HCAL: Advances in Hadron Calorimetry

• HCAL is a hadron calorimeter subsystem engineered to measure hadronic showers via diverse architectures such as scintillator and gaseous detectors.
• It integrates fine segmentation and advanced readout electronics to enable particle-flow reconstruction, leakage correction, and real-time anomaly detection.
• Modern HCAL designs employ rigorous calibration and quality control protocols to achieve precise energy resolution and robust performance in high-rate environments.

Searching arXiv for relevant HCAL papers mentioned in the provided corpus. HCAL most commonly denotes a hadron calorimeter, the calorimetric subsystem that measures hadronic showers, but the term is also used more specifically for detector implementations such as the Analog Hadron CALorimeter (AHCAL), the Semi-Digital Hadronic CALorimeter (SDHCAL), or the hadronic compartment of a larger imaging calorimeter such as CMS HGCAL. Across collider and test-beam programs, HCAL systems appear as scintillator–steel, tungsten–scintillator, GRPC-based semi-digital, MPGD-based semi-digital, and hybrid silicon/scintillator detectors, with designs driven by distinct objectives: particle-flow reconstruction, forward jet triggering, leakage control, timing, radiation tolerance, veto efficiency, or data-quality monitoring (Ebrahimi, 2016, Martelli, 2017, Nogach, 2012, Pellecchia et al., 2024).

1. Definition and detector role

In its broadest usage, HCAL is the hadron calorimeter: the subsystem designed to measure hadronic showers and, in particle-flow detectors, especially the neutral-hadron component of jets. In the CEPC baseline detector, HCAL is described as an essential sub-detector of a high-granularity calorimetry system used with the Particle Flow Algorithm (PFA), with the stated jet energy resolution target of about $30\%/\sqrt{E(\mathrm{GeV})}$ (Duan et al., 2021). In CALICE and ILD studies, the HCAL is a highly granular sampling calorimeter placed behind the ECAL and inside the coil, with the HCAL about 5 interaction lengths thick and the ECAL about 1 interaction length thick, a geometry that directly conditions shower containment and leakage behavior (Lu, 2012).

The term is not always used for a standalone coarse calorimeter. In CMS HGCAL, “HCAL” refers to the hadronic compartment of a single endcap imaging calorimeter composed of an electromagnetic section and hadronic sections, rather than the legacy barrel/endcap HCAL architecture (Martelli, 2017, Pitters, 2018). Conversely, in the RHIC AnDY setup, HCal denotes the principal forward hadron calorimeter used to measure forward hadronic energy, trigger on jet-like events, and reconstruct forward jets in polarized $pp$ collisions (Nogach, 2012).

A recurring theme across these implementations is that HCAL function extends beyond total energy measurement. Fine segmentation is exploited for shower imaging, particle-flow association, pileup rejection, software compensation, timing studies, and, in some cases, background vetoing or real-time detector monitoring (Israeli, 2018, Simon, 2011, Wang et al., 2023, Asres et al., 2023).

2. Principal architectures and technologies

HCAL implementations span several distinct technologies, each optimized for a specific detector environment.

Context	Active medium and readout	Representative features
CALICE/ILD AHCAL	Scintillator tiles with SiPMs	38-layer analog scintillator-steel sampling calorimeter; tile sizes from $30\times30~\mathrm{mm}^2$ to $120\times120~\mathrm{mm}^2$ (Lu, 2012)
CEPC AHCAL R&D	Plastic scintillator tiles with SiPMs, SPIROC2E	Steel absorber; $$40~\mathrm{mm}\times40~\mathrm{mm}\times3~\mathrm{mm}$$ tiles; planned 40-layer detector of size $$70~\mathrm{cm}\times70~\mathrm{cm}\times100~\mathrm{cm}$$ (Duan et al., 2021)
CMS Phase I HCAL	Scintillating tiles with Y11 fibers, SiPM readout	SiPMs replaced HPDs in HB/HE/HO to improve segmentation and remove anomalous noise issues (Heering et al., 11 Jun 2026)
CMS HGCAL hadronic section	Hybrid silicon + scintillator/SiPM	24 hadronic layers in FH and BH with stainless steel absorbers; about $8.5$ to $9\,\lambda$ total (Martelli, 2017, Pitters, 2018)
ILD SDHCAL	GRPCs with semi-digital readout	Up to 50 GRPC layers, $1~\text{cm}^2$ pads, 3 thresholds, embedded power-pulsed electronics (Grenier, 2014)
Muon Collider MPGD-HCAL	MicroMegas, $\mu$-RWELL, RPWELL	Semi-digital HCAL with $pp$0 cells, 2 cm iron absorbers, 5 mm argon gaps in simulation (Pellecchia et al., 2024)
sPHENIX HCal	Plastic scintillator + WLS fibers + SiPMs	Tilted ASTM A36 steel absorber plates, inner and outer HCal segments (Aidala et al., 2017)
DarkSHINE HCAL	Fe-Sc veto calorimeter	Optimized for neutron and muon veto efficiency rather than precision energy measurement (Wang et al., 2023)

The analog scintillator–steel architecture is central to several linear-collider-oriented programs. The CALICE AHCAL is described as a 38-layer sampling calorimeter with cell-by-cell SiPM readout and strong imaging capability, enabling topological observables such as the first hard interaction point and track segments inside hadronic showers (Lu, 2012). The CEPC AHCAL follows the same general paradigm, with steel absorber, scintillator tiles, SiPMs, and SPIROC2E front-end electronics, and places particular emphasis on channel-to-channel light-yield uniformity (Duan et al., 2021).

The semi-digital gaseous branch uses GRPCs or other gaseous technologies to maximize granularity at low cost. The SDHCAL technological prototype for ILD consists of up to 50 GRPC detectors of $pp$1 size and 3 mm thickness, with $pp$2 pads and 2-bit, 3-threshold readout (Grenier, 2014). An earlier GRPC study reported a 1×1 m$pp$3 chamber with 9216 channels, embedded HaRDROC electronics, and a detector concept explicitly aimed at PFA-driven calorimetry (Boudry, 2010). For a future Muon Collider, a distinct path uses micropattern gaseous detectors in a semi-digital HCAL, motivated by rate capability, spatial resolution, and operation under asynchronous beam-induced background (Pellecchia et al., 2024).

The hybrid high-radiation architecture is exemplified by CMS HGCAL. There, the hadronic section uses silicon sensors in the innermost, highest-radiation regions and highly segmented scintillators with SiPM readout in the outer region, combining radiation tolerance with cost-effective large-area coverage (Martelli, 2017, Pitters, 2018). This suggests that “HCAL” no longer implies a uniform active medium even within a single subsystem.

3. Segmentation, shower topology, and reconstruction paradigms

A defining contemporary HCAL trend is the move from coarse energy-summing devices to imaging calorimeters. In CMS HGCAL, a large fraction of the hadronic section uses hexagonal silicon cells of about $pp$4, with over 6 million channels across the detector, and the reconstruction is organized around 3D clustering that can be extended to a 5D representation using energy, $pp$5, $pp$6, $pp$7, and time (Martelli, 2017). The motivation is explicitly particle-flow reconstruction in conditions of 140/200 pileup (Martelli, 2017).

The CALICE AHCAL demonstrates how fine granularity enables software compensation and topological leakage correction. In combined ECAL+AHCAL+TCMT systems, hadronic energy can be reconstructed either by standard calibrated sub-detector sums or by density-based software compensation using local hit-energy information. The software-compensation algorithm assigns different weights to different hit-energy bins, with the weights parametrized by second-order polynomials in particle energy; in the Si-W ECAL + AHCAL + TCMT setup, the stochastic term improved from $pp$8 to $pp$9 under Full SC, corresponding to up to 30% improvement in hadronic energy resolution (Israeli, 2018).

For leakage, the CALICE analysis used two topological observables: the shower starting point and the end-fraction, the latter defined as the fraction of energy deposited in the last four HCAL layers relative to the total energy measured by SiW-ECAL + AHCAL. The end-fraction binning was

$30\times30~\mathrm{mm}^2$0

A lookup-table correction based on measured energy, shower start layer, and end-fraction restored the run energy with better than 0.5% precision in Monte Carlo and centered test-beam data around the beam energy with 1–2% accuracy, while improving relative resolution by about 25% at 80 GeV (Lu, 2012).

Semi-digital calorimetry uses a different reconstruction logic. In SDHCAL, pion reconstructed energy is expressed as

$30\times30~\mathrm{mm}^2$1

with $30\times30~\mathrm{mm}^2$2, where the coefficients are quadratic functions of total hit multiplicity. The reported response was linear with deviations from linearity below 5% between 7 GeV and 80 GeV, and the energy resolution reached about 8.9% at 80 GeV (Grenier, 2014). For the Muon Collider MPGD-HCAL concept, the emphasis similarly falls on semi-digital rather than purely digital readout, with simulation reporting ~8% energy resolution at 80 GeV pions for a 10 $30\times30~\mathrm{mm}^2$3 calorimeter, compared with ~14% in the purely digital case (Pellecchia et al., 2024).

4. Calibration, quality control, and instrumentation

HCAL operation depends on calibration chains that are highly technology-specific.

In the RHIC AnDY forward HCal, the energy scale was established using neutral-pion reconstruction and then corrected for the different response of a hadronic calorimeter to hadrons versus electromagnetic showers through the relation

$30\times30~\mathrm{mm}^2$4

where $30\times30~\mathrm{mm}^2$5 is the incident energy from the $30\times30~\mathrm{mm}^2$6-based calibration and $30\times30~\mathrm{mm}^2$7 is the calibrated HCal cell energy used in jet reconstruction. Cells were included in jet finding only above the threshold

$30\times30~\mathrm{mm}^2$8

The HCal-trigger condition was based on the energy sum in the Left/Right half, excluding the outer two perimeters, with threshold approximately $30\times30~\mathrm{mm}^2$9 (Nogach, 2012).

In the CEPC AHCAL production-quality program, calibration centers on scintillator-tile light yield. Light yield is defined as

$120\times120~\mathrm{mm}^2$0

with pedestal from a Gaussian fit and the MIP peak from a Landau-Gauss convolution. Temperature dependence is measured to be about $120\times120~\mathrm{mm}^2$1 around $120\times120~\mathrm{mm}^2$2, and the uniformity requirement is a light-yield window within 10%. For a mean response of about 12.9 p.e., this corresponds to

$120\times120~\mathrm{mm}^2$3

An automated 144-channel batch-test platform with an automated 3D servo motor tested 15,524 scintillators, yielding an average corrected light yield of about 12.99 p.e. and 14,219 qualified pieces, or about 91.6% (Duan et al., 2021).

The CMS Phase I HCAL SiPM upgrade also relied on production-scale quality control. Every channel was characterized for breakdown voltage, signal response under stable illumination, dark current, forward resistance, and capacitance. For HE, 1,400 production arrays were tested and 104 rejected; for HB, 1,680 arrays were tested and 82 rejected, giving better than 99% yield in both cases (Heering et al., 11 Jun 2026). The forward resistance and capacitance were essential because together they determine cell recovery time, which directly constrains the 40 MHz operating environment and the large photoelectron range of hadronic showers (Heering et al., 11 Jun 2026).

Dedicated calibration hardware has also been developed for scintillator–SiPM HCALs. The EUDET HCAL calibration prototype used a 6-channel quasi-resonant LED calibrator on a 4-layer PCB of size 250 × 147 mm², with pulse width about 3 ns in the abstract, amplitude tunable from 0 to 1.2 A, and frequency up to 100 kHz. A notched-fiber distribution system used a 1 mm diameter optical fiber with notches every 30 mm along 2 m, achieving light homogeneity within ±20% (Cvach et al., 2011). Its intended tasks were SiPM gain calibration, monitoring, and full response-function measurement from zero to saturation (Cvach et al., 2011).

5. Readout, DAQ, and timing

HCAL readout architectures reflect the competing demands of granularity, latency, dynamic range, power, and radiation hardness.

For the CALICE ILC-oriented tile HCAL, the front-end is built around SPIROC2b, with 36 channels per ASIC, 16 samples per channel analog memory depth, and a 12-bit Wilkinson ADC. The detector architecture uses the HCAL Base Unit (HBU) of size $120\times120~\mathrm{mm}^2$4, containing 144 channels and read out by 4 SPIROC2b ASICs. The multi-layer integration prototype combined these units with a scalable DAQ built from a Clock and Control Card (CCC) and Link and Data Aggregator (x-LDA) devices, including a Wing-LDA capable of supporting 96 detector layers (Ebrahimi, 2016).

The SDHCAL readout emphasizes autotriggering and power pulsing. HARDROC2 ASICs inspect discriminator outputs every 200 ns, store up to 127 events, and support the ILC duty cycle by turning on only about 0.5% of the time. The quoted power consumption is 1.425 mW per pad when fully on, below 0.2 $120\times120~\mathrm{mm}^2$5W when mostly off, and below 10 $120\times120~\mathrm{mm}^2$6W per channel at detector level (Grenier, 2014). An earlier GRPC implementation with HaRDROC used 64-channel ASICs, 2 independent adjustable thresholds above 10 fC, a 24-bit timestamp in 200 ns steps, and self-triggered storage of up to 127 events (Boudry, 2010).

CMS HGCAL imposes much more severe trigger and radiation constraints. The hadronic section shares the HGCAL trigger and readout philosophy, with stated requirements of 0.4 fC to 10 pC dynamic range, below 2000 electrons noise, below 50 ps timing precision, and radiation tolerance up to 150 MRad. The readout uses ROC-family ASICs with two gain stages, time-over-threshold, and time-of-arrival with 50 ps binning, operating under a 12.5 $120\times120~\mathrm{mm}^2$7s trigger-latency constraint (Pitters, 2018).

Timing itself can be an HCAL design driver rather than a secondary performance metric. In the CALICE tungsten-scintillator HCAL timing study, the T3B setup comprised 15 scintillator tiles of $120\times120~\mathrm{mm}^2$8 and 5 mm thickness, each read out by a Hamamatsu MPPC50P, digitized at 1.25 GS/s over 2.4 $120\times120~\mathrm{mm}^2$9s. The system achieved about 800 ps timing resolution for single muons, including trigger jitter, and allowed photon-by-photon timing reconstruction using dark-noise-based gain calibration (Simon, 2011). For 10 GeV pion showers in tungsten, QGSP_BERT_HP reproduced the late shower tail and radial mean first-hit times much better than QGSP_BERT, indicating that accurate neutron transport is essential in timing-aware HCAL simulation (Simon, 2011).

6. Performance regimes, physics use cases, and intrinsic limits

HCAL performance is strongly context-dependent: precision hadron measurement, jet reconstruction, trigger formation, vetoing, or LLP searches impose different criteria.

In the AnDY forward region, HCal provided the trigger and jet reconstruction capability needed for the first forward-jet analyzing-power measurements. The jet axis/parton matching reached 82% for $$40~\mathrm{mm}\times40~\mathrm{mm}\times3~\mathrm{mm}$$0, and the forward-jet analyzing power $$40~\mathrm{mm}\times40~\mathrm{mm}\times3~\mathrm{mm}$$1 was found to be small and positive, about the $$40~\mathrm{mm}\times40~\mathrm{mm}\times3~\mathrm{mm}$$2 level for $$40~\mathrm{mm}\times40~\mathrm{mm}\times3~\mathrm{mm}$$3. The asymmetry extraction used the standard cross-ratio form

$$40~\mathrm{mm}\times40~\mathrm{mm}\times3~\mathrm{mm}$$4

with a fill-averaged beam polarization of 0.52 and systematic uncertainties shown to be very small, below $$40~\mathrm{mm}\times40~\mathrm{mm}\times3~\mathrm{mm}$$5 (Nogach, 2012).

For sPHENIX, the HCal is part of a combined calorimeter system optimized for jet and heavy-flavor observables in heavy-ion collisions. The standalone HCal hadron resolution was reported as

$$40~\mathrm{mm}\times40~\mathrm{mm}\times3~\mathrm{mm}$$6

while the full EMCal+HCal system achieved

$$40~\mathrm{mm}\times40~\mathrm{mm}\times3~\mathrm{mm}$$7

a level judged sufficient for the experiment’s requirements (Aidala et al., 2017). In DarkSHINE, by contrast, HCAL is a veto detector. The optimized design uses a transverse size of $$40~\mathrm{mm}\times40~\mathrm{mm}\times3~\mathrm{mm}$$8, about $$40~\mathrm{mm}\times40~\mathrm{mm}\times3~\mathrm{mm}$$9 depth, and a mixed absorber scheme of 70 layers of 10 mm iron followed by 18 layers of 50 mm iron, chosen to improve sub-GeV neutron veto inefficiency while limiting mass and cost (Wang et al., 2023).

HCAL is also central to new signature definitions. A 2025 LLP study proposed the emerging photon jet in the HCAL, produced when a neutral LLP decays to photons after traversing the ECAL but before the HCAL outer boundary. The leading discriminant was the large ratio $$70~\mathrm{cm}\times70~\mathrm{cm}\times100~\mathrm{cm}$$0, and with cuts including

$$70~\mathrm{cm}\times70~\mathrm{cm}\times100~\mathrm{cm}$$1

the study reported final significances of approximately 7.6, 12.0, and 4.1 for three benchmark charged-Higgs masses at $$70~\mathrm{cm}\times70~\mathrm{cm}\times100~\mathrm{cm}$$2 (Kim et al., 28 Apr 2025). This suggests that HCAL can function not only as an absorber and energy estimator but also as a displaced-vertex-like discovery surface for neutral LLP decays.

At the same time, HCAL has irreducible limits. A phenomenological study of superboosted jets argued that the bottleneck is not just segmentation but the finite physical size of hadronic showers. It quoted

$$70~\mathrm{cm}\times70~\mathrm{cm}\times100~\mathrm{cm}$$3

and used these to define a minimal angular scale below which transverse jet substructure becomes unresolvable. The same work argued that roughly 15% of the transverse energy profile remains inaccessible because it is carried by long-lived neutral hadrons, with order-one fluctuations that are not removed by global corrections (Bressler et al., 2015). A common misconception is therefore that arbitrarily fine segmentation alone can recover arbitrarily fine jet substructure; the cited analysis states that shower physics imposes a harder limit (Bressler et al., 2015).

7. Operations, monitoring, and evolving directions

Modern HCAL systems are increasingly managed as large, high-dimensional sensor networks rather than static calorimeters.

The CMS GraphSTAD system illustrates this operational shift. It performs semi-supervised spatio-temporal anomaly detection on HCAL endcap digi-occupancy maps over $$70~\mathrm{cm}\times70~\mathrm{cm}\times100~\mathrm{cm}$$4, using a combination of CNN, GNN, and RNN components in an autoencoder. The HE maps have dimensions $$70~\mathrm{cm}\times70~\mathrm{cm}\times100~\mathrm{cm}$$5, a lumisection corresponds to about 23 s, and the model uses a time window of $$70~\mathrm{cm}\times70~\mathrm{cm}\times100~\mathrm{cm}$$6 (Asres et al., 2023). Channel-level anomaly scores are derived from reconstruction errors, and the system was validated on 2018 LHC Run-2 data with about 20K healthy lumisection maps. Reported inference time is about 0.05 s per sample, well below the lumisection timescale, and the system detected real faulty HE channels in RunId 324841 (Asres et al., 2023). This indicates that HCAL performance now includes data-quality intelligence as part of detector functionality.

Several R&D trajectories are also visible. The CEPC AHCAL work shows how mass-production metrology for scintillator tiles underpins scalable analog HCAL construction (Duan et al., 2021). The Muon Collider MPGD-HCAL study pushes semi-digital gaseous calorimetry toward high-rate, high-background environments (Pellecchia et al., 2024). The CRILIN software-compensation study, although centered on a crystal ECAL, treats HCAL as the downstream hadronic reference and shows that the combined ECAL+HCAL performance can be preserved if non-compensating ECAL response is corrected. Under a baseline HCAL assumption of

$$70~\mathrm{cm}\times70~\mathrm{cm}\times100~\mathrm{cm}$$7

the effective CRILIN contribution after GNN-based correction was summarized as

$$70~\mathrm{cm}\times70~\mathrm{cm}\times100~\mathrm{cm}$$8

and the result was found to be not significantly affected when the assumed HCAL stochastic term was varied from $$70~\mathrm{cm}\times70~\mathrm{cm}\times100~\mathrm{cm}$$9 to $8.5$0 (Ciccarella et al., 3 Jun 2026). A plausible implication is that future HCAL design will be increasingly evaluated as part of a coupled ECAL+HCAL+software system rather than as an isolated hardware block.

Taken together, these studies define HCAL as a family of detector systems unified by hadronic-shower measurement but differentiated by environment and reconstruction philosophy. In one regime HCAL is a fine-grained particle-flow imaging calorimeter; in another, a forward jet trigger; in another, a compact radiation-hard hybrid section; in another, a veto detector or an anomaly-monitored operational grid. The common technical core remains the same: controlled sampling of hadronic cascades, calibration of heterogeneous channel response, and reconstruction strategies that contend with leakage, non-compensation, pileup, timing structure, and the finite spatial extent of hadronic showers (Israeli, 2018, Martelli, 2017, Nogach, 2012, Bressler et al., 2015).