# A high-granularity calorimeter insert based on SiPM-on-tile technology
at the future Electron-Ion Collider

Miguel Arratia<EMAIL_ADDRESS>Kenneth Barish  Liam Blanchard  Huan Z. Huang
Zhongling Ji  Bishnu Karki  Owen Long  Ryan Milton  Ananya Paul  Sebouh J.
Paul  Sean Preins  Barak Schmookler  Oleg Tsai  Zhiwan Xu  Department of
Physics and Astronomy, University of California, Riverside, CA 92521, USA
Department of Physics and Astronomy, University of California, Los Angeles, CA
90095, USA

###### Abstract

We present a design for a high-granularity calorimeter insert for future
experiments at the Electron-Ion Collider (EIC). The sampling-calorimeter
design uses scintillator tiles read out with silicon photomultipliers. It
maximizes coverage close to the beampipe, while solving challenges arising
from the beam-crossing angle and mechanical integration. It yields a
compensated response that is linear over the energy range of interest for the
EIC. Its energy resolution meets the requirements set in the EIC Yellow Report
even with a basic reconstruction algorithm. Moreover, this detector will
provide 5D shower data (position, energy, and time), which can be exploited
with machine-learning techniques. This detector concept has the potential to
unleash the power of imaging calorimetry at the EIC to enable measurements at
extreme kinematics in electron-proton and electron-nucleus collisions.

###### Contents

  1. 1 Introduction
  2. 2 Proposed Design
    1. 2.1 External constraints
    2. 2.2 Sampling calorimeter layout
    3. 2.3 Scintillator cells
    4. 2.4 Silicon photo-multipliers
    5. 2.5 SiPM-carrying boards and backplane board
    6. 2.6 Accessibility for maintenance
    7. 2.7 Geometric acceptance
    8. 2.8 Total calorimeter thickness
  3. 3 Simulation and performance
    1. 3.1 Geometry and simulation setup with DD4HEP
    2. 3.2 Shower-shape examples
    3. 3.3 Hit distributions
    4. 3.4 Linearity for hadrons and electrons and $e/h$ ratio
    5. 3.5 Non-Gaussian tails due to leakage
    6. 3.6 Single-hadron energy resolution
    7. 3.7 Pseudorapidity dependence of performance
  4. 4 Summary and conclusions

##  1 Introduction

One of the key requirements for detectors at the future Electron-Ion Collider
(EIC) is to have tracking and full calorimetry with 2$\pi$ azimuthal coverage
over a large range in pseudorapidity—nominally $|\eta|<4.0$ [1]. This would
ensure a “$4\pi$, general-purpose detector” that could deliver the original
EIC scientific goals [2] and much beyond.

While both the ATHENA [3] and ECCE [4, 5] detector designs contemplate close-
to-full coverage with full calorimetry, the specifics on how to implement it
in the forward region remain undefined. Covering the region $3<|\eta|<4$ is
challenging due to the EIC beam-crossing angle, which is 25 mrad [1].

As illustrated in Fig. 1, the beampipe envelope crosses the region where the
forward hadronic calorimeter (HCal) would be located at an angle that
approximately corresponds to the proton direction. Any detector covering this
region needs to simultaneously fill a complex volume and keep clearance from
the beampipe, while fitting the other calorimeters without needing additional
support structures.

Figure 1: Left: Forward calorimeter endcap and beampipe without the insert,
with arrows detailing the directions of the electron and proton beams. Right:
Same, zoomed in to show details. The beampipe axis is slightly to the left of
the proton direction.

In addition, the detector in the $3<\eta<4$ region needs to be well matched to
the particle densities and energies expected at the EIC. At the highest energy
setting of 18 GeV electron beam and 275 GeV proton beam, the jet spectra reach
close to the proton-beam energy with a high rate at nominal luminosity [1].
Furthermore, single-particle measurements up to 60 GeV are set as a
requirement [1]. Given the large energies involved, an HCal becomes crucial
since poor tracking performance is expected at forward angles [6, 1].

Instrumenting the $3<\eta<4$ region demands a relatively small detector area
($\approx 0.6\times 0.6$ m2 for a detector located at $z=3.8$ m) but also high
granularity to yield a reasonable $\eta$ resolution and disentangle nearby
particles. Small cells can also tessellate the complex geometry near the
beampipe in an effective manner.

Good angular coverage and resolution would be beneficial for measurements of
jets and their substructure, which will enable a wide variety of studies at
the EIC, and inclusive deep-inelastic scattering at high-$x$ [1, 7].

The concept of high-granularity calorimetry has been developed for the last
two decades or so [8], driven by the CALICE collaboration, and motivated by
the particle-flow paradigm [9]. More recently, this approach has been adopted
for the CMS High-Granularity Calorimeter (HGCAL) upgrade [10], and is
envisioned for experiments at several proposed $e^{+}e^{-}$ colliders such as
ILC [11], CLIC [12], and CEPC [13, 14, 15].

Extensive R$\&$D efforts [8] and rapid progress in silicon-photomultiplier
(SiPM) technology [16] have culminated in the “SiPM-on-tile” concept for
hadronic calorimetry. In this approach, the active elements of the calorimeter
are small scintillator tiles ($\approx$ 3$\times$ 3 cm2) air coupled to a SiPM
at their center [17, 18], without using wavelength-shifting fibers that were
used in earlier designs [19, 20, 21, 22].

The advent of high-granularity calorimeters has boosted studies of machine-
learning algorithms [23] that could exploit the benefits of “imaging
calorimetry” for a variety of tasks [24, 25, 26, 27, 26, 28, 29, 30, 31, 32,
33, 34, 35, 36, 37, 38].

Some early proposals for EIC detectors, such as TOPSIDE, considered imaging
calorimetry over the entire solid angle [39, 1], including hadronic
calorimetry similar to the CALICE design, although those options were not
further pursued111In particular, they were not in any of the official EIC
proposals [3, 4, 40]. On the other hand, an imaging electromagnetic
calorimeter based on silicon-pixel sensors was included in the ATHENA proposal
[3]. Imaging calorimetry with silicon sensors is also envisioned for the zero-
degree calorimeters.. Instead, the forward HCals for both the ATHENA [3] and
ECCE [41] proposals included a more traditional steel-scintillator design with
longitudinal granularity that varies between 4 and 7 segments, which is
similar to that used in the ZEUS [42] and H1 [43] detectors at HERA.

The SiPM-on-tile technology represents an attractive option to instrument the
$3<\eta<4$ region at the EIC for various reasons. First, the expected energy
range for jets largely overlaps with that of proposed $e^{+}e^{-}$ Higgs
factories, so the vast CALICE literature and test-beam data [19, 20, 21, 44,
45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55] could inform designs and validate
simulations. Second, the radiation level expected at the EIC is orders of
magnitude smaller than the LHC so constraints from SiPM radiation damage are
not a limiting factor. Third, the forward geometry limits the detector volume,
numbers of channels, and cost, while still covering a significant range in
$\eta$–$\phi$ space.

In this paper, we present a concept for a high-granularity calorimeter insert
(HG-CALI) based on the SiPM-on-tile technology that achieves excellent
acceptance near the beampipe, while satisfying the mechanical constraints
imposed by integration with the rest of the detector. It is designed to be
compensated ($e/h\approx 1$) and meets the requirements set in the EIC Yellow
Report [1] with a basic reconstruction algorithm. Moreover, it will open up
potential for improvements based on machine-learning techniques that exploit
the 5D measurement of showers. It would be complemented with a high-
granularity electromagnetic calorimeter insert based on tungsten
powder/scintillating fiber technology [56], which will be described in a
separate publication.

##  2 Proposed Design

###  2.1 External constraints

Figure 2: Left: the proposed HCal insert inside the full HCal endcap (as
viewed from upstream). Right: Zoom-in of the insert surrounded by only the
endcap towers that are adjacent to it. The beampipe, and some of the absorbers
and dowel pins are hidden to show how the insert connects to the rest of the
detector.

Two main factors constrain the design of the proposed calorimeter insert.
First, it must integrate into the larger calorimeter endcap without additional
support structures that would create dead areas. Second, it must surround the
beampipe within some minimal acceptable clearance in order to maximize its
coverage.

In the ATHENA design [3], the forward HCal design is based on the technology
previously used in the STAR experiment [57, 58] and consists of alternating
layers of steel absorbers (consisting of $96\times 98\times 20$ mm blocks) and
scintillator tiles with a thickness of 3 mm. The absorber blocks of both the
endcap and the insert are held in place using dowel pins which go into the
holes on the top of each absorber block, through holes of the 1.9 mm thick
“master plates”, and then into the holes in the blocks above them. This is
illustrated in Fig. 2, which shows the high-granularity insert (described in
more detail in the following sections) surrounded by the full HCal endcap
(left), and zoomed-in with some of the adjacent structures within the endcap
(right).

The endcap HCal is designed to open up by splitting in half vertically for
maintenance, as it will rest on a support structure with a rail system [1].
Therefore, the insert is designed to split into two parts along with the
endcap.

The current design for the beampipe [59] is conically shaped and has an outer
radius of 11.15 cm at the upstream face of the HCal ($z=380$ cm) and 13.40 cm
at the front face of the last layer of the HCal ($z=498$ cm). Furthermore, the
beampipe axis is at a small angle ($-$24.3 mrad) relative to the lab-frame $z$
axis, which is defined parallel to the solenoidal magnetic field axis and to
the electron beampipe. The proton beam axis is at $-$25 mrad relative to the
electron axis. Distances and angles defined with respect to the proton axis
are labelled with an asterisk superscript throughout this paper. We assume a
clearance of about 4 cm along the entire volume of the HCal insert.

Based on these requirements, the proposed HG-CALI will cover the equivalent
area of 6$\times$6 blocks of the HCal endcap, or approximately 60$\times$60
cm. However, since the beampipe is offset in the negative $x$ direction, the
part of the insert on the left side when viewed from upstream (positive $x$)
covers the width of two HCal endcap blocks, plus the gaps between them, (19.6
cm), while the right side (negative $x$) of the insert covers the width of
four HCal endcap blocks and the gaps between them (39.6 cm). Together with the
4 mm gap between the two halves of the HCal, and the 4 mm of readout
backplanes on either side, the total width of the proposed insert is 60.4 cm.

To account for the beampipe, we include a hole in each layer of the insert, as
shown in the left side of Fig. 3. The shape of this hole is circular for the
most part. However, the right side of the insert is shaped like a capital
letter D, with flat extensions on the top and bottom to ensure clearance even
while the calorimeter is sliding open.

Figure 3: Transverse cross section of the first layer of the insert, detailing
the shape of the hole surrounding the beampipe. Left: The cross section of the
insert when it is in the closed configuration. Right: The insert as it is
being opened, illustrating the need for the D shape of the hole on the right
part of the detector in order to achieve clearance even while its being
opened.

The radii and position of the centers of the circles vary from layer to layer,
as shown in the top image of Fig. 4, because of the conical shape and tilt
(respectively) of the beampipe. This approach leads to an optimal layout, in
the sense that it covers all the available volume, being limited only by the
clearance from the beampipe. The dimensions of the insert are shown in the
bottom image of Fig. 4.

Figure 4: Top: Cross section of the beampipe and the calorimeter insert
surrounding it, as viewed from above. The $z$ (anti-parallel to the electron
beam) and $z^{*}$ (proton beam) axes are indicated as a solid line (blue
online) and a dashed line (red online), respectively. Bottom: 3D view of the
insert with one side replaced with a wireframe to show the beampipe inside of
it.

Although we have shown a specific way to implement the HG-CALI with the ATHENA
HCal design [3], this could be adapted to fit the ECCE HCal [41] design, which
also uses a modular assembly structure based on rectilinear towers that run
parallel to the $z$ axis. The HG-CALI could also be incorporated into the
second EIC detector [60]; for example, it is also compatible with the CORE
design [40, 61]. It could also be used in future experiments at the Chinese
EicC, which considers a crossing-angle of 50 mrad [62].

###  2.2 Sampling calorimeter layout

The HG-CALI consists of alternating absorber blocks and scintillator
assemblies. Each scintillator assembly consist of a plastic scintillator
sandwiched between a 2 mm cover on the upstream side of it and a printed-
circuit board (PCB) with SiPMs for readout on the downstream side. It has 50
layers, each of which is 2.34 cm thick, followed by a downstream absorber-only
layer. Figure 5 shows the longitudinal dimensions of the absorbers and the
different components of the scintillator assemblies.

Figure 5: Left: exploded view of the components within a layer of the insert.
Right: A zoom-in of one corner of the insert, detailing the longitudinal
dimensions of each component of the layers. These include the air gaps (0.02
cm) between the absorber and the scintillator covers and between the absorbers
and the PCB and the 0.015 cm ESR foil on either side of the scintillators. In
total, each layer is 2.34 cm thick.

The HG-CALI is divided into two sets of layers with different absorber
materials. In the first, tungsten is used; in the second, high-strength steel
is used. The use of tungsten is motivated for two reasons: first, it allows
for a compensated design; second, its lower radiation length and nuclear-
interaction lengths compared to steel ($X_{0}=$ 0.35 cm, $\lambda_{n}$= 9.95
cm for W and $X_{0}=$ 1.76 cm, $\lambda_{n}$= 16.8 cm for Fe) helps in
reducing leakage of the core of hadronic showers to the beampipe.

The use of magnetic steel is required to contain magnetic-field flux. The EIC
poses a strict requirement on fringe fields, mainly driven by the need of
accurate polarization of the beams. The amount of steel required in this
region is still under study and no formal requirement has been established. We
have assumed a total thickness of 33.81 cm of steel (the last 21 layers) for
the simulations presented in Sec. 3.

###  2.3 Scintillator cells

A single scintillator “megatile” is used for each half-layer, which has a
slightly different shape to match the corresponding absorber shape. The
scintillator panels are tessellated with hexagonal cells defined by grooves.

Each cell will have a dimple in its center above the SiPMs that are hosted on
the PCB. The grooves are filled with a mixture of epoxy and titanium dioxide
pigment, following procedures similar to the STAR electromagnetic calorimeter
[63]. An alternative could be to paint the cells’ edges with reflective paint,
such as Saint Gobain BC-621. The latter approach was used in the CMS HCAL
[64].

To fully tessellate each layer, some of the cells on the edges will be cropped
or extended. This is not necessarily an issue given that the design allows for
a cell-to-cell calibration based on minimum-ionizing particles.

The megatile is covered on the front and back with reflective foil like the
VM2000 enhanced specular reflector (ESR) to increase the light yield and to
improve uniformity across the cell area. The ESR foil on the downstream side
of the megatiles will include holes for the dimples in each cell. The ESR foil
will not be wrapped to facilitate assembly; instead, the edges of the
scintillator megatiles will be painted.

Figure 6: Left: cross-section view of one scintillator layer, detailing the
dimensions of the grooves and dimples thereof. The dimple design follows the
dimensions used in Ref. [65]. Right: Zoom-in of one of the scintillators
tiles.

The dimples in the center of each cell will have the same dimensions used in
the CMS HGCAL test beam [65], which define a spherical dome with a radius of
curvature of 3.8 mm and a depth of 1.6 mm, as shown in Fig. 6. The dimples
improve signal uniformity across the area of the cell by alleviating hot-spot
effects near the SiPM [17, 18].

The megatile concept has several advantages over a design in which each tile
is wrapped individually, such as the ones used in the CALICE prototype [21]
and the CMS HGCAL [10], especially for a small and complicated geometry such
as that of HG-CALI. The megatile design would simplify assembly and reduce
cell-to-cell variations caused by wrapping with ESR foil [66].

Previous experience with calorimeters that use megatiles such as the STAR
electromagnetic calorimeter [63] suggest that optical cross-talk can be
reduced to about 2$\%$ when using a mixture of epoxy and titanium dioxide to
fill the grooves that define the cells. This level of optical crosstalk is
acceptable for this application, given that hadronic showers encompass a large
number of hits over a wide area.

The megatile concept provides us with the flexibility to define the transverse
granularity of the detector, and thus optimize it. We envision that the area
of these cells will vary from layer to layer, for example as shown in Fig. 7,
with finer granularity in the furthest upstream layers and coarser granularity
in the downstream. The granularity is yet to be optimized, but we estimate
that a reasonable choice would yield a total of less than 5k channels.

Figure 7: Comparison between the levels of granularity of the insert and the
surrounding HCal endcap. Since the granularity of the insert varies from layer
to layer, we show from left to right layers 1, 8, and 15, which respectively
represent fine, medium, and coarse granularity.

Test-beam results by the CMS HGCAL collaboration [65] showed that the light
yield of 3 mm thick scintillator cells (Eljen Technology EJ-200) is about 32
photo-electrons for 9 cm2 cells; about 26 photo-electrons for 12 cm2 cells,
and about 20 photoelectrons for 36 cm2 cells.

###  2.4 Silicon photo-multipliers

Both the CALICE and CMS collaborations use 1.3$\times$1.3 mm2 SiPMs [65, 10].
Larger-area SIPMs were considered, e.g., by Jiang et al. in the context of
R$\&$D for the CEPC [67]. Unlike the applications for ILC or CEPC, which will
use millions of channels, or the CMS HGCAL, which uses about 200k channels,
our design will have just a few thousand channels. Therefore, the total cost
of SiPM would still be reasonable even if we choose models with larger areas.

We anticipate that larger area SiPMs will make the calorimeter more robust
against non-uniformity created by SiPM misalignment [66], as well as
saturation effects. The photoelectron yield increases linearly with the area
of the SiPM, so choosing a 9 mm2 SiPM could increase the light yield by
roughly a factor of 4.5 with respect to the CMS HGCAL [65].

As we will show in Sec. 3, the maximum hit energy reaches $\approx 200$ MeV or
250 MIPs. We anticipate an operation for 60 photo-electrons per MIP for the
$3\times 3$ cm2 cells. This high light yield would create a buffer to cover
for the reduced signal-to-noise ratio after radiation damage.

The Hamamatsu model S14160-3025 has about 40k pixels, which translates into a
dynamic range of more than 670 MIPs, so no saturation effect is expected for
$3\times 3$ cm2 cells.

The neutron fluence expected at the EIC near the insert region will not exceed
$10^{12}$ neutrons/cm2 per year from the electron-proton collisions at the top
luminosity $(10^{34}$ cm-2s${}^{-1})$ [1]. The corresponding ionizing
radiation dose is 25 Gy per year.

The expected SiPM radiation damage would be classified as “modest” in
Garutti’s review [68] on the topic. It would mainly lead to increased dark
current that can affect the ability to identify single-photon peaks. This
level of damage can partially be recovered with annealing [68], which could be
done after each run (as explained in Sec. 2.6).

For reference, CMS uses SiPM-on-tile technology for regions where the total
dose is less than 3000 Gy and fluences less than 8$\times$1013
$n_{\mathrm{eq}}$/cm2, although the SiPMs will be operated at $-$30 C to
reduce the impact of the increased noise [10].

The STAR experiment at RHIC is currently operating a steel-scintillator
calorimeter readout with SiPMs [57] that is expected to receive fluences that
are similar to those expected at the EIC. Detailed data on radiation-induced
noise taken with STAR will guide future iterations of the HG-CALI design.

###  2.5 SiPM-carrying boards and backplane board

The SiPMs will be hosted in a PCB with no active elements. The PCB will also
host LEDs next to each SiPM in the dimple area to be used for monitoring and
calibration purposes, similarly to the CMS HGCAL design [10]. The SiPM-
carrying board will host a high-density connector to connect to the backplane
board. The SiPMs will not be actively cooled.

On either side of the insert are 4 mm PCB backplanes used for readout, which
the PCB for each scintillator assemblies connect into like a traditional
crate. Figure 8 shows the location of the PCB backplanes.

Figure 8: The proposed calorimeter insert, consisting of alternating absorbers
and scintillator assemblies, with PCB backplanes on either side of the
detector.

The SiPM-carrying boards will be plugged in and unplugged one-at-a-time during
assembly and maintenance. The backplane board will also be used to power the
SiPMs and control the LED system for calibration and monitoring.

###  2.6 Accessibility for maintenance

The scintillator assemblies could be removed for maintenance by sliding them
out laterally from between the absorbers when the HCal is opened, as
illustrated in Fig. 9. This will be possible because the interaction point
will have a rail system that will be integrated to the support structure [1].

Figure 9: Top: Zoom-in of the downstream face of the HCal, including the
insert, in the closed configuration. Bottom: Same in the open configuration.
The support structure and rail system that will hold the entire endcap is not
shown.

This feature ensures that the SiPMs boards could be annealed at high-
temperature after each run to minimize radiation damage, and that SiPMs and
scintillator tiles could be replaced.

###  2.7 Geometric acceptance

The overall effects of the EIC crossing angle and other beam parameters are
discussed in Ref. [69]. Events in the lab frame, where the beams have a non-
zero crossing angle, can be Lorentz transformed into a frame where the beams
are anti-parallel and have energies very close to those in the lab frame. This
“minimally-transformed, collinear frame” is a natural choice to extract many
physics observables and the accompanying particles’ angular distributions.

In the hadron- (electron-) going direction, scattering angles defined in the
lab frame relative to the hadron (electron) beam will be equivalent to the
scattering angle in the minimally-transformed collinear frame [70]. In
particular, for a detector in the hadron-going direction, its angular
acceptance should be defined relative to the hadron beam.

To estimate the geometrical acceptance of the insert, we determined where
cones of constant $\eta^{*}$ (that is, pseudorapidity with respect to the
$z^{*}$ axis – the proton beam axis) would intersect the detector. Figure 10
shows projections of these $\eta^{*}$ cones superimposed on a $yz^{*}$
(vertical vs. longitudinal) cross-section of the insert. Within this slice,
the $\eta^{*}=4.0$ cone skims the inner edge of the detector, while those at
lower $\eta^{*}$ hit the face of the detector.

Figure 10: Contours of constant $\eta^{*}$, superimposed on a vertical vs.
longitudinal cross section of the insert. The thick curve (red online)
represents $\eta^{*}=3.7$.

To determine the geometrical acceptance over the full azimuthal range we
projected these cones of constant $\eta^{*}$ onto the faces of the
scintillators planes of the insert, resulting in elliptical rings of constant
$\eta^{*}$. An example is shown in the inset of Fig. 11 for $\eta^{*}$=3.7,
which covers the full azimuthal acceptance on all layers of the detector.

We show in Fig. 11 the cross sections of these cones for several values of
$\eta^{*}$ at the first layer (top left panel), one of the middle layers (top
right panel), and the last layer (bottom left panel). While there is some
acceptance up to $\eta^{*}=4.0$, this is limited to one side of the detector,
and it barely skims the first layer, causing a degradation of the signal, as
we quantify in Sec. 3.

Since the final detector design may differ from the baseline design presented
in this work, we discuss possible alternatives: with a clearance parameter of
3 cm instead of 4 cm, the entire $\eta^{*}=3.8$ ring fits entirely within the
first scintillator layer. If the clearance parameter were increased to 5 cm,
the full $\eta^{*}=3.7$ ring would still be within the acceptance of the
detector, but it would come very close to the edge, resulting in some
degradation.

\begin{overpic}[width=433.62pt]{acceptance_3.85cm_clearance.pdf}
\put(55.0,5.0){ \includegraphics[width=195.12767pt]{acceptance.png}}
\end{overpic} Figure 11: Contours of constant pseudorapidity relative to the
$z^{*}$ axis, $\eta^{*}$, in the first layer (top left), one of the middle
layer (top right), and the last layer (bottom left) of the insert, using the
baseline value of the clearance (3.85 cm). The scintillator cell boundaries
are superimposed. Inset: Example cone of particles at $\eta^{*}$=3.7
(corresponding to the thick red ring on the other panels) projected into the
calorimeter insert, showing cross-sections of the cone at the first, middle,
and last scintillator layers.

The relevant scale to compare various clearance options has to be the
effective radiation length of the insert, which in our design is minimized
using mostly tungsten as an absorber. This is because the relevant metric is
whether or not the core of the hadronic showers can be well contained, as we
describe more in Sec. 3.

Given that even seemingly small differences of clearance definitions can have
a large impact in extending the $\eta^{*}$ coverage of the detector, careful
engineering design and studies are required to minimize the clearance as much
as possible.

###  2.8 Total calorimeter thickness

We determined the amount of material (in nuclear interaction lengths,
$\lambda_{n}$) that a particle travelling in a straight line would pass
through in the HG-CALI and the beampipe as modeled in Ref. [59], as a function
of its polar angle $\theta^{*}$ with respect to the $z^{*}$ axis. We averaged
this with respect to the azimuthal angle $\phi^{*}$ and show the results in
the left panel of Fig. 12.

The HG-CALI covers polar angles from about 2∘ to 6∘, with up to about 7
nuclear interaction lengths. Between 3∘ and 6∘, there is overlap between the
HG-CALI and the HCal endcap. The HCal endcap has a somewhat lower number of
nuclear interaction lengths (about 6) than the insert. There is a small amount
of material traversed by particles passing through the sides of the beampipe
(about 1$\lambda_{n}$), which may allow the detection of showering at very
small $\theta^{*}$.

We show in the right panel of Fig. 12 the dependence of the amount of material
traversed in the HCal insert on $\phi^{*}$ and $\eta^{*}$. The amount of
material is nearly uniform in $\phi^{*}$ in the $3.5\leq\eta^{*}\leq 3.8$
range. Since the insert’s outer shape is (approximately) a square, the value
of $\eta^{*}$ at the edge of the insert depends non-trivially on $\phi^{*}$.
At about $3.0<\eta^{*}<3.3$ (depending on $\phi^{*}$) particles may skim the
edge of the insert, creating a signal in both the insert and the HCal.
Particles with $3.3<\eta^{*}<3.9$ encounter at least two nuclear interaction
lengths of material in the insert at all azimuthal angles.

Figure 12: Left: Number of nuclear interaction lengths of material traversed
by a particle moving in a straight line from the origin as a function of
$\theta^{*}$. These values are integrated over $\phi^{*}$. The different
colors represent the material in the beampipe only (dotted curve, blue
online), the beampipe and the HCal insert (solid curve, orange online), the
beampipe + the proposed HCal insert + the HCal endcap (dashed curve, green
online). Right: Number of nuclear interaction lengths of material in the HCal
insert traversed by a particle moving in a straight line from the origin, as a
function of both $\phi^{*}$ and $\eta^{*}$.

The HG-CALI can complement the HCal endcap at angles where the effective
thickness is not maximal by providing a measurement of the shower-start
position and incident-particle angle, both of which will be better measured in
the insert.

##  3 Simulation and performance

###  3.1 Geometry and simulation setup with DD4HEP

We used the DD4HEP framework [71] to define the geometry and ran the Geant4
framework [72] to evaluate the performance of the HG-CALI. The version of
Geant4 used is 10.7.p03.

Table 1 shows the materials, thicknesses, and numbers of interaction lengths
for each component of a single layer of the insert (see Fig. 5). The
previously described layer design is followed: 30 layers W/Sc, 20 layers
steel/Sc, and 1 final layer of steel.

For simplicity, the granularity of the insert was assumed to be 3$\times$3 cm2
for all the layers. Additionally, the model did not include the dimples and
grooves in the scintillator layers, nor the SiPMs in the PCB. The model
included a realistic beampipe geometry and material description [59].

We also included in the simulation an HCal model similar to the STAR/ATHENA
design [57, 3], assuming a granularity of 10$\times$10 cm2, 20 mm thick
absorbers, and 3 mm thick scintillators.

Table 1: Summary of a single layer of sampling calorimeter structure. Separate values are given for layers with tungsten absorbers and those with steel absorbers. Material | density | thickness | $n_{\lambda}$
---|---|---|---
| (g/cm3) | (cm) |
Absorber (tungsten) | 19.3 | 1.61 | 0.15566
Absorber (steel) | 7.85 | 1.61 | 0.09364
Air | 0.0012 | 0.02 | $3\times 10^{-7}$
Aluminum | 2.699 | 0.20 | 0.00502
ESR | 1.06 | 0.015 | 0.00022
Scintillator | 1.06 | 0.30 | 0.00436
ESR | 1.06 | 0.015 | 0.00022
PCB | 1.86 | 0.16 | 0.00352
Air | 0.0012 | 0.02 | $3\times 10^{-7}$
Total (tungsten) | – | 2.34 | 0.16899
Total (steel) | – | 2.34 | 0.10697

The solenoidal magnetic field is expected to be low in the forward region
relevant for the insert, but is not precisely known at this time so it was not
included in the simulation.

For the simulation of the particle shower in the material, we used the
FTFP_BERT_HP physics list of Geant4, which well describes the CALICE test-beam
data [52], including the time evolution of hadronic showers in both tungsten
and steel absorbers [50]. To model saturation effects in the scintillator
response we applied Birks’ law [73] with a constant 0.126 mm/MeV.

The particle origin position was assumed to be at $z=0$ and the first layer of
the HCal insert was placed at $z=380$ mm.

No noise was included in the simulation, as a realistic implementation is not
available at this time, but its effect was accounted for with an energy
threshold as described in the next section. For the digitization step, a
12-bit dynamic range for the ADC and maximum value set to 200 MeV.

Each cell was assigned a timestamp dictated by the particle with the earliest
time of arrival to the cell. The effect of the time resolution was included as
a cell-by-cell smearing with a Gaussian with $\mu=0$, $\sigma=$1 ns. Unlike in
Ref. [52], no SiPM-saturation effect was simulated since this effect is
expected to be negligible with the model chosen as baseline222For reference,
the SiPM used in the CALICE W-AHCAL prototype contained about 1k channels
whereas the one used in our design has 14.4k channels..

The hits were also required to have $E_{\mathrm{hit}}>0.1E_{\mathrm{MIP}}$,
where $E_{\mathrm{MIP}}$ is the most-probable energy deposited by a minimum-
ionizing particle (MIP), which is about 0.8 MeV as obtained from simulations
of high-energy muons. This energy cut was assumed to reduce the noise to a
negligible level, as it will correspond to a cut of about 6 photoelectrons.
Our selection was more relaxed than the CALICE studies [21] that used an older
generation of SiPMs with significantly larger noise, after-pulsing, and cross-
talk.

We used a time cut of $t<50$ ns, where $t=0$ is defined when the generated
particle hit the front of the insert. As we will show in Sec. 3.4, this
selection yields a compensated response with a basic reconstruction algorithm.
Much larger integration times might be possible given the EIC bunch structure
and absence of pileup. Such time information can be exploited with advanced
algorithms, such as those proposed in Refs. [74, 30, 75].

###  3.2 Shower-shape examples

Figure 13: Examples of reconstructed shower shapes in HCal insert for 50 GeV
$\pi^{-}$ at $\eta^{*}=3.7$. Threshold and timing cuts are applied, as
described in the text. The color code and size of the marker shown represent
the hit energy. A wireframe shows the boundaries of the HCal insert, and the
hole is shown in grey. In the top row the showers are shown in 3D, and in the
bottom row these are projected in 2D for the same set of events.

Figure 13 shows some example shower shapes for a 50 GeV $\pi^{-}$ with
$\eta^{*}=3.7$ and a random $\phi^{*}$. As expected, the $\pi^{-}$ showers can
be roughly described as having a narrow core from electromagnetic sub-showers
and a halo from hadronic sub-showers. The core typically contains cells with
large energy deposits, whereas the halo is composed of mainly low-energy
cells. The latter are dominated by the copious production of neutrons produced
in tungsten. Similar observations have been made with CALICE prototypes [8].

The hadronic-shower shapes, although irregular, provide a hint on the
performance of the insert. The production of neutrons, which drives the
hadronic halo, occurs over wide angles. Some of the neutrons will be emitted
in the direction of the beampipe hole, but often these appear in the other
side of the calorimeter instead of being lost altogether. On the other hand,
the core of the shower is electromagnetic in nature so its size is driven by
the radiation length, which is short in tungsten.

###  3.3 Hit distributions

Figure 14 shows the hit-energy and multiplicity distributions for a 50 GeV
$\pi^{-}$ with $\eta^{*}=3.7$. We show the distributions separately for all
hits above the 0.1 MIP threshold, all hits that have more energy than the
average of all the hits in their respective showers, and those with more than
5 MIPs of energy.

The average hit energy was found to be about 1.6 MeV, with 17% of the hits
containing energy above 1.6 MeV and 7.6% containing energy above 5 MIPs (4
MeV). The maximum hit energy was about 200 MeV. The hits-per-shower
distribution shows a broad peak around 275 hits, whereas the hits above
average show a narrower distribution centered around 50 hits, and those above
5 MIPs show an average of 20 hits.

Figure 14: Reconstructed hit distributions for 50 GeV pions at $\eta^{*}$=3.7
with different hit energy thresholds. Top: Hit energy distribution. Bottom:
Hit multiplicity.

###  3.4 Linearity for hadrons and electrons and $e/h$ ratio

Figure 15: Sum of the hit energies for $\pi^{-}$ (top row) and $e^{-}$ (bottom
row) with different energies and $\eta^{*}=3.7$. The filled histogram (blue
online) is the sum of the energies of the hits from the HCal insert while the
outlined one (red online) is the sum of energies of hits from the HCal and the
HCal insert, weighted by their respective sampling fractions. The dashed
curves represent Gaussian fits to the energy response of the respective
distribution. The fits are restricted to the range $\pm 2.5$ $\sigma$ from the
peak with an iterative procedure.

Figure 15 shows the energy distributions of showers at $\eta^{*}$= 3.7 both
for $\pi^{-}$ and $e^{-}$ with various energies. The total reconstructed
energy was computed as:

$E_{total}=\frac{E_{Insert}}{SF_{Insert}}+\frac{E_{HCal}}{SF_{HCal}}$ (1)

where $E_{Insert}$ and $E_{HCal}$ are the sum of hit energies in the insert
and HCal respectively, and $SF_{Insert}$ and $SF_{HCal}$ are the sampling
fractions for the insert and HCal, respectively. The sampling fraction is
computed by taking the ratio of the output energy to the input energy in the
calorimeter. The sampling fraction is 0.9$\%$ for the insert and 2.2$\%$ for
the HCal.

The response for pions in the insert is mostly Gaussian but it shows a low-
energy tail, which is much less pronounced with the combined measurement using
the HCal insert and the HCal (this is quantified in Sec. 3.5). This suggests
that the low-energy tail is due to leakage in the transverse direction from
the HCal insert towards the HCal.

The response for electrons is mostly Gaussian. This also suggests that that
the electromagnetic core of the hadronic showers is well contained due to
short radiation length of tungsten.

Figure 16 shows the mean energy deposited in the HCal insert for electrons and
pions, along with the $e/h$ ratio, which is found to be about 0.97 on average.

Figure 16: Top: Mean energy of a shower for electrons (triangles, blue online)
and pions (circles, red online) at different energies. The dashed and dotted
lines (blue and red online) are linear fits for electrons and pions,
respectively. Bottom: Ratio of the mean shower energies deposited for
electrons to that of pions.

###  3.5 Non-Gaussian tails due to leakage

Leakage is quantified as the fraction of events in which the shower energy is
below $\mu-3\sigma$, where $\mu$ and $\sigma$ are obtained from the Gaussian
fit to the distribution. Figure 17 shows the leakage for $\pi^{-}$ and $e^{-}$
at different energies and $\eta^{*}$=3.7. The leakage in the insert alone for
$\pi^{-}$ is about 10% for the entire energy range but relatively small (about
1% or lower) for electrons. After considering both the HCal and the HCal
insert, the leakage for $\pi^{-}$ showers drops to about $1\%$, suggesting
most of the leakage at $\eta^{*}$=3.7 is in the transverse direction with a
minimal amount of it leaking through the beampipe. This indicates that
neutrons, which are produced over a large solid angle, traverse the hole and
are measured rather than being lost in the small solid angle of the beampipe
exit (as illustrated in Fig. 13).

Figure 17: Leakage of shower for $\pi^{-}$ (red circles) and electron (blue
triangles) as a function of energy for $\eta^{*}$=3.7 (colored online). The
open markers represent the analysis done considering the HCal insert only,
while the solid markers represent the case where both the HCal and the HCal
insert are taken into account.

###  3.6 Single-hadron energy resolution

Figure 18 shows that the resolution, defined as ratio of the width ($\sigma$)
to the mean value of the fitted energy distribution, for charged pions at
$\eta^{*}$=3.7. The HCal insert meets the requirements set in the EIC Yellow
Report [1], even beyond the pseudorapidity range for which it was set.

Figure 18: Energy resolution of HCal insert (solid circles, blue online) and
the CALICE W-AHCAL test-beam data [52] (solid squares, blue online) for
$\pi^{-}$ at $\eta^{*}$=3.7. The EIC Yellow-Report [1] requirement is shown by
the solid orange line.

The expected resolution for the HG-CALI is similar to the CALICE test-beam
data [52]. We have also implemented the CALICE geometry in DD4HEP for both the
steel and tungsten prototypes and were able to reproduce the linearity and the
resolutions reported in Ref. [52] to within 10$\%$, indicating that the
similarity that we see in Fig. 18 is not coincidental.

###  3.7 Pseudorapidity dependence of performance

Figure 19 shows the distribution of shower energies at a constant pion energy
of 50 GeV but with different $\eta^{*}$. The measured distributions using both
the HCal insert and HCal can be well described by a Gaussian fit, but the fit
quality deteriorates with increasing $\eta^{*}$. For $\eta^{*}>$3.9, the
fraction of events in the low-energy tail increases due to losses to the
beampipe hole. This stems from the worse geometrical acceptance of the HCal
insert here (see Sec. 2.7).

Figure 19: Sum of the hit energies in the calorimeter for $\pi^{-}$ generated
at constant energy 50 GeV but at different pseudorapidity ($\eta^{*}$). The
filled histogram (blue online) is the sum of energy of hits from the HCal
insert while the outlined histogram (red online) represent the total energy
deposited in the HCal insert and the HCal, weighted with their respective
calorimeter sampling fractions. The dashed curves represent Gaussian fits to
the energy responses.

Figure 20 shows the leakage for 50 GeV $\pi^{-}$ and $e^{-}$ at different
$\eta^{*}$. Taking both the HCal endcap and the HCal insert into account
removes most of the leakage, which is in the transverse direction and can be
recovered, as shown by solid markers. At the high $\eta^{*}$ the leakage
increases sharply but is still only about 5$\%$ at $\eta^{*}=3.9$ for
$\pi^{-}$ and about 2$\%$ for $e^{-}$.

Figure 21 shows the energy resolutions obtained with the HCal insert and the
HCal as a function of $\eta^{*}$ for 50 GeV $\pi^{-}$. The resolution obtained
with HG-CALI only is constant at about $9\%$ over the region
$3.4<\eta^{*}<3.8$ and it degrades at lower and higher $\eta^{*}$. Including
the HCal improves the resolution only at low $\eta^{*}$ but not at high
$\eta^{*}$. The horizontal line represents the EIC Yellow Report requirement
[1], which is defined up to $\eta=3.5$, beyond which only “degraded
performance” is specified. The HG-CALI resolution meets the YR requirement up
to $\eta^{*}=3.8$, and gets slightly worse at the highest $\eta^{*}$ region
due to the poorer acceptance as discussed in Sec. 2.7.

Figure 20: Shower energy leakage as a function of $\eta^{*}$ for 50 GeV pions
and electrons. Pions and electrons are shown with red circles and blue
triangles, respectively (colored online). The open markers show the leakage
when considering only the HCal insert, while the solid markers show the
leakage when considering both the HCal and the insert. Figure 21: Resolution
as a function of pseudorapidity for 50 GeV pions. Resolution is shown when
considering only the HCal insert (blue circles) and when considering both the
HCal and the insert (red triangles). The YR requirement reported up to
$\eta^{*}<$3.5 is shown in solid orange and the extrapolation beyond
$\eta^{*}=$3.5 is presented with the dashed line.

##  4 Summary and conclusions

We have presented a design for a high-granularity calorimeter insert (HG-CALI)
for the forward hadronic calorimeter of the EIC detector. Its sampling design
is based on the CALICE “SiPM-on-tile” concept and uses scintillator megatiles
that are grooved to define hexagonal cells. Each layer is distinctly shaped to
adapt to the conical beampipe shape that accommodates a beam-crossing angle of
25 mrad.

The HG-CALI represents the first concrete proposal to instrument the
$3<\eta^{*}<4$ range, which is challenging due to the EIC crossing angle. It
offers an optimal acceptance coverage that is limited only by the clearance
from the beampipe. It thus represents a way to maximize acceptance up to
nearly $\eta^{*}=4.0$, which is a key requirement set in the EIC Yellow Report
[1].

The HG-CALI is designed to integrate well with the rest of the endcap
calorimeters and will enable easy access to the scintillator layers and SiPMs
for maintenance and upgrades. Such a feature will enable frequent annealing of
the SiPMs, which will keep radiation damage within manageable levels.

The energy resolution of the HG-CALI meets the EIC Yellow Report requirements
even with a basic reconstruction algorithm. Moreover, this device will provide
5D shower information (energy, time, and 3D position) that can be exploited
with machine-learning techniques.

The HG-CALI will complement the forward HCal in the region $3.0<\eta^{*}<3.4$
or so by providing an accurate estimate of the shower start position and
incident angle over some range in azimuth. Such information could be used with
machine-learning approaches to account for shower fluctuations and thus
improve the energy resolution of the combined system.

This design will be complemented by a high-granularity electromagnetic
calorimeter insert based on tungsten-powder/scintillating fiber with SiPM
readout. The complete insert system will be compensated, yielding the prospect
of precise and accurate measurements.

The HG-CALI has the potential to unleash the promise of imaging calorimetry at
the EIC, which could support a rich physics program centered on forward jets
and their substructure in polarized electron-proton and electron-nucleus
collisions.

## Model availability

The Google Sketchup model, as well as the CAD file in .step format, for the
proposed detector can be found in Ref. [76]. The DD4HEP model can be found in
Ref. [77].

## Acknowledgements

We thank members of the EIC Detector-1 proto-collaboration for useful
discussions about the insert, as well as help from their Software Team on
matters related to the DD4Hep framework. We thank Oskar Hartbrich for pointing
out the importance of the timing cuts and the choice of resolution metric to
reproduce CALICE results. We also thank Gerard Visser for feedback on the
readout scheme. We also thank members of the California EIC consortium for
their feedback on our design. This work was supported by MRPI program of the
University of California Office of the President, award number 00010100. M.A,
A.P and S.P acknowledge support from DOE grant award number DE-SC0022324. M.A,
K.B, and B.K acknowledge support from DOE grant award number DE-SC0022355.

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