# Design and Simulated Performance of Calorimetry Systems for the ECCE
Detector at the Electron Ion Collider

F. Bock  N. Schmidt  P.K. Wang  N. Santiesteban  T. Horn  J. Huang  J. Lajoie
C. Munoz Camacho  J. K. Adkins  Y. Akiba  A. Albataineh  M. Amaryan  I. C.
Arsene  C. Ayerbe Gayoso  J. Bae  X. Bai  M.D. Baker  M. Bashkanov  R.
Bellwied  F. Benmokhtar  V. Berdnikov  J. C. Bernauer  W. Boeglin  M. Borysova
E. Brash  P. Brindza  W. J. Briscoe  M. Brooks  S. Bueltmann  M. H. S. Bukhari
A. Bylinkin  R. Capobianco  W.-C. Chang  Y. Cheon  K. Chen  K.-F. Chen  K.-Y.
Cheng  M. Chiu  T. Chujo  Z. Citron  E. Cline  E. Cohen  T. Cormier  Y.
Corrales Morales  C. Cotton  J. Crafts  C. Crawford  S. Creekmore  C.Cuevas
J. Cunningham  G. David  C. T. Dean  M. Demarteau  S. Diehl  N. Doshita  R.
Dupré  J. M. Durham  R. Dzhygadlo  R. Ehlers  L. El Fassi  A. Emmert  R. Ent
C. Fanelli  R. Fatemi  S. Fegan  M. Finger  M. Finger Jr  J. Frantz  M.
Friedman  I. Friscic  D. Gangadharan  S. Gardner  K. Gates  F. Geurts  R.
Gilman  D. Glazier  E. Glimos  Y. Goto  N. Grau  S. V. Greene  A. Q. Guo  L.
Guo  S. K. Ha  J. Haggerty  T. Hayward  X. He  O. Hen  D. W. Higinbotham  M.
Hoballah  A. Hoghmrtsyan  P.-h. J. Hsu  G. Huber  A. Hutson  K. Y. Hwang  C.
E. Hyde  M. Inaba  T. Iwata  H.S. Jo  K. Joo  N. Kalantarians  G. Kalicy  K.
Kawade  S. J. D. Kay  A. Kim  B. Kim  C. Kim  M. Kim  Y. Kim  Y. Kim  E.
Kistenev  V. Klimenko  S. H. Ko  I. Korover  W. Korsch  G. Krintiras  S. Kuhn
C.-M. Kuo  T. Kutz  D. Lawrence  S. Lebedev  H. Lee  J. S. H. Lee  S. W. Lee
Y.-J. Lee  W. Li  W.B. Li  X. Li  X. Li  X. Li  X. Li  Y. T. Liang  S. Lim
C.-h. Lin  D. X. Lin  K. Liu  M. X. Liu  K. Livingston  N. Liyanage  W.J.
Llope  C. Loizides  E. Long  R.-S. Lu  Z. Lu  W. Lynch  S. Mantry  D. Marchand
M. Marcisovsky  C. Markert  P. Markowitz  H. Marukyan  P. McGaughey  M.
Mihovilovic  R. G. Milner  A. Milov  Y. Miyachi  A. Mkrtchyan  P. Monaghan  R.
Montgomery  D. Morrison  A. Movsisyan  H. Mkrtchyan  A. Mkrtchyan  M. Murray
K. Nagai  J. Nagle  I. Nakagawa  C. Nattrass  D. Nguyen  S. Niccolai  R.
Nouicer  G. Nukazuka  M. Nycz  V. A. Okorokov  S. Orešić  J.D. Osborn  C.
O’Shaughnessy  S. Paganis  Z. Papandreou  S. F. Pate  M. Patel  C. Paus  G.
Penman  M. G. Perdekamp  D. V. Perepelitsa  H. Periera da Costa  K. Peters  W.
Phelps  E. Piasetzky  C. Pinkenburg  I. Prochazka  T. Protzman  M. L. Purschke
J. Putschke  J. R. Pybus  R. Rajput-Ghoshal  J. Rasson  B. Raue  K.F. Read  K.
Røed  R. Reed  J. Reinhold  E. L. Renner  J. Richards  C. Riedl  T. Rinn  J.
Roche  G. M. Roland  G. Ron  M. Rosati  C. Royon  J. Ryu  S. Salur  R. Santos
M. Sarsour  J. Schambach  A. Schmidt  C. Schwarz  J. Schwiening  R. Seidl  A.
Sickles  P. Simmerling  S. Sirca  D. Sharma  Z. Shi  T.-A. Shibata  C.-W. Shih
S. Shimizu  U. Shrestha  K. Slifer  K. Smith  D. Sokhan  R. Soltz  W. Sondheim
J. Song  J. Song  I. I. Strakovsky  P. Steinberg  P. Stepanov  J. Stevens  J.
Strube  P. Sun  X. Sun  K. Suresh  V. Tadevosyan  W.-C. Tang  S. Tapia Araya
S. Tarafdar  L. Teodorescu  D. Thomas  A. Timmins  L. Tomasek  N. Trotta  R.
Trotta  T. S. Tveter  E. Umaka  A. Usman  H. W. van Hecke  C. Van Hulse  J.
Velkovska  E. Voutier  P.K. Wang  Q. Wang  Y. Wang  Y. Wang  D. P. Watts  N.
Wickramaarachchi  L. Weinstein  M. Williams  C.-P. Wong  L. Wood  M. H. Wood
C. Woody  B. Wyslouch  Z. Xiao  Y. Yamazaki  Y. Yang  Z. Ye  H. D. Yoo  M.
Yurov  N. Zachariou  W.A. Zajc  W. Zha  J.-L. Zhang  J.-X. Zhang  Y. Zhang
Y.-X. Zhao  X. Zheng  P. Zhuang

###### Abstract

We describe the design and performance the calorimeter systems used in the
ECCE detector design[1] to achieve the overall performance specifications
cost-effectively with careful consideration of appropriate technical and
schedule risks. The calorimeter systems consist of three electromagnetic
calorimeters, covering the combined pseudorapdity range from -3.7 to 3.8 and
two hadronic calorimeters covering a combined range of $-1.1<\eta<3.8$. Key
calorimeter performances which include energy and position resolutions,
reconstruction efficiency, and particle identification will be presented.

###### keywords:

ECCE , Electron Ion Collider , Tracking , Calorimetry

††journal: Nuclear Instruments and Methods A

[AANL]organization=A. Alikhanyan National Laboratory, city=Yerevan,
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[AcademiaSinica]organization=Institute of Physics, Academia Sinica,
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[MIT]organization=Massachusetts Institute of Technology, city=Cambridge,
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[NCKU]organization=National Cheng Kung University, city=Tainan, country=Taiwan

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[NMSU]organization=New Mexico State University, city=Las Cruces, state=NM,
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[NRNUMEPhI]organization=National Research Nuclear University MEPhI,
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[NRCN]organization=Nuclear Research Center - Negev, city=Beer-Sheva,
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[NTHU]organization=National Tsing Hua University, city=Hsinchu, country=Taiwan

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[ODU]organization=Old Dominion University, city=Norfolk, state=VA, country=USA

[Ohio]organization=Ohio University, city=Athens, state=OH, country=USA

[ORNL]organization=Oak Ridge National Laboratory, city=Oak Ridge, state=TN,
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[PNNL]organization=Pacific Northwest National Laboratory, city=Richland,
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[Pusan]organization=Pusan National University, city=Busan, country=Republic of
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[Rice]organization=Rice University, city=Houston, state=TX, country=USA

[RIKEN]organization=RIKEN Nishina Center, city=Wako, state=Saitama,
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[Rutgers]organization=The State University of New Jersey, city=Piscataway,
state=NJ, country=USA

[CFNS]organization=Center for Frontiers in Nuclear Science, city=Stony Brook,
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[StonyBrook]organization=Stony Brook University, city=Stony Brook, state=NY,
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[RBRC]organization=RIKEN BNL Research Center, city=Upton, state=NY,
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[SDU]organizaton=Shandong University, city=Qingdao, state=Shandong,
country=China

[Seoul]organization=Seoul National University, city=Seoul, country=Republic of
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[Shinshu]organization=Shinshu University, city=Matsumoto, state=Nagano,
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[USTC]organization=University of Science and Technology of China, city=Hefei,
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[Tsinghua]organization=Tsinghua University, city=Beijing, country=China

[Tsukuba]organization=Tsukuba University of Technology, city=Tsukuba,
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country=Canada

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[UTsukuba]organization=University of Tsukuba, city=Tsukuba, country=Japan

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[York]organization=University of York, city=York, country=UK

[Zagreb]organization=University of Zagreb, city=Zagreb, country=Croatia

###### Contents

  1. 1 Introduction
  2. 2 Calorimeter Design
  3. 3 Calorimeter Performance
  4. 4 Summary
  5. 5 Acknowledgements

##  1 Introduction

We report the design and performance of the calorimeter systems for the ECCE
detector [1]. Homogeneous and sampling calorimeter technologies are employed
in the different pseudorapidity regions (backwards, central, and forward)
aiming to achieve the overall performance requirements outlined in the EIC
Yellow Report (YR) [2] cost effectively and with consideration of technical
and schedule risks. The main physics program of the EIC imposes strong
detector performance requirements on the calorimeter systems. While single
inclusive DIS, jets and heavy quark reconstruction require an excellent energy
resolution for the electromagnetic and hadronic calorimeters, further
requirements for $\pi$ / $e$ separation at the $3\sigma$ level are imposed,
for example, by spin asymmetry measurements, TMD evolution, and $XYZ$
spectroscopy. In order to probe the requested kinematic regions for such
processes, a large acceptance in pseudorapidity for the calorimeters is
required with special focus on continuous coverage from the backward region to
the forward region. The key performances of the ECCE calorimeter systems are
reported and put in context to their impact on physics analyses. This includes
the reconstruction performance, expected energy and position resolution, as
well as particle identification via matching to charged particle tracks
obtained from the ECCE tracking systems [3].

##  2 Calorimeter Design

Figure 1:  $\eta-\varphi$ coverage of the ECCE HCals (a) and ECals (b),
highlighting the non-uniform tower distributions in azimuth in the forward
region due to the crossing angle of the beam pipe.

The ECCE calorimeters are designed to address the full range of physics the
EIC Whitepaper, the National Academy of Sciences report, and the EIC Yellow
Report. Consequently, particular focus is placed on an excellent electron
detection with the broadest possible pseudorapidity ($\eta$) coverage. Driven
by these concerns, homogeneous electromagnetic calorimeters (ECals) for the
electron end cap and the barrel region are selected, while a highly granular
shashlik sampling calorimeter is chosen in the hadron going direction. The
gaps between these calorimeters in $\eta$ are minimized by reducing the
support structures for the inner most detectors and even adopting a projective
design for the barrel ECal.
During the proposal preparations, the ECCE consortium could not identity a
physics process which would benefit from a Hadronic Calorimeter (HCal) in the
electron end cap. Thus, in the presented baseline design for the hadronic
calorimeters no HCal is forseen in that direction and instead the two sPHENIX
plugdoors will serve as magnet flux return.

Figure 2: Integrated radiation lengths (left) and nuclear interaction lengths
(right) in the full ECCE detector configuration as a function of
pseudorapdity. Contributions of individual detector systems are summed up
according to six material categories.

For the barrel we propose to repurpose the existing outer HCal from the
sPHENIX collaboration, which is currently under construction at BNL [4]. This
HCal surrounding the BaBar magnet will be complemented by an instrumented
steel support frame that holds the barrel ECal. Despite its limited depth,
this inner HCal will be able to serve as calibration point before the magnet.
In the hadron going direction we propose to construct a new longitudinally
separated HCal in order to capture the rather collimated hadrons going in this
direction with the best possible energy resolution. The acceptance of the
envisioned detectors in $\eta$ and azimuth ($\varphi$) according to the ECCE
GEANT4 implementations for all HCals (top) and ECals (bottom), can be found in
Figure 1. The figure also shows that the calorimeters cover the full azimuth
($0<\varphi<2\pi$) in most of the pseudorapdity regions. In the forward
region, the 25 mrad crossing angle of the beam pipe results in a
$\varphi$-asymmetric setup in particular at high pseudorapidities.

The performance of the above described calorimeters strongly depends on the
material budget of the inner detectors, as early material interactions can
deteriorate the reconstruction performance. A special focus here is put on the
ECals where excess material of the inner detectors could quickly add up to
several percent of a radiation length ($X/X_{0}$). Thus, the material of all
inner detector systems and support frames in ECCE has been greatly minimized
by design, resulting in a material budget of only $0.2-1X/X_{0}$ in the barrel
and approximately $0.15X/X_{0}$ in the forward and backward direction with
slight modulations depending on $\eta$. The corresponding $\eta$-distribution
of $X/X_{0}$ including the ECals is shown in Fig. 2 (left), while the
respective distribution of the nuclear interaction length
($\lambda/\lambda_{0}$) including the HCals can be found in Fig. 2 (right). As
can be seen, the bulk of material in front of the ECals stems from the
Cherenkov (mRICH, dRICH, DIRC) detector systems and from the TOF systems. The
$\eta$ regions between the barrel and forward/backward calorimeters shows
several significant passive support structures in the distribution, whose
material we aim to reduce considerably. For the HCals, the bulk of upstream
material is given by the ECals as well as by the passive magnet material in
the barrel. The final number of nuclear interaction lengths and radiation
lengths of the different calorimeters that are described in this article can
also be obtained from Fig. 2, which is based on a GEANT4 material scan of the
full ECCE detector as implemented in the Fun4All framework [5].

###  2.1 Electron-End-Cap Electromagnetic Calorimeter: EEMC

The electron-end-cap calorimeter will to cover a dynamic energy range of
0.1–18 GeV for electromagnetic showers of the scattered electron based on e+p
Pythia simulations at 18x275 GeV2. The choice of technology and detector
dimensions are therefore optimized to provide the optimal performance for this
expected energy range.

The EEMC is a high-resolution ECal designed for precision measurements of the
energy of scattered electrons and final-state photons in the electron-going
region. The requirements for energy resolution in the backward region is
driven by inclusive DIS where precise determination of the scattered electron
properties is critical to constrain the event kinematics. The EEMC is designed
to address the requirements outlined in the EIC Yellow Report. Its baseline
design is based on an array of approximately 3000 lead tungsten crystals
(PbWO4) $2\times 2\times 20$ cm3 in size, which correspond to approximately 20
$X/X_{0}$ longitudinally and a transverse size equal to the PbWO4 Molière
radius. The PbWO4 crystal light yield is in the range of 15 to 25 photo-
electrons per MeV, providing an excellent energy resolution of
$\sigma_{E}/E\approx 2\%/\sqrt{E}\oplus 1\%$ [6, 7] within a very compact
design.
The EEEMCAL Consortium is leading the efforts to further develop the EEMC
design concept and has summarized their intentions in an Expression Of
Interest in 2021. They have begun to organize activities into mechanical
design, scintillator, readout, and software/simulation among the collaborating
institutions. Pre-design activities of the mechanical support structure
commenced in 2021 and a document on mechanical design and integration has been
prepared [8]. The concept is based existing detectors that the team has
constructed, and in particular the Neutral Particle Spectrometer at Jefferson
Lab.

Figure 3: The Electron-End-Cap Calorimeter conceptual design and integration
with the beampipe and surrounding detectors as prepared by the EEEMCAL
Consortium [8]. The EEMC consists only of PbWO4 crystals and uses the
displayed design concept.

Figure 3 shows an overview of the different components of the EEMC as prepared
by the EEEMCAL Consortium [8]. It has four main parts: the detector (PbWO4
crystals), the mechanical structure (internal and external), cooling, and
electronics (SiPM and cables). With crystal dimensions of $2\times 2\times 20$
cm3, a density of 8.28 g/cm3, and a mass of 0.6624 kg per crystal the total
weight of the EEMC is slightly more than two metric tons. The crystals are
aligned and separated using carbon plates of thickness 0.5 mm. The
configuration for the first ring of PbWO4 crystals depends on the final design
of the beam pipe. Its minimum diameter will be on the order of 22.5 cm with an
additional clearance gap. An additional support and cooling structure with a
maximum thickness of 5 mm will be needed to support the crystals directly
above the beam pipe. For which detailed calculations will have to be carried
out once the final beam pipe design is available. The EEMC is located inside
the universal support frame, which also houses the Detection of Internally
Reflected Cherenkov light (DIRC) detector [1], and covers the pseudorapdity
region of $-3.4<\eta<-1.5$. The main constraints for its acceptance are
imposed by the surrounding detector systems and passive materials, as seen in
Fig. 3. The integration of the EEMC into the frame is only possible if the
beam pipe is removed, which implies that the flange must be disconnected. To
improve the inner diameter of the EEMC and to improve the acceptance up to
$-3.7<\eta<-1.5$, an inner calorimeter is being considered. This option also
requires the modification of the overall structure of the EEMC to ensure no
significant gaps in scattered electron detection between the electron-end-cap
and barrel. Overall, the inner diameter of the EEMC will depend on the design
of the beam pipe, and in particular the angle between the electron and the
hadron tube.
Currently, the EEMC readout is based on silicon photomultipliers (SiPMs) of
pixel sizes of 10$\mu$m or 15$\mu$m and a photosensitive area of $3\times 3$
mm2. There are two configuration options: 4 SiPM per crystal or 16 SiPM per
crystal. Since a mechanical structure is required for mounting the PCBs, its
width in turn will determine the positioning of the SiPMs. Assuming a machined
grid with a width of about 5 mm the PCBs can be mounted with small screws.
PbWO4 crystals are sensitive to temperature changes with a variation of 2%/∘C
in light output. Thus, the specification is to keep the crystal temperature
stable within $\pm$0.1 ∘C. To ensure this stability the additional heat
generated by the electronics needs to be removed and the following cooling
structures are being considered. As internal cooling structure several
machined copper blocks with internal coolant circulation will be used around
the beam pipe. To reduce the spatial extend support structures the EEEMC
consortium is moreover planning to use cooling plates in between the readout
cables which are linked to the support structure surrounding the EEMC with
tubes. This system is composed of 12 plates with a 5-8 mm spacing in which
water can be circulated. The cooling near the crystals will likely not be
enough to meet specification. These challenges could be overcome by outside
cooling with standard cooling blocks with airflow in front of the electronics
or additional cooling added at the back of the assembly. The main constraint
is the space available in the electron end-cap.
The mechanical integration of the EEMC presently envisions that the detector
is assembled in its own support structure, mounted on a platform, and then
inserted into the universal support frame. The detailed steps and main points
of the assembly are described in Ref. [8]. The mechanical integration starts
when the assembly is complete. The platform is adjusted on rails with an
additional support to link the support to the detector. The platform is
removed once the EEMC is mounted in the universal support frame. Clearances of
at least 5 mm on all sides between the EEMC and the universal support frame
are required to perform maintenance without lifting the detector.

Figure 4: Left: Single BEMC tower as implemented in the GEANT4 simulations.
Middle: BEMC projective tower layout in $\eta$. The towers are centered at
$z=-10$ cm. Right: BEMC layout layout as a function of $\varphi$ for one
$\eta$ slice. The towers are tilted in $\varphi$ by $10^{\circ}$ to avoid
channeling in the gaps between adjacent towers.

###  2.2 Barrel

Based on Pythia simulations of e+p collisions at 18x275 GeV2, the expected
energy range of particles at mid-rapidity is 0.1–50 GeV in high $Q^{2}$
events. The ECCE detector therefore requires calorimeters that can cover these
expected energies for electromagnetic and hadronic shower reconstruction.

##### Barrel Electromagnetic Calorimeter: BEMC

The barrel electromagnetic calorimeter is designed to cover the central region
of the detector ($-1.72<\eta<1.31$). Its total length along the $z$-axis is
584 cm and the detector is fully contained within solenoid magnet, but
positioned at a larger radial position than the DIRC detector. The absolute
radial position of the calorimeter is $85<R<135$ cm from the beampipe, where
the inner radius is fixed for all towers but the outer radius varies depending
of the position in eta due to the required projective design.
The calorimeter is composed of 8960 towers made out of scintillating glass
(SciGlass), which are organized in 128 towers per $\varphi$ slice and 70
blocks in the $\eta$ direction. The middle and left panels of Fig. 4 show $x$
and $z$ slices of the BEMC geometry as it is modeled in GEANT4. The colors
show the different $\eta$ towers, and the variation in the outer radius can be
observed. The interaction point is marked by a red star, from which the left
and right directions in the figure correspond to the electron and hadron-going
sides, respectively. The detector is designed asymmetric towards the electron
and hadron sides, resulting in a length of 389 and 195 cm on the respective
sides. The BEMC is designed with offset projectivity in $\eta$ and $\varphi$
in order to avoid channeling of particles produced in the collision within the
passive material between the towers. Thus the front face of the towers is
tilted such that it is facing the interaction point shifted by $\Delta z=-10$
cm. This requires that the tower tilt angle depends on its location within the
calorimeter. Additionally, the towers have a stronger inclination at higher
absolute pseudorapidities, leading to an asymmetric tapered shape of the glass
blocks, which increases with $|\eta|$. All the towers are tilted by
$\Delta\varphi=10^{\circ}$ to avoid any gaps in $\varphi$ and further
tunneling of particles through inactive detector material. A summary of all
BEMC detector parameters is given in Table 1.

Parameter | Value
---|---
Inner radius (envelope) | 85 cm
Outer radius (envelope) | max. 135 cm ($\eta-\text{dependent})$
Length (envelope) | 584 cm ($-389<z<195$ cm)
Pseudorapidity coverage | $-1.72<\eta<1.31$
Active material | SciGlass
# towers in azimuth | 128
# towers in pseudorapidity | 70
Tower dimensions |
inner face: |  $4\times 4$ cm
length: |  $45.5$ cm
outer face ($\eta=0$): |  $5\times 5$ cm
outer face ($|\eta|>1.1$): |  $6.6\times 6.6$ cm
$\eta$ projectivity point |  $z=-10$ cm
$\varphi$ projectivity tilt | $10^{\circ}$
Sampling fraction | 0.97
Tower depth | $X/X_{0}\approx 16.0$
Molière radius |  $R_{\mathrm{M}}=3.58$ cm
Table 1: Design parameters for the barrel electromagnetic calorimeter BEMC.

The layout for a single tower around $\eta=0$ is shown in Fig. 4 (left). All
towers currently have an inner size of $4\times 4$ cm2 and the same length of
45.5 cm, which corresponds to approximately 16 $X/X_{0}$. However, their outer
face dimension varies from $5^{2}$ to $6.6^{2}$ cm2 depending on their
position in $|\eta|$. In addition, the considered SciGlass towers have a
Molière radius of 3.58 cm, which is approximately double the transverse tower
size. Each tower is composed of a SciGlass core, surrounded by a 1 mm carbon
fiber enclosure. The electronics are currently modeled by Kapton, SiO2 and
carbon fiber layers in the outer part of the blocks. The SciGlass block length
is optimized to contain at least $95\%$ of the energy of a 10 GeV electron,
whilst still fitting into the BABAR 1.5T magnet with at most an inner radius
of 80 cm and at least 8 cm space for the electronics and support structure.
The electron energy mentioned above corresponds to the average scattered
electron energy in the BEMC acceptance. Constraining the BEMC to not stretch
further into the detector allows for more space for other PID and tracking
detectors which are necessary for electron, pion, kaon and proton separation.
In particular, towards the electron end cap (negative $\eta$) it could be
studied in the future, whether the tower depth could be increased up to 60 cm
for higher $|\eta|$ to decrease the energy leakage for high energetic
electrons, which are more probable in this region. Here the projective design
allows for such an extension at least for parts of the calorimeter.

##### Barrel Hadronic Calorimeter: IHCAL & OHCAL

Figure 5: Left: Scintillator tiles in a layer of the OHCAL. Right: Transverse
cutaway view of an OHCAL module, showing the tilted tapered absorber plates.
Light collection and cabling is on the outer radius at the top of the drawing.

The Outer Hadronic Calorimeter (OHCAL) will be reused from the sPHENIX HCal
[9], which instruments the large steel-based barrel flux return of the BABAR
magnet. The Inner Hadronic Calorimeter (IHCAL), as currently implemented in
ECCE, is very similar in design to the sPHENIX inner HCAL in that it
instruments the support for the barrel HCal to provide an additional
longitudinal segment of hadronic calorimetry. The IHCAL provides useful data
for overall calibration of the combined calorimeter system.
In the following, the construction of the scintillating tiles used in the
outer and inner HCals is described, followed by a mechanical description of
each calorimeter system.

Parameter | Value
---|---
Inner radius (envelope) | 1820 mm
Outer radius (envelope) | 2700 mm
Length (envelope) | 6316 mm
Material | 1020 steel
# towers in azimuth ($\Delta\varphi$) | 64
# tiles per tower | 5
# towers in pseudorapidity ($\Delta\eta$) | 24
# electronic channels (towers) | $64\times 24=1536$
# optical devices (SiPMs) | 5 $\times$ 1536 = 7680
# modules (azimuthal slices) | 32
# towers per module | $2\times 24=48$
Total # absorber plates | $5\times 64=320$
Tilt angle (relative to radius) | 12∘
Absorber plate thickness at inner radius | 10.2 mm
Absorber plate thickness at outer radius | 14.7 mm
Gap thickness | 8.5 mm
Scintillator thickness | 7 mm
Module weight | 12247 kg
Sampling fraction | 0.035
Calorimeter depth | 4.0$\lambda/\lambda_{0}$
Molière radius $R_{M}$ for $\pi^{\pm}$ | 14.4 cm
Table 2: Design parameters for the Outer Hadronic Calorimeter (OHCAL). Parameter | Value
---|---
Inner radius (envelope) | 1350 mm
Outer radius (envelope) | 1385 mm
Material | 310 stainless steel
# towers in azimuth ($\Delta\varphi$) | 64
# towers per module | $2\times(12+15)=56$
# tiles per tower | 4
# towers in pseudorapidity ($\eta>0$) | 24
# towers in pseudorapidity ($\eta<0$) | 30
# electronic channels (towers) | $64\times 27=1728$
# optical devices (SiPMs) | 4 $\times$ 1728 = 6912
Tilt angle (relative to radius) | 32 ∘
Absorber plate thickness | 13 mm
Gap thickness | 8.5 mm
Scintillator thickness | 7 mm
# modules (azimuthal slices) | 32
Sampling fraction | 0.059
Calorimeter depth | 0.17$\lambda/\lambda_{0}$
Table 3: Design parameters for the Inner Hadronic Calorimeter (instrumented
frame) for ECCE.

The basic calorimeter concept for the IHCAL/OHCAL is a sampling calorimeter
with absorber plates tilted in the radial direction. This design provides more
uniform sampling in azimuth and provides information on the longitudinal
shower development. The current design uses tapered plates for the OHCAL and
non-tapered plates for the IHCAL. Based on detailed studies, this design
choice lowers the IHCAL machining cost without decreasing its performance.
Extruded tiles of plastic scintillator with an embedded wavelength shifting
fiber are interspersed between the absorber plates and read out at the outer
radius with SiPMs. The tilt angle is chosen so that a radial track from the
center of the interaction region traverses at least four scintillator tiles.
Each tile is read out by a single SiPM, and the analog signal from each tile
in a tower (five for the OHCAL, four for the IHCAL) are ganged to a single
preamplifier channel to form a calorimeter tower. Tiles are divided in slices
of $\eta$ so that the overall segmentation is
$\Delta\eta\times\Delta\varphi\approx 0.1\times 0.1$.
The scintillating tiles are similar to the design of the scintillators for the
T2K experiment by the INR group (Troitzk, Russia) who designed and built 875
mm long scintillation tiles with a serpentine wavelength shifting fiber
readout [10]. Similar extruded scintillator tiles were also developed by the
MINOS experiment. The properties of the HCal scintillating tiles and of the
WLS fibers are detailed in Ref. [9]. The Kuraray single clad fiber is chosen
due to its flexibility and longevity, which are critical in the geometry with
multiple fiber bends.
The OHCAL is north-south symmetric and requires 24 tiles along the $\eta$
direction, whereas the IHCAL is asymmetric and has 12 towers in the forward
direction and 15 towers in the backward direction. The OHCAL design therefore
requires 12 different shapes of tiles for each longitudinal segment. Figure 5
shows the tile and embedded fiber pattern for the OHCAL.
The major components of the OHCAL are tapered steel absorber plates and 7680
scintillating tiles which are read out with SiPMs along the outer radius of
the detector. The detector consists of 32 modules, which are wedge-shaped
sectors containing 2 towers in $\varphi$ and 24 towers in $\eta$ equipped with
SiPM sensors, preamplifiers, and cables carrying the differential output of
the preamplifiers to the digitizer system on the floor and upper platform of
the detector. Each module comprises nine full-thickness absorber plates and
two half-thickness absorber plates, so that as the modules are stacked,
adjoining half-thickness absorber plates have the same thickness as the full-
thickness absorber plates. The tilt angle is chosen to be 12 degrees relative
to the radius, corresponding to the geometry required for a ray from the
vertex to cross four scintillator tiles. Table 2 summarizes the major design
parameters of the OHCAL, which are illustrated in Figure 5. Since the OHCAL
will serve as the flux return of the solenoid, the absorber plates are single,
long plates running along the field direction. The IHCAL occupies a radial
envelope bounded by a 50 mm clearance inside the solenoid cryostat and the
outer radius of the BEMC. The inner radius provides support for the BEMC and
the HCal, while the end of the structure carries load to the OHCAL.
Table 3 shows the basic mechanical parameters of the IHCAL reference design.
The detector is designed to be built in 32 modules, which are wedge-shaped
sectors comprising 8 gaps with 7 full-thickness plates and 2 half-thickness
plates (so that as the modules are stacked, adjoining half-thickness plates
have the same thickness as the full-thickness plates). The modules contain 2
towers in $\varphi$ and 27 towers in $\eta$ equipped with SiPM sensors,
preamplifiers, and cables carrying the differential output of the
preamplifiers to the digitizer system on the floor and upper platform of the
detector. The instrumentation consists of 6912 scintillating tiles and optical
devices, 1728 preamplifiers, and cabling.

###  2.3 Hadron-End-Cap

We envision the forward calorimeter system as an integrated ECal and HCal,
where the installation units, where appropriate, are constructed in a common
casing. These so-called modules consist of an electromagnetic calorimeter
segment in the front which is part of the forward EMCal (FEMC) followed by a
HCal segment which is part of the longitudinally separated HCal (LFHCAL). In
between these segments a read-out section is foreseen for the ECal. The
modules of up to 4 different sizes will be installed in half shells
surrounding the beam pipe, which are movable on steel trolleys to give access
to the inner detectors in the barrel in the hadron going direction. Each of
these trolley should carry about 150 metric tons of weight. This integrated
ECal and HCal design reduces the dead material in the detector acceptance and
allows for an easier installation in the experimental hall. This implies that
the construction of the modules has to happen in the same location to reduce
shipping and assembly costs. In the following, details on the FEMC will be
discussed, followed by the design considerations and plans for the
longitudinally separated HCal.

parameter | FEMC | LFHCAL
---|---|---
inner radius (envelope) | 17 cm | 17 cm
outer radius (envelope) | 170 cm | 270 cm
$\eta$ acceptance | $1.3<\eta<3.5$ | $1.2<\eta<3.5$
tower information |  |
x, y ($R<$/$>0.8$ m) | 1 cm/ 1.65 cm | 5 cm
z (active depth) | 37.5 cm | 140 cm
z read-out | 5 cm | 20 cm
$\\#$ scintillor plates | 66 (0.4 cm each) | 70 (0.4 cm each)
$\\#$ aborber sheets | 66 (0.16 cm Pb) | 60 (1.6 cm steel)
|  | 10 (1.6 cm tungsten)
weight |  $\sim 6.4$ kg |  $\sim 30.6$ kg
radiation lengths |  18.5 $X/X_{0}$ | -
interaction lengths |  1.0 $\lambda/\lambda_{0}$ |  6.9 $\lambda/\lambda_{0}$
Molière radius $R_{M}$ |  5.2 cm (e± shower) |  21.1 cm ($\pi^{\pm}$ shower)
Sampling fraction $f$ | 0.220 | 0.040
$\\#$ towers (inner/outer) | 19,200/ 34,416 | 9040
$\\#$ read-out channels | 53,616 | 7 x 9,040 = 63,280

Table 4: Overview of the calorimeter design properties for the FEMC and the
LFHCAL.

Assembly Module Type | # modules
---|---
8 LFHCAL tower modules (8M) | 1091 (total)
no FEMC towers in front | 538
200 FEMC towers (inner) | 87
72 FEMC towers (outer) | 466
4 LFHCAL tower modules (4M) | 76 (total)
no FEMC towers in front | 36
100 FEMC towers (inner) | 16
36 FEMC towers (outer) | 24
2 LFHCAL tower modules (2M) | 2 (total)
50 FEMC towers (inner) | 2
1 LFHCAL tower modules (1M) | 4 (total)
25 FEMC towers (inner) | 4

Table 5: Number of assembly modules for the full combined FEMC and LFHCAL
detector.

Both detector systems need to be able to handle the expected energies of
incoming particles up to 150 GeV, based on simulated Pythia events for e+p
collisions at 18x275 GeV2. Due to the asymmetric collision system, these
calorimeters are therefore focused strongly on high energetic particle shower
containment while still providing good energy resolution down to lower
energies.

Figure 6: Design pictures of the forward calorimeter assembly (left), 8-tower
module design (top right) and single scintillator plates of the LFHCAL (bottom
middle) and FEMC (bottom right) for an 8M tower module with embedded
wavelength shifting fibers.

##### Hadron End-Cap Electromagnetic Calorimeter: FEMC

The forward ECal (FEMC) is a Pb-Scintillator shashlik calorimeter. It is
placed at a distance of $z=3.07$ m from the interaction point in the hadron-
going direction after the tracking and particle identification detectors. The
detector is made up of two half disks with a radius of about 1.7m. The
calorimeter is based on traditional Pb-Scint-Shashlik calorimeter designs like
they have previously been used in ALICE, STAR and PHENIX. However, it employs
more modern techniques for the readout and the scintillation tile separation.
Its towers have an active depth of 37.5 cm with additional space for the
readout of about 5 cm. Each tower consists of 66 layers of alternating 0.16 cm
Pb sheets and 0.4 cm scintillator material, as listed in Table 5. Due to the
high occupancy of the detector at large pseudorapities and the collimation of
the particles in this area in physical space, the tower size varies depending
on the radial position with respect to the beam axis. Towers which are close
to the beam pipe ($R<0.8$ m) have an approximate tower size of $1\times
1\times 37.5$ cm3. For the outer radii this granularity is not necessary and
thus the size is increased to $1.65\times 1.65\times 37.5$ cm3. These numbers
are intentionally well below the Molière radius of $R_{m}=5.18$ cm, thus
showers will spread transversely over multiple towers. In order to collect the
light produced in the scintillator tiles, each scintillator and Pb-plate is
pierced by four 0.2 mm diameter wavelength shifting fibers. These fibers are
used to collect the light generated in the scintillators across all 66 layers.
All four fibers are read out together by a single SiPM.
Multiple towers are contained in modules of either $20\times 10$ cm2 (8M),
$10\times 10$ cm2 (4M), $5\times 10$ cm2 (2M) or $5\times 5$ cm2 (1M) in size.
These module sizes match the 8-, 4-, 2- and 1-tower modules of the LFHCAL with
which they share a 1.5 mm thin steel enclosure. Depending on the radial
position, the FEMC packs 72 or 200 read-out towers in an 8M module. Due to the
integration of the FEMC towers in the LFHCAL modules, the combined ECal and
HCal modules are about 2.05 m long. A detailed drawing of the 8M inner
scintillator tile design for the FEMC can be found in Figure 6 (bottom right).
The full 8M tile is made out of one piece. In order to separate the light
produced in different segments of the 8M-tile, the tile surface is subdivided
into $1\times 1$ cm2 readout segments by CNC cutting or edging into the
scintillator using a laser. These 0.37 mm deep gaps (about 92% of the tile
thickness) are then refilled with a mixture of epoxy and Titanium-oxide (TiO2)
in order to reduce the light cross talk among different towers. The 4 fibers
per tower are combined in a small light-collecting prism, which is directly
attached to the SiPM with an effective photosensitive area of 9-16 mm2 (ie.
Hamamatsu S14160-3050HS). These SiPMs are most sensitive around wavelengths of
450 nm, thus the wave length shifting fibers have to be chosen accordingly to
peak in a similar region.
The first signal processing happens after the ECal part of the module within
the 5 cm space currently assigned for the FEMC read-out, realized using CMS
HGCROC chips mounted on custom PCBs [11], which can simultaneously process 72
channels. The signals are then transmitted via fiber optic cables to the end
of the module for further processing.
A first full mechanical design for the joint LFHCAL and FEMC inner 8M module
can be seen in Figure 6. Additionally, a first full illustration of a half
shell is shown. The higher granular 8M and 4M FEMC-LFHCAL modules are
indicated in green and red respectively, while the yellow and dark blue towers
show the lower granularity 8M and 4M FEMC-LFHCAL modules. The lighter blue and
orange modules reflect the modules only containing LFHCAL towers.
The majority of the FEMC is build of 8M modules, supplemented by 4M, 2M and 1M
modules as outlined in Table 5 to come closer to the beam pipe and allow for a
vertical separation of the two half shells. The entire detector consists of
approximately 53600 readout channels and provides a measurement of the energy
of photons and electrons created in the collision going in the hadron-going
(forward) direction.

##### Hadron-End-Cap Hadronic Calorimeter: LFHCAL

The longitudinally separated forward HCal (LFHCAL) is a Steel-Tungsten-
Scintillator calorimeter. The initial idea is based on the PSD calorimeter
employed in the forward direction for the NA61/SHINE experiment [12], but it
has been extensively modified to meet the desired physics performance laid out
in the Yellow Report. This longitudinally separated HCal is positioned after
the tracking and PID detectors at $z=3.28$m from the center of the detector
and is made up of two half disks with a radius of about 2.6m.
The LFHCAL towers have an active depth of $\Delta z=1.4$ m with an additional
space for the readout of about 20-30 cm depending on their radial position, as
summarized in Table 5. Each tower consists of 70 layers with alternating 1.6
cm absorber and 0.4 cm scintillator material and has transverse dimensions of
$5\times 5$ cm2. For the first 60 layers the absorber material is steel, while
the last 10 layers serve as tail catcher and are thus made of tungsten to
maximize the interaction length within the available space.
In each scintillator, a loop of wavelength shifting fiber is embedded, as can
be seen in Figure 6 (bottom center). Ten consecutive fibers in a tower are
read out together by a single SiPM, leading to 7 samples at different depth
per tower. The towers are constructed in units of 8-, 4-, 2- and 1-tower
modules to ease the construction and to reduce the dead space between the
towers. Similar to the FEMC, the scintillator tiles in the larger modules are
made out of one piece and then separated by gaps refilled with epoxy and
Titanium oxide to reduce light cross-talk among the different readout towers.
The wavelength shifting fibers running on the sides of the towers are grouped
early on according to their readout unit and separated by thin plastic pieces
over the full length. The corresponding fiber bundles are indicated in Figure
6 by different colors. They terminate in one common light collector, which is
directly attached to a SiPM with an effective photosensitive area of 9-16 mm2
(ie. Hamamatsu S14160-3050HS). These 7 SiPMs per tower are then read out by a
common readout design between the FEMC and LFHCAL based on the CMS HGCROC
chips. Alternatively, a common readout board which could be used for nearly
all ECCE calorimeters is being pursued. The entire detector consists of 63280
readout channels grouped in 9040 read-out towers and provides a measurement of
the energy of hadronic particles created in the collision in the hadron-going
(forward) direction.
The majority of the calorimeter is built of 8-tower modules ($\sim$1091) which
are stacked in the support frame using a lego-like system for alignment and
internal stability. The remaining module sizes are necessary to fill the gaps
at the edges and around the beam pipe to allow for maximum coverage. The
absorber plates in the modules are held to their frame by 4 screws each. To
leave space for the read-out fibers, the steel and scintillator plates are not
entirely square but equipped with 1.25 mm notches, creating the fiber channels
on the sides, as can be seen in Figure 6 (bottom center) for a scintillator
plate. In order to protect the fragile fibers, the notched fiber channels are
covered by 0.5 mm thin steel plates after module installation and testing.For
internal alignment we rely on the usage of 1-2 cm steel pins in the LFHCAL
part which are directly anchored to the steel or tungsten absorber plates.
Consequently, the modules are self-supporting within the outer support frame.
The support frame for the half disks is arranged on rails which allows the
HCal and ECal to slide out to the sides and gives access to the inner
detectors. In addition, the steel in the LFHCAL serves as flux return for the
central 1.5T BABAR magnet. As a consequence, a significant force is exerted on
the calorimeter, which needs to be compensated for by the frame and internal
support structure.

##  3 Calorimeter Performance

The ECCE electromagnetic and hadronic calorimeters are designed to meet the
criteria outlined in the Yellow Report. In the following, the expected
performance of the different systems is presented based on standalone and full
detector GEANT4 simulations.

Figure 7: Clusterization algorithms visualized on an example energy deposit
from two particles ($E_{1}^{\mathrm{true}}=6$ GeV and
$E_{2}^{\mathrm{true}}=4$ GeV) in calorimeter towers of arbitrary size.
Presented are the AA (Aggregate-All) and the MA (Modified-Aggregation)
clusterizers. The found clusters are outlined in color and their reconstructed
energy is indicated in the figure. The same seed and aggregation energy
thresholds are assumed for both algorithms in this example.

###  3.1 Clusterization

The energy deposit from an electromagnetic or hadronic shower is generally
spread over multiple towers. The magnitude of this effect depends on the tower
size relative to the Molière radius ($R_{M}$) of the material used and is more
prominent for hadronic showers. The Molière radius is defined as the radius in
which 90% of the shower energy is contained, where electron-induced showers
are used for the ECals and charged pion-induced showers are used for the
HCals. Since $R_{M}$ is in all cases larger than the individual tower sizes in
the different calorimeters, it becomes apparent that the full shower can only
be reconstructed when the information of multiple towers is combined.
Different reconstruction algorithms can be employed in order to group towers
containing energy deposits into so-called clusters, which are the main objects
used in physics analyses. The performance of these algorithms mostly depends
on the calorimeter occupancy for a given event. While showers from single
electromagnetic particles are mostly trivial to reconstruct, a significant
challenge is posed by overlapping particle showers, for example in a jet or
from high energetic neutral meson decays. In the latter case, the decay photon
showers, e.g. from $\pi^{0}\rightarrow\gamma\gamma$, can not be separated
within the calorimeter granularity above a certain particle energy due to the
decay kinematics. Thus, extensive studies were performed to increase the
separation power between single and multi-particle showers and to absorb as
much of the deposited energy as possible during the so-called clusterization
procedure. This procedure always starts with the highest energetic tower in
the calorimeter, which is required to contain an energy deposit above a seed
energy threshold ($E_{\mathrm{seed}}$).

Figure 8: Mean number of clusters per generated particle (a) and average
number of towers aggregated within a cluster (b) as a function of generated
particle energy using the MA clusterizer for the different ECCE calorimeters.
Figure 9: Cluster reconstruction efficiencies in the EEMC, BEMC and FEMC for
electrons (a–c) and in the OHCAL and LFHCAL for charged pions (b and c)
reconstructed with the MA-Clusterizer. The efficiencies are calculated
according to Equation 1.

Additional neighboring towers are added to the cluster if their energy exceeds
a certain aggregation threshold ($E_{\mathrm{agg}}$). The thresholds
($E_{\mathrm{seed}}$ and $E_{\mathrm{agg}}$) for the different ECals and HCal
have been optimized to reduce false seeding from minimum ionizing particles
and to suppress noise during aggregation. Their values are tower size and
calorimeter type dependent, with approximate values of
$E_{\mathrm{seed}}^{\mathrm{ECal}}=100$ MeV and
$E_{\mathrm{agg}}^{\mathrm{ECal}}=$ 5–10 MeV or
$E_{\mathrm{seed}}^{\mathrm{HCal}}=$ 100–500 MeV and
$E_{\mathrm{agg}}^{\mathrm{HCal}}=$ 5–100 MeV for the ECals or HCals,
respectively. Two main algorithms have been explored for the cluster
reconstruction: the so-called aggregate-all (AA) and modified-aggregation (MA)
clusterizers. The AA clusterizer associates all towers sharing a common side
with already aggregated towers in the cluster and only stops the aggregation
when no further tower above $E_{\mathrm{agg}}$ can be found. At this point,
the already aggregated towers are removed from the sample and a new seeding
starting from the next highest energetic tower is performed. Since this
approach can aggregate energy deposits from multiple particles depending on
the occupancy, a subsequent splitting of the cluster should be performed based
on the number of maxima found in the energy distribution. This cluster
splitting procedure is necessary when AA clusters are meant to be used for
single particle analyses. The MA clusterizer works similar to the AA
clusterizer, however the algorithm stops when a neighboring tower with larger
energy than the already aggregated tower is found. It also aggregates towers
that share a common corner, thus a $3\times 3$ tower window around each
already aggregated tower is inspected. This algorithm is preferred for the
reconstruction of hadronic showers in high granularity calorimeters, since the
energy deposits can fragment over a large amount of towers. Figure 7 shows
these algorithms applied to an example energy deposit in a calorimeter, where
different clusters are reconstructed based on the various aggregation
conditions. The MA clusterizer is also the only clusterizer employed in the
LFHCAL cluster reconstruction due to the additional z-segmentation of the
calorimeter. For this, the MA clusterizer also allows the inclusion of
neighboring towers in z-direction sharing an edge or corner with already
aggregated towers.
As can be seen in Fig. 8, the various ECCE calorimeters show visible
differences in the average number of towers they aggregate per MA-based
cluster. In addition, the top panel of the same figure shows the mean number
of clusters per generated particle, which is approximately one at low energies
for the MA clusterizer, but reaches up to two clusters per particle at higher
energies for the LFHCAL and FEMC.
Overall it was found that the MA clusterizer performs slightly better than the
AA clusterizer for all calorimeters and especially in events with a higher
occupancy in the different detectors. The MA clusterizer is therefore chosen
as default for the following detector performance studies.
An important property of any clusterization algorithm and calorimeter is the
efficiency with which a cluster can be reconstructed for any given particle.
Fig. 9 shows the reconstruction efficiencies for electrons and charged pions
for the different ECals and HCal as a function of generated particle
pseudorapidity calculated according to Equation 1.

$\epsilon\cdot a=\frac{N_{\mathrm{clus,Ntow}>1}\text{ in
calorimeter}}{N_{\text{MC gen. particles}}\text{ in acceptance}}$ (1)

In the calculation, only clusters formed according to the seeding and
aggregation thresholds are used and additionally required to be made of more
than a single tower. Furthermore, only one cluster per generated particle is
considered for the calculation of $\epsilon\cdot a$ to avoid counting multiple
clusters of a single particle (e.g. due to an induced pre-shower). The latter
requirement is necessary to reject secondary low energy clusters or showers
that are not contained in the calorimeter (e.g. on the outer and/or inner
edges). The efficiencies show that at low energies, the seed and aggregation
thresholds decrease the reconstruction efficiency. Moreover, an edge effect at
low and high pseudorapidity (e.g. strong shower leakage) can be observed even
at higher energies also reflecting a small remaining effect from acceptance
losses in the calorimeters mostly due to deflection of the original particles
in the inner detectors. Additionally, the non-uniform $\varphi$-coverage of
the LFHCAL and FEMC is clearly visible, yielding a lower average efficiency
for $\eta>3$.

Figure 10: Energy resolution for different particles generated in single
particle simulations at fixed energies as measured by the electromagnetic
calorimeters EEMC, BEMC, and FEMC (a–c) and the hadronic calorimeters OHCAL
and LFHCAL (d and e).

###  3.2 Energy resolution

The energy resolution for the ECals and HCals is evaluated based on single
particle simulations for photons, electrons, pions and protons generated for
$0.2<E<30(50)$ GeV. For these studies the reconstructed energy deposits in the
towers are combined into clusters using the MA clusterizer with the
aforementioned seed and aggregation energy settings for each calorimeter. The
energy scale of the calorimeters is calibrated such that in simulations
without material in front of the calorimeter the reconstructed electron energy
over the generated energy is approximately unity. Thus, this calibration
corrects the ECals and HCal to approximately the same energy scale. No $\eta$
dependent corrections for the energy response are introduced so far.

Figure 11: Comparison of the energy resolution for electrons generated in
single particle simulations at $E=1$ GeV (top) and $E=8$ GeV (bottom) as
measured by the BEMC (left) and FEMC (right) without additional material in
front of the calorimeter and in the full detector setup.

Figure 12: Energy resolution for electrons (charged pions) generated in single
particle simulations with energies between 0.2 and 20 (50) GeV as measured by
the different ECals (top) and the different HCals (bottom) in the central
acceptance of the corresponding detectors. The shaded bands show the
requirements as extracted from the yellow report for the different
calorimeters. The data points and fits indicated as $\sigma_{g}/E$ are based
on the Gaussian width of the resolution peaks, while $\sigma_{F}/E$ is based
on the FWHM. The energy resolution based on a test beam for the OHCAL is shown
for comparison [9].

Figure 10 shows the energy response $E^{\mathrm{rec}}/E^{\mathrm{MC}}$ for the
various particle species and in each calorimeter. By construction, the
electron and photon response in the ECals peaks around unity with a strong
excess that is accompanied by a visible tail towards lower values. This tail
is a result of multiple effects. First, the clusterization in the calorimeter
is not perfect (see clusterization chapter) and thus not all energy of an
incoming particle is reconstructed. In addition, for these studies only the
highest energetic cluster in each event is selected, which combined with the
clusterizer performance leads to a smearing to lower $E^{\mathrm{rec}}/E$
values. Further smearing comes from bremsstrahlung losses of the electrons in
the magnetic field as well as from material interaction of photons that could
lead to photon conversions, as seen in Fig. 11. The figure shows a comparison
of the energy response for the BEMC with and without the remaining ECCE
detector material in front, highlighting an increasing tail at lower
$E^{\mathrm{rec}}/E$ due to the additional material. In the following studies,
contributions from photon conversions are not rejected and thus are still
contained in the photon sample. The left side tails of the resolution peaks
can also arise through particles hitting the support material in between the
towers. The reconstructed energy loss from hitting and subsequently channeling
in the passive support structures is a major factor to be considered for the
calorimeter design. Initial studies have shown that already a 2 mm carbon
fiber support structure between the EEMC towers is enough to significantly
deteriorate the energy resolution. As such, the supports were optimized to the
current design of 0.5 mm carbon sheets, which greatly improves the energy
resolution. Further improvements are possible with carbon support grids
holding multiple crystals that are further separated by a thin foil. Similar
support material considerations are to be made for the BEMC, where the current
design employs 2 mm carbon fiber sheets. Charged hadrons deposit in the
majority of cases only a minimum ionizing signal in the ECals, which is
visible as a strong peak at low $E^{\mathrm{rec}}/E$ values. However, there is
also a non-negligible amount of charged hadrons that deposit 40% or more of
their energy in the ECals, which can negatively impact the HCal energy
resolution. For the HCals, the charged pions and protons peak around unity,
whereas remaining shower leakage from electron showers out of the ECals is
mostly negligible. Figure 10 also highlights a shifted peak for protons
compared to pions in the HCals which can be explained by a loss of visible
energy for baryons. In future studies, this effect could be counteracted for
the LFHCAL by shower depth analyses and subsequent application of a correction
factor for the loss of visible energy.
In order to determine the energy resolutions of the different calorimeters,
the $E^{\mathrm{rec}}/E$ distributions are fitted with crystalball functions
in order to determine the peak width. This width can either be taken from the
Gaussian component or from the full width at half maximum (FWHM). The slightly
larger values of the latter are a reflection of the asymmetric
$E^{\mathrm{rec}}/E$ distribution as described above. Based on the fit values,
Fig. 12 shows the energy resolution for electrons in their generated energy
range in the ECals and for charged pions in the HCals.
All ECal resolutions, based either on the Gaussian sigma
($\sigma_{\mathrm{g}}$) or the FWHM ($\sigma_{\mathrm{F}}$), are well within
the limits imposed by the YR and even exceed the requirements in the case of
the BEMC by a significant amount. Thus, despite the smeared
$E^{\mathrm{rec}}/E$ peaks from the full ECCE detector simulation, the
resolution is still within the imposed limits. In addition, a minimal
pseudorapidity dependence for all calorimeters is observed, but none of the
$\eta$-regions fail to deliver the required YR performance.
For the HCals, I/OHCAL and LFHCAL, a similar behavior is observed, where the
resolutions are found to be better than the YR requirements with
$\sigma/E=(31-34\%)/\sqrt{E}\oplus(17-18\%)$ and
$\sigma/E=(33-44\%)/\sqrt{E}\oplus(1.4\%)$ by about 1–20% and constant 8%,
respectively. This also holds true for both tested particle species
($\pi^{\pm}$ and protons) and in each $\eta$ region individually. In addition,
the HCal resolution is compared to the sPHENIX test beam data and shows a
better resolution in the presented simulations [9], which can be explained by
an imperfect simulation setup of the details of the calorimeter response.

###  3.3 Position resolution

A significant fraction of physics observables either directly or indirectly
require a good position resolution of the reconstructed clusters in the
calorimeters. For example, the jet reconstruction clusters objects which are
reconstructed in a given radial cone and thus position inaccuracies especially
in difficult pseudorapdity regions can deteriorate the physics performance.
Moreover, charged particle association or neutral cluster determination via
track matching (see next section) depends on the cluster position resolution
as much as on the tracking resolution.

Figure 13:  Position resolution in $\eta$ (top) and $\varphi$ (bottom) for
electrons or charged pions generated in single particle simulations with
energies between 0.2 and 40 GeV as measured by the different calorimeters in
the central acceptance of the corresponding destectors without a magnetic
field.  Figure 14: Track matching efficiencies for electrons reconstructed
with the MA-Clusterizer in the EEMC (a), the BEMC (b) and the FEMC (c) and for
charged pions reconstructed in the OHCAL (b) and the LFHCAL (c). The
efficiencies are relative to the number of reconstructed tracks according to
Equation 2.

To determine the pure position resolution of the clusterization algorithm and
intrinsic calorimeter granularity single particle simulations without a
magnetic field have been used. This setup allows to separate between the
intrinsic position resolution in the respective calorimeters and effects
arrising from a larger inclination angle at the calorimeter surface as well as
inaccuracies in the particle propagation through the material due to the 1.4T
magnetic field. For the track-to-cluster matching under realisitic conditions
within a magnetic field the $\eta$ and $\varphi$ coordinates for charged
particles are calculated by propating the tracks through the detector material
to approximately half the depth of each calorimeter. The median cluster depth
is however $\eta$ dependent for non projective calorimeters. Consequently, the
mean shift in the $\eta$-position has to be corrected for the forward and
backward calorimeters based on the zero-field data. Figure 13 presents the
width of the difference of the generated particle $\eta$($\varphi$) and the
reconstructed cluster position in $\eta$($\varphi$) in the different
calorimeters. For all electro-magnetic calorimeters an excellent resolution of
about $0.01-0.015$ in pseudorapidity is observed which only degrades slightly
towards lower energies. The $\varphi$-resolution for highly energetic
particles is similarly good with $\Delta\varphi=0.02$ (corresponding to $1.15$
degrees). It is mainly determined by the size of the single towers in
$\Delta\varphi$ of the respective calorimeter and the width of the electro
magnetic shower. Due to the larger tower sizes and wider spread of hadronic
showers without a very well defined core the $\eta$ and $\varphi$ resolutions
of the hadronic calorimeters are slightly worse in both dimensions. The
resolutions for the LFHCAL could be further improved in the future by taking
into account the correct depth of the shower as well, which so far has not
been considered in the position calculation.

###  3.4 Track-Cluster matching

The position resolution described in the previous chapter is a necessary
ingredient for performance studies of the cluster-to-track matching. This
matching is needed for particle identification studies, like electron
selection via charged pion rejection or cluster neutralization for photon
analyses. Moreover, the track matching procedure is a crucial ingredient for
particle flow-based jet measurements.
The track matching efficiency can be calculated as the number of track-matched
clusters relative to the number of reconstructed tracks in the full
calorimeter acceptance via

$\epsilon_{\mathrm{TM}}=N_{\mathrm{clus}}^{\text{matched}}/N_{\mathrm{tracks}}^{\text{in
acc.}},$ (2)

or relative to the number of reconstructed clusters via

$\kappa_{\mathrm{TM}}=N_{\mathrm{clus}}^{\text{matched}}/N_{\mathrm{clus}}.$
(3)

Figure 14 shows the track matching efficiencies ($\epsilon_{\mathrm{TM}}$) for
the different calorimeters for single particle simulations of either electrons
or charged pions in the full ECCE GEANT4 detector setup. For a majority of the
ECal acceptance, an excellent efficiency of $\epsilon_{\mathrm{TM}}>95\%$ is
observed. Expected deviations towards lower particle momenta are observed,
where the track to cluster association breaks down due to a cut-off in the
particle cluster reconstruction imposed by the minimum seeding and aggregation
thresholds. An additional pseudorapdity dependence for the track matching
efficiencies is expected due to the previously observed cluster position
resolution, which deteriorates for certain $\eta$ regions as wellas the
reducted cluster finding efficiency due to remaining acceptance effects.
Moreover, the particles might be stronger deflected in the $\eta$-regions with
higher amounts of material due to support structures.
Further insights into the track matching efficiency are given by Fig. 15,
where the track matching efficiencies $\kappa_{\mathrm{TM}}$ are shown for all
calorimeters in their nominal acceptance. The comparison of
$\epsilon_{\mathrm{TM}}$ and $\kappa_{\mathrm{TM}}$ highlights that the track
matching efficiency depends equally on the cluster finding efficiency and the
track finding efficiency. This can clearly be seen in the electron matching
efficiency for the ECals, where $\epsilon_{\mathrm{TM}}$ is nearly unity when
calculated according to Equation 2, meaning that if a track is found, it is
nearly always matched to a cluster. On the other hand, $\kappa_{\mathrm{TM}}$
shows a reduced efficiency, meaning that for a large portion of clusters no
track is found for matching, especially in the forward region. For the HCals,
the performance is generally worse as particles can pre-shower in the ECals,
resulting in clusters with distorted positions on the HCals, thus not for all
tracks a matching cluster is found.

Figure 15: Track matching efficiencies calculated relative to the number of
reconstructed clusters ($\kappa_{\mathrm{TM}}$). Single particle simulations
of electrons in the detector acceptance of the ECals and of charged pions in
the acceptance of the HCals are used to obtain the efficiencies.

###  3.5 Particle Identification

The information provided by the ECals and HCal can help distinguish between
particle species and thus provide highly efficient particle identification,
which is crucial for a variety of physics analyses. This section therefore
focuses first on the PID capabilities of the ECals and subsequently the
additional benefits from the HCals. The electromagnetic calorimeters (EEMC,
BEMC and FEMC) are most commonly used to identify electromagnetic showers
coming from a single particle. They can differentiate between photons and
their background from merged $\pi^{0}$ decay photons. If tracking information
is used in addition, the calorimeters can be used to provide a strong
separation power between electrons and charged hadrons like $\pi^{\pm}$, kaons
or protons. In the following, the different PID approaches are briefly
explained and the expected performance is shown based on full detector GEANT4
simulations.

Figure 16: Invariant mass $M_{\gamma\gamma}$ distribution for generated
$\pi^{0}$ mesons in the energy range from 2.5 to 3.0 GeV for EEMC, BEMC, and
FEMC including a composite Gaussian fit function that includes a left-sided
exponential tail component. Figure 17: Invariant mass $M_{\gamma\gamma}$ peak
width (top) and position (bottom) obtained from a composite Gaussian fit
including a left-sided exponential tail. Figure 18: $E/p$ distribution for
electrons (blue) and charged pions (red) in the EEMC (right) and the BEMC
(left). The $E/p$ distribution is shown for two different approaches where
$E/p$ is either calculated using the generated (true) particle momentum or the
reconstructed tracking based (rec.) momentum. For both distributions, the full
ECCE detector has been simulated using its GEANT4 implementation. Figure 19:
Fraction of neutral pions for which the showers from their decay photons are
merged into a single cluster and can not be reconstructed using an invariant-
mass-based approach for the different ECals.

####  3.5.1 Single photon and neutral pion separation

A significant background for photon analyses originates from $\pi^{0}$ meson
decay photons, which end up in the same reconstructed cluster due to their
close proximity. In general, when the decay photons can still be reconstructed
separately, their calculated invariant mass
($M_{\gamma\gamma}=\sqrt{2E_{\gamma_{1}}E_{\gamma_{2}}(1-\cos{\theta_{12}})}$)
can be used to veto decay photon clusters if the mass falls in a certain
window around the nominal $\pi^{0}$ mass. Example invariant mass distributions
for the ECals are shown in Fig. 16 for a selected energy range of the two-
photon meson candidates including a composite Gaussian fit with a left-sided
exponential tail. The BEMC invariant mass distribution is significantly wider
than that of the EEMC or FEMC, as can also be seen in Fig. 17, where the peak
width (obtained from the width of the Gaussian fit component) is shown as a
function of $\pi^{0}$ energy. The broadening of the peak width with increasing
energy and the cutoff of the BEMC data at $E\approx 12$ GeV is further
elaborated in the following. Above a certain energy, the decay kinematics of
the $\pi^{0}$ together with the granularity and resolution of the calorimeter
no longer allow to reconstruct separate decay photons due to a merging of
their showers. Thus, the separation power between meson decay photons and
single photons decreases and the reconstructed meson mass starts to deviate
from the nominal meson mass as seen in Fig. 17.
The energy dependence of this cluster merging effect is shown in Fig. 19 for
the three ECals. The close proximity of the BEMC to the interaction point
together with its $4\times 4$ cm tower size results in a large fraction of
merged decay photon clusters already at 5 GeV around $\eta=0$. For
$|\eta|>0.9$ within the BEMC the merging starts to set in at around $10$ GeV
due to the larger distance of the calorimeter surface from the interaction
point and thus a larger average distance of the two decay photons on the
calorimeter surface. In contrast, the higher granularity and larger distance
from the IP of the EEMC and FEMC, respectively, results in a much later onset
of the cluster merging. For the FEMC this effect becomes only significant
above 25 GeV, while the EEMC experiences this effect already above 15 GeV.

####  3.5.2 Electron PID via charged pion rejection

Several observables of EIC physics require a clean electron sample [2]. One of
the largest backgrounds for electrons stems from charged pions ($\pi^{\pm}$),
which can be distinguished on a statistical basis from electrons with a high
efficiency using ECal information. The so-called pion rejection factor is a
handle on how strong this $e^{\pm}$–$\pi^{\pm}$ separation is for a given
calorimeter. It can be calculated by simulating the response for single
electron and separate single pion events. The quantity $E/p$, meaning the
reconstructed cluster energy relative to the incident particle momentum
exhibits only slightly overlapping distributions for both particles. This is
shown in Fig. 18 where electrons (blue) show a strong enhancement around
$E/p\approx 1$, while charged pions (red) are smeared towards lower $E/p$
values for all three ECCE ECals. In realistic events, e.g. based on the Pythia
event generator, one expects significantly more hadrons relative to electrons
and thus the hadronic tail overlap is expected to be stronger than shown in
Fig. 18. This effect is further enhanced by the presence of jets which result
in shower overlaps in the calorimeters. The track momentum in the following is
determined using the full ECCE tracking capabilities [3].

Due to the small overlap of the $E/p$ distribution for different particle
species, a minimum $E/p$ cut can be employed to reject the majority of charged
pions in the sample while retaining a high efficiency electron sample. In
previous studies, a minimum cut of $\Delta=1.6\,\sigma_{E}/E$ has been
determined to result in a high electron efficiency of $\varepsilon_{e}\approx
95\%$. However, the asymmetric electron resolution distributions of the
calorimeters within the full ECCE integration, as shown in Fig. 10 lead to a
significantly reduced electron efficiency when applying a 1.6$\sigma$-based
cut. Especially for the BEMC where a strong tail in the energy resolution
distribution is visible, the cut results in an electron efficiency of
$\varepsilon_{e}\approx 70\%$, while for the other ECals values of about
90–95% are observed. Thus, an additional $E/p$ cut value has been determined
that allows for $\varepsilon_{e}=95\%$, which is indicated as
$\varepsilon_{95\%}$ in the following. This cut value corresponds to
approximately $2\sigma$ for the EEMC, $6\sigma$ for the BEMC, and $3\sigma$
for the FEMC, highlighting the difference in the energy resolution peak
asymmetry for the various ECCE ECals.

Figure 20: Pion rejection factor for the different ECals with
$E/p>1-1.6\,\sigma_{e}/E$ or based on a $\varepsilon_{e}\approx 95\%$ cut.

Applying these cuts on the single pion event simulations results in the
rejection factors shown in Fig. 20. Values up to $6\times 10^{4}$ are reached
for the EEMC using the $1.6\,\sigma$-based cut, while for the other
calorimeters $\pi^{\pm}$ rejection factors ranging from 20 to more than
$10^{3}$ are reached. For the EEMC the pion rejection capabilities are so
striking that an accurate pion rejection factor is hard to determine with the
currently available single particle production statistics and the reported
values should be interpreted as lower limits. A significant reduction of about
an order of magnitude in the $\pi^{\pm}$ rejection is observed for the
$\varepsilon_{e}=95\%$ based cut for the FEMC and BEMC, which therefore stands
in no reasonable relation to the efficiency loss observed for the other $E/p$
cut values. This loss mainly arrises from the significant tails observed for
these two calorimeters in their current configuration.

Figure 21: The shower shape distribution ($\sigma_{\mathrm{long}}^{2}$) for
electrons (blue) and charged pions (red) in the EEMC using the full ECCE
detector simulations at a fixed generated energy of $E=1.3$ GeV. The gray
vertical line indicates the $\sigma_{\mathrm{long}}^{2}$ cut value below which
90% of the electrons would be kept.

####  3.5.3 Hadron PID

Besides using an $E/p$ cut to differentiate between electrons and hadrons the
shape of the shower and thus the cluster can be used. The distribution of
energy within a cluster is referred to as “shower shape”, which is described
using a parametrization of the shower surface ellipse axes [14, 15]. The
shower surface is defined by the intersection of the cone containing the
shower with the front plane of the calorimeter. The energy distribution along
the $\eta$ and $\varphi$ directions is represented by a covariance matrix with
terms ${\sigma_{\varphi\varphi}}$, ${\sigma_{\eta\eta}}$ and
${\sigma_{\varphi\eta}}$, which are calculated using logarithmic energy
weights $w_{i}$. The tower dependent weights are expressed as:

$w_{i}={\rm Maximum}(0,w_{0}+\ln(E_{i}/E_{\mathrm{cluster}}))$ (4)

and

$w_{\mathrm{tot}}=\sum_{i}w_{i},\\\ $ (5)

where $w_{0}$ = 4.5 for the EEMC [16], which excludes towers with energy
smaller than 1.1% of the cluster energy. For the BEMC and FEMC $w_{0}$ = 4.0
and $w_{0}$ = 3.5 are used, respectively, in order to compensate for the
different Moliere radii and tower size. The covariance matrix terms can then
be calculated as follows

$\sigma^{2}_{\alpha\beta}=\sum_{i}\frac{w_{i}\alpha_{i}\beta_{i}}{w_{\mathrm{tot}}}-\sum_{i}\frac{w_{i}\alpha_{i}}{w_{\mathrm{tot}}}\sum_{i}\frac{w_{i}\beta_{i}}{w_{\mathrm{tot}}}\,,$
(6)

where $\alpha_{i}$ and $\beta_{i}$ are the tower indices in the $\eta$ or
$\varphi$ direction. Similarly, also the average cluster position in the
$\eta$ and $\varphi$ direction in the calorimeter plane is determined using
the tower positions weighted logarithmically by their deposited energy [16].
The shower shape parameters $\sigma_{\mathrm{long}}^{2}$ (long axis) and
$\sigma_{\mathrm{short}}^{2}$ (short axis) are defined as the eigenvalues of
the covariance matrix, and are calculated as

$\displaystyle\sigma_{\mathrm{long}}^{2}=0.5(\sigma^{2}_{\varphi\varphi}+\sigma^{2}_{\eta\eta})+\sqrt{0.25(\sigma^{2}_{\varphi\varphi}-\sigma^{2}_{\eta\eta})^{2}+\sigma^{2}_{\eta\varphi}},$
(7)
$\displaystyle\sigma_{\mathrm{short}}^{2}=0.5(\sigma^{2}_{\varphi\varphi}+\sigma^{2}_{\eta\eta})-\sqrt{0.25(\sigma^{2}_{\varphi\varphi}-\sigma^{2}_{\eta\eta})^{2}+\sigma^{2}_{\eta\varphi}},$
(8)

Previous experiments have determined that the short axis
$\sigma_{\mathrm{short}}^{2}$ carries significantly less discriminative power
compared to $\sigma_{\mathrm{long}}^{2}$ and thus only the long axis is
considered in the following.

Figure 22: Left: Fraction ($R_{\pi}$) of cluster originating from charged
pions, which can be rejected due to the chosen shower shape cut as a function
of the incident pion energy. Right: Pion rejection factor for the different
ECals with $E/p>1-1.6\,\sigma_{e}/E$ (w$/$o PID) or $E/p>1-1.6\,\sigma_{e}/E$
and the additional $\sigma_{\mathrm{long}}^{2}$ selection (w$/$ PID) applied
as a function of the true track momentum.

Using these parameters symmetric electromagnetic showers with a small spread
originating either from photons or electrons can be distinguish from non-
symmetric showers caused by hadronic interactions. The shower shape of charged
particles can also be elongated by the angle of incidence. calorimeters.
Furthermore, the merging of showers from electromagnetic processes, i.e. ${\rm
e^{+}e^{-}}$ pairs from conversions within a close distance to the calorimeter
or photons from neutral meson decays with high transverse momenta, also lead
to asymmetric shower shapes.
An example distribution of the shower shape parameter
$\sigma_{\mathrm{long}}^{2}$ for electrons (blue) and pions (red) as seen by
the EEMC can be found in Fig. 21. As can be seen, the energy deposits from an
electrons at the same incident energy are significantly more collimated than
those of charged pions. Consequently, electron clusters have predominantly
lower shower shape values. As these distributions strongly change as a
function of the incident energy a $\sigma_{\mathrm{long}}^{2}$ cut value
function is calculated that preserves 90% of the electrons. Using these cut
values based on the shower shape alone up to 90% of the pions can be rejected
in the EEMC as shown in Fig. 22 (top). By simultaneously using the
aforementioned $E/p$ and $\sigma_{\mathrm{long}}^{2}$ cuts, the pion rejection
quoted in Fig. 20 is improved by at least a factor two in most momentum bins
as seen in Fig. 22 (bottom).

##  4 Summary

In summary, the ECCE calorimeter systems have been designed to support the
full scope of the EIC physics program as presented in the EIC white paper [17]
and in the 2018 report by the National Academies of Science (NAS) [18]. These
systems can be built within the budget envelope set out by the EIC project
while simultaneously managing cost and schedule risks.

##  5 Acknowledgements

We acknowledge support from the Office of Nuclear Physics in the Office of
Science in the Department of Energy, the National Science Foundation, and the
Los Alamos National Laboratory Laboratory Directed Research and Development
(LDRD) 20200022DR.

We thank (list of individuals who are not coauthors) for their useful
discussions and comments.

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