the individual chambers have a size of
$1\,{\rm m}^{2}$. For a detector at ILC, individual chambers would cover
several square meters. These sizes are too large to be covered with a single
PCB, so the basic unit size is given by the PCB size, which is determined by
the size that commercial PCB manufacturers and assembly companies can handle.

SiPM-on-tile:

The module assembly, which comprises the assembly of electronics components
including SiPMs as well as the gluing of individual scintillator tiles or
strips, can be performed with commercial pick-n-place machines. This has been
demonstrated with the CALICE AHCAL prototype, and is planned to be used for
the CMS HGCAL. An alternative concept are megatiles, where the full module is
covered by one large scintillator. The optical separation between neighboring
channels is obtained by milled grooves filled with reflective material. In
both cases, the SiPM-on-tile module size is determined by a practical PCB
size.

####  3.4.3 Industrialization

Even though the overall channel counts of PF calorimeters are hundred-
thousands to millions and the covered areas in the active layers are hundreds
of square meters, these products are a niche for most industry areas. Usually,
only the components and some of the first assembly steps can be bought from or
done by companies. Examples are silicon sensors (but the requirements are
unusual, so there are very few suppliers), SiPMs, Micromegas, and production
and component assembly of PCBs. The production of modules (joining the active
sensor with the readout electronics) and everything from there on is typically
not possible in industry.

###  3.5 Power Implications

As mentioned above, the large channel count of PF calorimeters usually implies
having the front end electronics fully embedded in the active layers. The
amount of heat produced by the electronics needs to be minimized or removed by
cooling inside the active layers.

####  3.5.1 $\mathbf{e^{+}e^{-}}$ Linear Collider – Power Reduction Between
Interactions

Detectors planned for linear electron-positron colliders like ILC and CLIC can
use the bunch train structure of the beam to minimize the power consumption.
In these calorimeter concepts, no active cooling is foreseen, in order to
avoid dead regions in the detector and keep the material as homogeneous as
possible. The readout electronics is adapted to the low duty cycle of a linear
electron-positron collider, in which short bunch trains ($1\,{\rm ms}$ long
for ILC) are interleaved with long gaps without particles ($199\,{\rm ms}$
long for ILC). This is taken into account in the readout electronics by having
two phases: a data acquisition phase in which the ASICs are acquiring and
storing the data, and a readout phase in which the data are digitized and sent
off detector. During the readout phase, all non-necessary components of the
ASIC can be switched off (power pulsing). Typical numbers for the power
consumption goal are tens of ${\rm\mu W}$ per channel. The consumption in
power pulsing mode compared to continuous running is reduced down to a few
percent. This running mode is not possible for colliders without a similar
bunch train structure, so it can be applied neither at circular electron-
positron nor at hadron colliders.

####  3.5.2 Hadron Colliders - Systemic Heating and Cooling

For colliders where the beam structure does not allow the use of power
pulsing, the heat has to be removed by the cooling system. As an example, the
power consumption of the CMS HGCAL is expected to be $\sim 110\,{\rm kW}$ per
endcap, of which roughly 2/3 comes from the readout electronics [2]. The power
consumption of the sensors is less than $10\%$ after the radiation damage
accumulated during an integrated luminosity of $3000\,{\rm fb}^{-1}$. The
HGCAL foresees a dedicated ${\rm CO}_{2}$ cooling system with the modules in
the active layers mounted on copper cooling plates. A similar power
consumption would also be expected for a detector at a circular electron-
positron collider. At hadron colliders, the mitigation of the effects of
radiation damage might pose additional requirements on the operation
conditions. For the HGCAL, the operating temperature is foreseen to be
$-30^{\circ}\,{\rm C}$ to reduce the radiation-induced noise in the silicon
sensors as well as in the SiPMs.

###  3.6 Cost Implications

Due to the large channel count, readout electronics are an important cost
driver for PF calorimeters. As example, for the CMS HGCAL the electronics and
electrical system together with the back-end (trigger and DAQ) system make up
nearly one third of the total cost, and are the second largest cost item after
the silicon sensors [2]. For hadron calorimeters with their large areas of
active layers, the cost of the PCB production and assembly can be significant,
independent of the active material that is used.

##  4 Event Reconstruction Techniques

In general, the high granularity and large channel count are not only a
challenge for the design and construction of a particle flow calorimeter, but
also for the software needed to simulate and analyze the data.

###  4.1 Simulation Methodologies

Most detector simulation packages rely on the Geant4 toolkit [21, 22, 23] for
the simulation of the passage of particles through matter. As discussed in
Section 5, in the Geant4 versions available in recent years, simulations with
the recommended physics lists agree with available testbeam data with an
accuracy of a few percent for most choices of absorber and sensor material.
Therefore, the simulations can be used to optimize the designs.

Special attention is needed for calorimeters with gaseous active material,
where the agreement with data is typically less good than for other active
materials. In addition, for these detectors the digitization, which describes
the step from the energy deposition by a traversing particle in the active
material to the recorded hit (or hits) in the detector, needs to be handled
carefully. For gaseous detectors operated in avalanche mode, the size of the
avalanche and the recorded energy depend on the depth within the active layers
where the avalalche starts, which needs to be taken into account in the
digitization.

For detectors with neutron-rich absorber material (e.g. tungsten) and neutron-
sensitive detection technique (e.g. plastic scintillator), it is important
that low-energy neutrons are tracked with enough precision. Geant4 provides a
set of physics lists labeled ”high precision” (with suffix _HP in the name).
This is essential for a good agreement of the simulation with data.

The large number and small volume of readout cells (e.g. silicon pads or
scintillator tiles/strips) usually makes handling of these as individual
detection volumes impractical in Geant4. However, simulating larger volumes
and subdividing these in the digitization by particle impact point or the
position of the energy deposition step in Geant4 works well.

Even with tricks like this, the simulation of PF calorimeters can be very time
consuming. Machine Learning techniques are being developed to speed up the
process by training the models either with samples simulated with Geant4 as
input, or with measurements from testbeam prototypes. First results look
encouraging, but are not yet at a stage where they can (partly) replace Geant4
in the production of general purpose simulation samples.

###  4.2 Calibration Methodologies

The absolute calibration of individual cells in a PF calorimeter is less
important than in ”classical” calorimeters, where the energy of a particle
shower is contained in a few cells, while typically hundreds of cells
contribute to the measurement of a shower energy in highly granular
calorimeters. Therefore, many small calibration errors in the individual cells
can cancel out, meaning that they will not lead to a bias in the reconstructed
energy, but can have an influence on the resolution. For hadron calorimeters,
usually the intrinsic fluctuations of the hadron showers are so large that the
influence of the calibration errors on the resolution is negligible. These
individual cell errors can only cancel and lead to no bias, if they are
statistically distributed. If all cells have an error in the same direction,
or if there are large regions with error in the same direction, this is no
longer true. Therefore, for the large number of cells, efficient calibration
methods are needed that avoid these possible biases. They also need to allow
the long-term monitoring of the detector stability. In addition to dedicated
calibration systems, the signal of minimum-ionizing particles like muons can
be used as reference in the calibration: either the most probable hit
amplitude, or (if no amplitude information is recorded) the efficiency and hit
multiplicity.

###  4.3 Analysis Methodologies

The measurement of jets with particle flow algorithms in detectors optimized
for this reconstruction technique has originally been proposed for linear
electron-positron Higgs factories [24, 25]. Since then, several software
frameworks for particle flow reconstruction have been developed. For Higgs
factories, the Pandora PFA [26] is widely used and performing very well.
Pandora uses both the topological information and the energy measurement in
the calorimeter to assign calorimeter cells with energy deposits to clusters
and calorimeter clusters to tracks. The Pandora Software Development Kit [27]
aims to provide a robust, reliable and easy-to-use environment for developing
and running pattern recognition algorithms. An alternative PFA, ARBOR [28], is
based only on the topological information. Recently, ideas from deep learning
and computer vision [29] have been proposed for improved PF reconstruction.

PFAs are also used and tuned for detectors which were not optimized for their
application. Current examples are the PFA algorithms employed by the ATLAS
[30] and CMS [31] experiments. In the harsh environment at the LHC, it is
essential for a reliable reconstruction of jets and missing energy to apply
pile-up mitigation algorithms in addition.

##  5 Assessing Performance of Current PF Calorimeters

Several of the design goals of particle flow calorimeters depend on the
performance of the whole detector system including the tracker, and on the
response to many impacting particles, e.g. for the jet energy resolution
reconstructed with a PFA or for the suppression of pile-up. Therefore, it is
difficult or not possible to assess these quantities in beam tests, where
usually only limited information from tracking detectors and only single
particles are available. Nevertheless, beam tests provide important insight
into some basic performance measures of the calorimeters, and into the
agreement with simulation programs that are used to determine the expected
performance of the complete detector system with real data. Long term
stability of the detector technologies can be evaluated to some extent by beam
tests with the same prototype over several years, although this is not
directly comparable to the continuous operation over several years in a
collider experiment.

###  5.1 Results From Beam Testing

An overview of the results of PF calorimeters in beam tests until 2015, mainly
conducted within the CALICE collaboration, can be found in [32]. Since then,
progress has been made within CALICE on further beam test analyses of existing
prototypes as well as construction and first beam tests of technological
prototypes of the AHCAL and the SiW ECAL. For the SiD ECAL, results have been
obtained from an initial 9-layer prototype and further R&D is foreseen on a
full-depth stack. For the CMS HGCAL, several beam tests have been performed
ranging from single-layer setups to a system consisting of an electromagnetic
and a hadronic silicon section and a SiPM-on-tile section.

For PF Calorimeter designs, notably those instrumented with silicon detectors
to provide high spatial resolution such as the CMS HGCAL, the attendant
sampling fraction is very small (few %) impacting EM energy resolution. This
is not an oversight, but rather represents a design choice taken by the
collaboration.

####  5.1.1 CALICE

Within CALICE, all technologies (SiW ECAL, Sci ECAL, AHCAL, DHCAL and SDHCAL)
have been studied with large prototypes in muon, electron and hadron beams,
either with a physics prototype or a technological prototype. Also combined
tests have been performedof an ECAL and an HCAL to validate the performance of
the calorimeter system.

The strategy in all cases is to use the response to mips (muons) to monitor
the stability of the detector and to derive a calibration at low hit energies
to: assess the response to electrons or positrons with their well-known shower
development to validate the detector modeling of the prototypes and to study
the behavior at high hit energies, and assess the response to hadrons to study
how well hadronic showers are described by the simulation. In addition,
single-particle reconstruction algorithms including software compensation and
important ingredients into particle flow algorithms like the separation of
close-by showers have been investigated.

The most important findings in [32] were: ”[…] all technologies have been
successfully commissioned, have recorded large data sets and, in the results
presented so far, demonstrated their basic performance. No show stoppers were
found. Therefore the proof of principle based on the full analyses holds for
the feasibility of particle-flow type reconstruction in fine-grained
calorimeters in general. […] The CALICE data confirm the progress made in
recent years in improving the theory-motivated shower models implemented in
the Geant4 framework, which had been driven by test beam studies with LHC
calorimeter prototypes […] Overall, the more recent hadron shower models
reproduce the pion and proton data in the relevant energy range with an
accuracy of a few percent. Shower shapes are well described in terms of
average depth, while their width remains somewhat under-estimated as energies
increase. […] A test of the particle flow reconstruction methods was performed
by applying the Pandora algorithm to test beam events overlaid on each other,
and quantifying confusion effects by measuring the degradation of neutral
hadron energy measurement through the presence of close-by charged hadron
showers, and comparing results with real data to those with simulations. […]
The excellent agreement represents important underlying evidence for the
applicability of the method for jet measurements at future colliders.”

Since then, further studies of electron showers measured with the DHCAL
physics prototype (without absorber) [33] and hadron showers with the SiW ECAL
physics prototype [34], the AHCAL physics prototype with steel [35] and
tungsten absorber [36], the DHCAL physics prototype [37] and the SDHCAL
prototype [38, 39] have been published. Overall, they confirm the assessments
made in 2015.

For several technologies developed within CALICE, technological prototypes
have been constructed or are being constructed. The large AHCAL technological
prototype has been tested with particle beams in 2018, and a paper on the
construction and commissioning is in preparation. Further publications on
shower analyses as well as further beam tests are planned. For the SiW ECAL
and the SiECAL, the construction of the technological prototypes is in
progress (or completed), but no beam test results of multi-layer systems are
available as yet.

####  5.1.2 FoCal

In the context of the R&D for the ALICE FoCal upgrade, a prototype of a Si-W
EM calorimeter was built with Monolithic Active Pixel Sensors as the active
elements [40]. It was based on MIMOSA chips with a pixel size of $30\,{\rm\mu
m}$ and had 39 million pixels in 24 layers. Energy and position resolution for
electron showers were determined, and the shape of the showers was measured in
unprecedented detail.

####  5.1.3 SiD

Recent results obtained with the 9-layer prototype in 12.1 GeV electron beam
have been shown at conferences [41], and are in reasonable agreement with
simulation. The testing did uncover an important issue related to many pixels
being triggered simultaneously. Such systemic issues are not unique to SiD,
and are important and challenging in PF designs, necessitating the need for
extensive system testing.

####  5.1.4 CMS HGCAL

During the R&D for the CMS HGCAL, beam test of prototype modules in various
configurations have been performed. First hexagonal silicon modules, using the
existing Skiroc2 front-end ASIC developed for CALICE, have been tested in
beams at Fermilab and CERN in 2016 [42]. With up to 16 modules, system
stability, calibration with minimum-ionizing particles and resolution (energy,
position and timing) for electrons were determined, and were found to be
described well by the GEANT4-based simulation.

Next, a larger prototype was built based on modules constructed with 6-inch
hexagonal silicon sensors with cell areas of $1.1\,{\rm cm}^{2}$, and the
SKIROC2-CMS readout ASIC [43]. Beam tests of different sampling configurations
were conducted with the prototype modules at DESY and CERN in 2017 and 2018.
The up to $\sim 12,000$ channels of silicon sensors were arranged in up to 28
layers of single modules mounted on copper cooling plates for the
electromagnetic section and up to 12 layers with up to 7 neighboring modules
for the hadronic section. Measurements of the prototype energy resolution and
linearity, position resolution, resolution on the positron angle of incidence
derived from the shower axis reconstruction and shower shapes were performed
and compared to detailed GEANT4 simulations [44]. For the measurement of
hadron showers, the silicon section was complemented with the CALICE AHCAL
technological prototype as SiPM-on-tile hadronic calorimeter. Publications on
the hadron shower measurements as well as the hit time measurement are in
preparation.

The HGCAL prototype modules used in the beam tests differ in several aspects
from the final HGCAL design, e.g. in the size of the silicon sensors and in
the readout electronics, so the final assessment of the HGCAL performance will
only be possible with further beam tests of (pre-)production modules or the
HGCAL itself.

###  5.2 Results from experimental operation

To date there has been no direct experimental application of particle flow
calorimeters, only results from extensive beam testing. The first full
demonstration of the technique will be the CMS HGCAL, which will be the first
to break ground in this new technological territory.

##  6 Future Directions of the Particle Flow Technique

The Particle Flow approach has emphasized performance enhancement through the
effective extension of particle tracking into the calorimetry itself,
facilitated by very high spatial granularity. This is an appropriate match to
ILC operation, where few interactions are expected during beam collisions.
However at circular machines, and particularly hadron colliders, event pileup
and radiation backgrounds are a fundamental challenge, as are the association
of identified particles with the multitude of possible production vertices
created during beam crossings. Hence precision timing of particles is also
significant, and is important to the detector designs. New technologies
continue to be developed, some presented in this summer study, which directly
address the simultaneous, precision measurement of energy, position and time
of particles, furthering the development of Particle Flow Calorimetry.

##  7 Assessment of long-term importance of PF Calorimeters to the field

The promise of Particle Flow Calorimetry is its potential for excellent jet
resolution and identification of neutral hadron energy, performance measures
that are challenging to reach through other calorimetric approaches. While
initially envisaged and designed to address the challenging requirements of
Higgs Factories such as the ILC, the first actual experimental application
will be provided in the hadron collider environment at the HL-LHC, with the
CMS HGCAL. When it is brought into operation later in this decade, the HGCAL
will serve as a ”stress test” of the PF approach, and will provide important
information about future application of such instrumentation at hadron
colliders such as FCChh and circular lepton colliders such as FCCee, where
power considerations, event pileup or radiation backgrounds are significantly
different than for linear lepton colliders. The impact of the Particle Flow
Calorimetry Technique rests on demonstrations of its successful experimental
application. The CMS HGCAL will be the first of these.

## References

  * [1] H.L. Tran, K. Krüger, F. Sefkow, S. Green, J. Marshall, M. Thomson et al., _Software compensation in Particle Flow reconstruction_ , _Eur. Phys. J. C_ 77 (2017) 698 [1705.10363].
  * [2] CMS collaboration, _The Phase-2 Upgrade of the CMS Endcap Calorimeter_ , Tech. Rep. CERN-LHCC-2017-023, CMS-TDR-019, CERN, Geneva (Nov, 2017).
  * [3] D.M. Asner et al., _ILC Higgs White Paper_ , in _Community Summer Study 2013: Snowmass on the Mississippi_ , 10, 2013 [1310.0763].
  * [4] I. Adachi et al., _The International Linear Collider: Report to Snowmass 2021_ , 2203.07622.
  * [5] M. Stanitzki and A. White, _SiD LOI Snowmass 2021_ ,  Letter of Interest to the Snowmass2021 Community Summer Study, https://www.snowmass21.org/docs/files/summaries/IF/SNOWMASS21-IF3_IF6-EF1_EF4_Andy_White,_Marcel_Stanitzki-027.pdf.
  * [6] M. Benoit et al., _Detector optimisation and detector technology R &D for the CLIC detector and for the CLD detector of FCC-ee_,  Letter of Interest to the Snowmass2021 Community Summer Study, https://www.snowmass21.org/docs/files/summaries/IF/SNOWMASS21-IF3_IF6_Mathieu_Benoit-188.pdf.
  * [7] J. Liu, Y. Liu and H. Yang, _Particle Flow Calorimeters for the Circular Electron Positron Collider_ ,  Letter of Interest to the Snowmass2021 Community Summer Study, https://www.snowmass21.org/docs/files/summaries/IF/SNOWMASS21-IF6_IF0-176.pdf.
  * [8] CMS HGCAL collaboration, R. Yohay, _The High Granularity Calorimeter Upgrade to the Compact Muon Solenoid Detector_ ,  Letter of Interest to the Snowmass2021 Community Summer Study, https://www.snowmass21.org/docs/files/summaries/IF/SNOWMASS21-IF6_IF0-165.pdf.
  * [9] M. Dong et al., _Development of Highly Granular Scintillator Strip Electromagnetic Calorimeter_ ,  Letter of Interest to the Snowmass2021 Community Summer Study, https://www.snowmass21.org/docs/files/summaries/IF/SNOWMASS21-IF6_IF0_CALICE-058.pdf.
  * [10] V. Boudry, R. Pöschl and T. Suehara, _CALICE R &D for a highly granular silicon tungsten electromagnetic calorimeter, SiW-ECAL_,  Letter of Interest to the Snowmass2021 Community Summer Study, https://www.snowmass21.org/docs/files/summaries/IF/SNOWMASS21-IF6_IF0_CALICE-077.pdf.
  * [11] V. Borshchov et al., _Towards ultra-high granularity calorimetry_ ,  Letter of Interest to the Snowmass2021 Community Summer Study, https://www.snowmass21.org/docs/files/summaries/IF/SNOWMASS21-IF6_IF0-067.pdf.
  * [12] Y. Onel, B. Bilki and J. Repond, _Digital Hadron Calorimetry_ ,  Letter of Interest to the Snowmass2021 Community Summer Study, https://www.snowmass21.org/docs/files/summaries/IF/SNOWMASS21-IF6_IF0_Yasar_Onel-048.pdf.
  * [13] A. Colaleo et al., _Advanced GEM detectors for future collider experiments_ ,  Letter of Interest to the Snowmass2021 Community Summer Study, https://www.snowmass21.org/docs/files/summaries/IF/SNOWMASS21-IF5_IF6-EF4_EF0_COLALEO-068.pdf.
  * [14] K. Krüger and F. Sefkow, _Developments Towards a SiPM-on-Tile Based Analogue Hadron Calorimeter (AHCAL)_ ,  Letter of Interest to the Snowmass2021 Community Summer Study, https://www.snowmass21.org/docs/files/summaries/IF/SNOWMASS21-IF6_IF0_CALICE-099.pdf.
  * [15] S. Eno et al., _High-Granularity Crystal Calorimetry Letter of Intent_ ,  Letter of Interest to the Snowmass2021 Community Summer Study, https://www.snowmass21.org/docs/files/summaries/IF/SNOWMASS21-IF6_IF0_Yong_Liu-064.pdf.
  * [16] R. Ruchti et al., _Advanced Optical Instrumentation for Ultra-compact, Radiation Hard EM Calorimetry Applications_ ,  Letter of Interest to the Snowmass2021 Community Summer Study, https://www.snowmass21.org/docs/files/summaries/IF/SNOWMASS21-IF6_IF4-EF1_EF4-102.pdf.
  * [17] T. Anderson et al., _RADiCAL: Precision-timing, Ultracompact, Radiation-hard Electromagnetic Calorimetry_ , 2203-12806.
  * [18] M. Aleksa et al., _Calorimeters for the FCC-hh_ , 1912.09962.
  * [19] Y. Onel, B. Bilki, J. Wetzel and D. Winn, _Photomultiplier and Dynode Techniques for in-situ Calorimeter Sensors to Survive in the Forward Region of Future Colliders, High Intensity and Low Earth orbit Cosmic Frontiers_ ,  Letter of Interest to the Snowmass2021 Community Summer Study, https://www.snowmass21.org/docs/files/summaries/IF/SNOWMASS21-IF6_IF9_David_R_Winn-036.pdf.
  * [20] K. Krüger, R. Pöschl and T. Suehara, _CALICE R &D for compact readout systems for highly granular calorimeters_,  Letter of Interest to the Snowmass2021 Community Summer Study, https://www.snowmass21.org/docs/files/summaries/IF/SNOWMASS21-IF6_IF0_CALICE-082.pdf.
  * [21] S. Agostinelli, J. Allison, K. Amako, J. Apostolakis, H. Araujo, P. Arce et al., _Geant4—a simulation toolkit_ , _Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment_ 506 (2003) 250.
  * [22] J. Allison, K. Amako, J. Apostolakis, H. Araujo, P. Arce Dubois, M. Asai et al., _Geant4 developments and applications_ , _IEEE Transactions on Nuclear Science_ 53 (2006) 270.
  * [23] J. Allison, K. Amako, J. Apostolakis, P. Arce, M. Asai, T. Aso et al., _Recent developments in geant4_ , _Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment_ 835 (2016) 186.
  * [24] J.-C. Brient and H. Videau, _The Calorimetry at the future e+ e- linear collider_ , _eConf_ C010630 (2001) E3047 [hep-ex/0202004].
  * [25] V.L. Morgunov, _Calorimetry design with energy-flow concept (imaging detector for high-energy physics)_ , in _10th International Conference on Calorimetry in High Energy Physics (CALOR 2002)_ , pp. 70–84, 3, 2002.
  * [26] M.A. Thomson, _Particle Flow Calorimetry and the PandoraPFA Algorithm_ , _Nucl. Instrum. Meth. A_ 611 (2009) 25 [0907.3577].
  * [27] J.S. Marshall and M.A. Thomson, _The Pandora Software Development Kit for Pattern Recognition_ , _Eur. Phys. J. C_ 75 (2015) 439 [1506.05348].
  * [28] M. Ruan and H. Videau, _Arbor, a new approach of the Particle Flow Algorithm_ , in _International Conference on Calorimetry for the High Energy Frontier_ , pp. 316–324, 2013 [1403.4784].
  * [29] F.A. Di Bello, S. Ganguly, E. Gross, M. Kado, M. Pitt, L. Santi et al., _Towards a Computer Vision Particle Flow_ , _Eur. Phys. J. C_ 81 (2021) 107 [2003.08863].
  * [30] ATLAS collaboration, _Jet reconstruction and performance using particle flow with the ATLAS Detector_ , _Eur. Phys. J. C_ 77 (2017) 466 [1703.10485].
  * [31] CMS collaboration, _Particle-flow reconstruction and global event description with the CMS detector_ , _JINST_ 12 (2017) P10003 [1706.04965].
  * [32] F. Sefkow, A. White, K. Kawagoe, R. Pöschl and J. Repond, _Experimental Tests of Particle Flow Calorimetry_ , _Rev. Mod. Phys._ 88 (2016) 015003 [1507.05893].
  * [33] CALICE collaboration, _DHCAL with Minimal Absorber: Measurements with Positrons_ , _JINST_ 11 (2016) P05008 [1603.01652].
  * [34] CALICE collaboration, _Characterisation of different stages of hadronic showers using the CALICE Si-W ECAL physics prototype_ , _Nucl. Instrum. Meth. A_ 937 (2019) 41 [1902.06161].
  * [35] CALICE collaboration, _Hadron shower decomposition in the highly granular CALICE analogue hadron calorimeter_ , _JINST_ 11 (2016) P06013 [1602.08578].
  * [36] CALICE collaboration, _Shower development of particles with momenta from 15 GeV to 150 GeV in the CALICE scintillator-tungsten hadronic calorimeter_ , _JINST_ 10 (2015) P12006 [1509.00617].
  * [37] CALICE collaboration, _Analysis of Testbeam Data of the Highly Granular RPC-Steel CALICE Digital Hadron Calorimeter and Validation of Geant4 Monte Carlo Models_ , _Nucl. Instrum. Meth. A_ 939 (2019) 89 [1901.08818].
  * [38] CALICE collaboration, _First results of the CALICE SDHCAL technological prototype_ , _JINST_ 11 (2016) P04001 [1602.02276].
  * [39] CALICE collaboration, _Tracking within Hadronic Showers in the CALICE SDHCAL prototype using a Hough Transform Technique_ , _JINST_ 12 (2017) P05009 [1702.08082].
  * [40] A.P. de Haas et al., _The FoCal prototype—an extremely fine-grained electromagnetic calorimeter using CMOS pixel sensors_ , _JINST_ 13 (2018) P01014 [1708.05164].
  * [41] A. Steinhebel and J. Brau, _Studies of the Response of the SiD Silicon-Tungsten ECal_ , in _International Workshop on Future Linear Colliders_ , 3, 2017 [1703.08605].
  * [42] N. Akchurin et al., _First beam tests of prototype silicon modules for the CMS High Granularity Endcap Calorimeter_ , _JINST_ 13 (2018) P10023.
  * [43] CMS HGCAL collaboration, _Construction and commissioning of CMS CE prototype silicon modules_ , _JINST_ 16 (2021) T04002 [2012.06336].
  * [44] CMS HGCAL collaboration, _Response of a CMS HGCAL silicon-pad electromagnetic calorimeter prototype to 20-300 GeV positrons_ , 2111.06855.