Chromatic Calorimetry: Spectral Shower Analysis

• Chromatic calorimetry is a detector strategy that leverages spectral separation to extract extra observables for refined shower reconstruction and particle identification.
• It utilizes dual-readout in homogeneous crystals or spectrally segmented layers to encode longitudinal shower profiles and mitigate detector non-linearity.
• Demonstrated studies reveal enhanced energy resolution, effective particle discrimination, and potential integration with particle-flow calorimetry for improved overall performance.

Searching arXiv for papers on chromatic calorimetry and related calorimetry concepts. Chromatic calorimetry (CCAL) denotes a class of calorimeter concepts in which spectral information is used to recover otherwise hidden structure in shower development. In contemporary usage, the term has at least two distinct but partially convergent meanings. In one lineage, CCAL is the homogeneous-crystal realization of dual-readout calorimetry, where scintillation and Cherenkov components are separated primarily by chromatic content and, where advantageous, by timing, to estimate the electromagnetic fraction $f_{\mathrm{em}}$ event by event and correct hadronic response (Hirosky et al., 2024). In another lineage, CCAL refers to spectrally segmented calorimetry, in which scintillators or wavelength-shifting layers with distinct emission bands are ordered by decreasing wavelength so that longitudinal shower development is encoded into multiple optical channels, enabling shower tomography, particle identification, and energy reconstruction without conventional longitudinal sampling (Arora et al., 2024). A still earlier and unrelated usage applied “chromatic calorimetry” to the correlation-curves method in thin calorimeters, where local longitudinal correlations rather than optical color carried the discriminating information (Grushevskaya et al., 2014). Across these meanings, the common theme is the extraction of additional shower observables from a compact calorimetric system by exploiting differential response channels.

1. Terminological scope and historical usage

The current research literature uses “Chromatic Calorimetry” in two technically distinct ways. The first is dual-readout CCAL in homogeneous crystals. Here, the same crystal produces both scintillation and Cherenkov light, and the detector separates these components using spectral filters, waveform analysis, and sometimes timing, thereby implementing dual-readout in a single medium rather than in separate sampling media (Hirosky et al., 2024). This usage places CCAL within the broader dual-readout program discussed in community calorimetry planning, where particle flow, dual readout, precision timing, and material trends are identified as key directions for the next decade (White et al., 2022).

The second usage is chromatic longitudinal encoding. In this approach, the calorimeter is built from scintillators or wavelength-shifting layers with different emission peaks arranged from longer to shorter wavelength along the shower axis. Photons from earlier layers propagate through later layers with limited re-absorption, so the multi-band optical response approximates a depth profile of the shower. This formulation was validated in SPS beam tests with stacks such as GAGG–PWO–BGO–LYSO and GAGG–PbF$_2$–EJ262–EJ228, and extended in simulation to quantum-dot-based architectures (Arora et al., 14 Jan 2025).

A third usage appears in earlier cosmic-ray calorimetry work, where “chromatic calorimetry” referred to reconstruction from correlation curves in thin calorimeters. There, the observables were $\log N(t)$ and $dN \equiv \log N(t)-\log N(t+\Delta t)$ rather than optical wavelengths, and the method exploited the quasi-universality of shower development beyond the first interaction point (Grushevskaya et al., 2014). This historical usage is terminologically important because it demonstrates that the acronym CCAL has not always referred to spectral calorimetry.

This coexistence of meanings suggests that the contemporary literature should be read with attention to implementation context. In dual-readout papers, “chromatic” usually means scintillation/Cherenkov separation within one medium. In recent SPS and quantum-dot studies, it means spectral depth encoding by stacked emitters or wavelength shifters.

2. Dual-readout CCAL in homogeneous crystals

In the dual-readout formulation, CCAL targets the dominant source of hadronic calorimeter non-linearity and poor resolution: event-by-event fluctuations of the electromagnetic fraction $f_{\mathrm{em}}$ and of invisible energy from nuclear breakup. The core method is to measure two quasi-independent optical signals with different sensitivity to electromagnetic and non-electromagnetic shower components, then solve for $f_{\mathrm{em}}$ and the corrected energy on an event-by-event basis (White et al., 2022).

In homogeneous-crystal CCAL, the two channels are scintillation $S$ and Cherenkov $C$. Electromagnetic sub-showers generate abundant prompt Cherenkov light, while scintillation tracks the total ionizing energy deposit. Separation is achieved primarily through chromatic filtering because Cherenkov light is broadband and extends into the UV/blue and beyond the scintillation band, while crystal scintillation is relatively narrow. Timing adds an orthogonal discriminator because Cherenkov emission is prompt and scintillation is slower, particularly in crystals such as BGO with $\tau > 300$ ns (Hirosky et al., 2024).

A standard dual-readout signal model writes

$$S = E\big[f_{\mathrm{em}}\,s_e + (1-f_{\mathrm{em}})\,s_h\big], \qquad C = E\big[f_{\mathrm{em}}\,c_e + (1-f_{\mathrm{em}})\,c_h\big].$$

With calibrated channel constants, one can construct an unbiased dual-readout energy estimator

$_2$0

where $_2$1 and $_2$2, or equivalently infer $_2$3 from $_2$4 (Hirosky et al., 2024). The broader calorimetry roadmap describes the same algebraic structure using $_2$5 and $_2$6, emphasizing that chromatic implementations and classic fiber dual-readout are equivalent at the reconstruction level even when their optical realizations differ (White et al., 2022).

The practical distinction from classic dual-readout is architectural. Classic implementations often use separate media and optical paths, such as scintillating and quartz fibers in an absorber matrix. Chromatic CCAL instead aims to extract both observables from one homogeneous or quasi-homogeneous active medium, which can simplify mechanical integration and improve compactness, but requires more demanding optical filtering, precise gain calibration, and careful treatment of spectral cross-contamination.

3. Spectrally segmented CCAL and longitudinal shower encoding

In the spectrally segmented formulation, CCAL encodes longitudinal shower development into a vector of wavelength-separated signals. The fundamental design rule is to stack emitters in decreasing emission wavelength along the beam direction. Longer-wavelength photons produced upstream then traverse downstream, shorter-wavelength layers with limited re-absorption, so the color composition of the collected light carries depth information (Arora et al., 2024).

The 2023 prototype used GAGG, PWO, BGO, and LYSO. The 2024 prototype replaced the intermediate and late layers with PbF$_2$7, EJ262, and EJ228 to improve spectral separation and timing. In the 2024 configuration, GAGG provided a 540 nm front response, PbF$_2$8 acted as a Cherenkov radiator and dense shower-development medium, EJ262 provided a 481 nm channel with $_2$9 ns, and EJ228 a 391 nm channel with $\log N(t)$0 ns. Readout used a Hamamatsu R7600U-200 MaPMT with filters FELH0550, FESH0400, FB475-10, and a 420 nm band-pass channel, with 50 ns integration windows and calibration through MIPs and LED runs (Arora, 11 Sep 2025).

The primary observables are the amplitude fractions

$\log N(t)$1

and the energy-weighted longitudinal center of gravity

$\log N(t)$2

These observables trace shower development: front channels dominate for early electromagnetic deposition, while later channels acquire more weight as the shower deepens or leakage increases (Arora, 11 Sep 2025). For interpretation and fitting, the literature also invokes the gamma-function shower form

$\log N(t)$3

and a logarithmic evolution of $\log N(t)$4 with energy, parameterized in data as $\log N(t)$5 (Arora, 11 Sep 2025).

This version of CCAL is explicitly differentiated from dual-readout in the concept-validation literature. It does not require separation of Cherenkov and scintillation as its defining principle. Instead, it uses multiple scintillation bands, and in some implementations a Cherenkov radiator such as PbF$\log N(t)$6, to infer where energy was deposited inside the stack. The resulting detector behaves as a monolithic or quasi-monolithic calorimeter with effective longitudinal sensitivity but without conventional fine longitudinal sampling (Arora et al., 2024).

4. Materials, optics, and detector architectures

The material choices in CCAL are governed by density, radiation hardness, emission spectrum, attenuation, and compatibility with spectral separation. In dual-readout crystal CCAL, PbWO$\log N(t)$7 and BGO are prominent because they are high-density, high-$\log N(t)$8 scintillators that also act as Cherenkov radiators. For PbWO$\log N(t)$9, the scintillation spectrum peaks at 424 nm; for BGO it peaks at 462 nm; and in both cases the full-width half-maximum is about 90 nm. Long-pass or notch filters can suppress scintillation while transmitting longer-wavelength Cherenkov light, which is less attenuated in the crystal and better matched to modern SiPM photon-detection efficiency (Hirosky et al., 2024).

In stacked-emitter CCAL, the materials are selected for distinct emission peaks and favorable transport properties. The proof-of-concept studies used GAGG at approximately 540 nm, BGO around 480 nm, LYSO and PWO around 420 nm, and later plastic scintillators EJ262 at 481 nm and EJ228 at 391 nm. Ordering by decreasing wavelength was chosen specifically to reduce re-absorption and spectral contamination (Arora et al., 2024). The 2024 SPS implementation further used a light-tight anodized aluminum enclosure, alignment to $dN \equiv \log N(t)-\log N(t+\Delta t)$0 mm, beam tracking with two drift chambers at 200 $dN \equiv \log N(t)-\log N(t+\Delta t)$1m resolution, MCP timing at 10 ps, and environmental control at $dN \equiv \log N(t)-\log N(t+\Delta t)$2C with humidity below 50% (Arora, 11 Sep 2025).

Quantum-dot proposals generalize this architecture by embedding or interleaving wavelength-shifting layers with tunable narrow emission bands. The proposed hybrid module used four PbWO$dN \equiv \log N(t)-\log N(t+\Delta t)$3 blocks and QD-doped PMMA layers with emission peaks at 630, 519, 463, and 407 nm, read out by filtered SiPM channels. Because QDs provide size-controlled emission peaks and narrow FWHM, the design goal is to achieve multiple distinct chromatic channels and “successive transparency” via Stokes shift (Haddad et al., 22 Jan 2025).

The main optical constraints recur across implementations. These include filter bandwidth and angular response, internal absorption at short wavelengths, wavelength-dependent attenuation, spectral overlap, reflections at interfaces, and detector spectral response. In the QD study, echo photons were explicitly quantified, with green-to-red echo contribution to the green channel of about 1.3%, blue-layer echo about 2%, and purple-layer echo about 8% (Haddad et al., 22 Jan 2025). In beam-test stacks, lower-energy separation was limited by contamination from PWO into neighboring filtered channels and by overlap between EJ262 and EJ228 bands (Arora et al., 14 Jan 2025).

5. Reconstruction formalisms and calibration strategies

The reconstruction formalism depends on the CCAL variant. In dual-readout CCAL, the central task is calibration of the $dN \equiv \log N(t)-\log N(t+\Delta t)$4 and $dN \equiv \log N(t)-\log N(t+\Delta t)$5 channels to a common electromagnetic scale and determination of the hadronic responses needed to solve for $dN \equiv \log N(t)-\log N(t+\Delta t)$6 and $dN \equiv \log N(t)-\log N(t+\Delta t)$7. The community formulation expresses the resolution as

$dN \equiv \log N(t)-\log N(t+\Delta t)$8

and uses event-by-event correction through the measured $dN \equiv \log N(t)-\log N(t+\Delta t)$9 response to mitigate non-compensation (White et al., 2022). In the CalVision homogeneous-crystal study, the full channel constants $f_{\mathrm{em}}$0 and the coefficients of the linear estimator had not yet been reported; the emphasis was instead on establishing that the Cherenkov component is large enough and separable enough to support such a reconstruction (Hirosky et al., 2024).

In spectrally segmented CCAL, the reconstructed energy is typically modeled as a linear combination of channel amplitudes,

$f_{\mathrm{em}}$1

with coefficients extracted from beam data. Equalization can be performed through MIP-based factors such as

$f_{\mathrm{em}}$2

or related normalized responses (Arora, 11 Sep 2025). One formulation makes the covariance structure explicit:

$f_{\mathrm{em}}$3

where $f_{\mathrm{em}}$4 is the covariance matrix of correlated channel fluctuations and $f_{\mathrm{em}}$5 the unit response vector (Arora et al., 14 Jan 2025). This suggests that CCAL reconstruction is naturally a multichannel estimation problem rather than a simple sum over independent layers.

The analysis workflows reported for the SPS studies are relatively standardized. They include fitting channel amplitude spectra with Crystal Ball functions, studying two-dimensional scatter plots of selected channel pairs, computing amplitude fractions and their energy dependence, extracting $f_{\mathrm{em}}$6, reconstructing energy from weighted sums, and comparing against Geant4 longitudinal profiles and optical transport simulations (Arora, 11 Sep 2025).

The earlier correlation-curves method, although conceptually separate from optical chromatic calorimetry, is also a multivariate local reconstruction scheme. It fits

$f_{\mathrm{em}}$7

for fixed primary energy and then parameterizes the coefficients as functions of energy. Energy is reconstructed by matching measured $f_{\mathrm{em}}$8 and $f_{\mathrm{em}}$9 to the calibrated correlation curve, reducing sensitivity to the first interaction depth (Grushevskaya et al., 2014). A plausible implication is that this older method belongs to the same broad family of “extra-observable calorimetry,” where internal shower correlations are leveraged to stabilize energy estimates in compact detectors.

6. Demonstrated performance, discriminants, and limitations

The strongest published demonstration for dual-readout crystal CCAL is proof of sufficient Cherenkov yield in homogeneous scintillating crystals. In BGO exposed to 120 GeV protons, template fits to filtered waveforms extracted 5.2 detected Cherenkov photons for a mean deposited energy of 25.4 MeV in the transverse MIP-like geometry, corresponding to 203 detected Cherenkov photons per GeV; optical-simulation correction for long-axis incidence yielded approximately 300 photons per GeV. This exceeds the previously identified threshold of more than 50 Cherenkov photons per GeV required to keep the hadronic stochastic term below about $f_{\mathrm{em}}$0, thereby establishing proof of principle for crystal-based CCAL (Hirosky et al., 2024).

The same study reported timing performance in PbWO$f_{\mathrm{em}}$1 for MIP-like signals of about 420 ps for a single rear SiPM and about 225 ps when combining four rear channels after time-walk correction. Data and optical simulation agreed at the few-percent level in waveform fits, and the spatial dependence of Cherenkov collection was reproduced with a relative spread of about 10% in the data/simulation ratio (Hirosky et al., 2024).

For spectrally segmented CCAL, the 2023 and 2024 SPS prototypes reported electromagnetic energy resolutions of approximately 2.5% at 100 GeV and 1.6% at 91.51 GeV, respectively, with the improvement in 2024 attributed to higher-yield plastics and optimized filters (Arora, 11 Sep 2025). The same program reported $f_{\mathrm{em}}$2 electron-versus-pion PID purity at 100 GeV in both prototypes using $f_{\mathrm{em}}$3-means clustering with $f_{\mathrm{em}}$4, with silhouette scores of 0.85 in 2023 and 0.88 in 2024; misidentification was approximately 5% (Arora, 11 Sep 2025). The 2024 setup also reportedly reduced misidentification by about 3% relative to 2023 (Arora, 11 Sep 2025).

The earlier concept-validation study was more conservative in its claims. It demonstrated qualitative longitudinal sensitivity and analytical discrimination between electrons and pions up to 100 GeV, but did not report calibrated depth resolution, energy resolution, ROC curves, or misidentification rates (Arora et al., 2024). This distinction matters because it separates proof of physical principle from validated quantitative performance.

QD-based simulations extend the performance envelope but remain prospective. The Geant4 study reported energy linearity with $f_{\mathrm{em}}$5 over 5–100 GeV, a constant term $f_{\mathrm{em}}$6, and PID purity up to 98% among electrons, pions, and muons at 20 and 60 GeV, with up to about 20 spectrally resolved layers considered feasible using approximately 20 nm bands (Haddad et al., 22 Jan 2025). These are simulation-based results rather than beam-test measurements.

Limitations recur across all variants. In dual-readout crystal CCAL, the main issues are robust spectral separation across large areas, calibration stability of $f_{\mathrm{em}}$7 and $f_{\mathrm{em}}$8, internal absorption at short wavelengths, SiPM PDE variations with wavelength, and angular dependence of Cherenkov collection (Hirosky et al., 2024). In stacked-emitter CCAL, the dominant systematics include gain variations, filter misalignment, spectral overlap, temperature dependence, and calibration quality; for the SPS prototypes, aggregate energy uncertainties were reported as approximately 10% at 100 GeV in 2023 and approximately 7% in 2024 (Arora, 11 Sep 2025).

7. Relation to broader calorimetry programs and future directions

CCAL is embedded in several broader calorimetry trajectories. In the Snowmass topical-group view, dual-readout approaches, precision timing, particle flow, imaging calorimetry, and radiation-hard materials are complementary rather than mutually exclusive (White et al., 2022). Dual-readout CCAL can supply event-by-event compensation via two observables, while imaging front sections or particle-flow layers supply spatial topology. Spectrally segmented CCAL can provide longitudinal sensitivity in geometries that would otherwise be homogeneous, and quantum-dot implementations aim to expand the number of effective depth channels without introducing conventional mechanical segmentation (Haddad et al., 22 Jan 2025).

The relation to particle-flow calorimetry is especially important. Community discussions emphasize that CCAL can complement highly granular front sections or PF calorimeter layers by improving neutral-hadron measurement, tightening jet energy resolution, and aiding pileup rejection when combined with timing (White et al., 2022). In spectrally segmented implementations, the depth-sensitive fraction vector and $f_{\mathrm{em}}$9 provide additional features for PID and clustering (Arora, 11 Sep 2025). A plausible implication is that future systems may combine chromatic depth encoding with timing and imaging rather than choosing one modality alone.

Several R&D directions follow directly from the published work. For dual-readout crystal CCAL, these include full determination of channel constants in PbWO$S$0 and BGO, optimization of filters and possibly dichroic splitters, improved photon-counting calibration, and geometry refinements that improve light collection and timing (Hirosky et al., 2024). For stacked-emitter and QD-based CCAL, the priorities are narrower emission bands, reduced crosstalk, radiation-hard emitters, automated filter alignment, expanded muon calibration, and scaling to larger and deeper modules suitable for collider conditions (Arora, 11 Sep 2025). The QD proposals additionally identify radiation hardness, quantum-yield stability, polymer-matrix interactions, and more complete nanophotonic modeling as unresolved issues (Haddad et al., 22 Jan 2025).

A recurrent misconception is that CCAL is a single, settled detector concept. The literature instead shows a family of related strategies linked by the use of spectral information. One branch is fundamentally about dual-readout compensation in a homogeneous medium; another is about chromatic shower tomography through wavelength-ordered layers; an older branch concerns correlation observables in thin calorimeters. Their commonality lies not in a unique hardware design, but in the methodological move of encoding extra shower information into differential response channels that can be calibrated and exploited in reconstruction.