LDMX Electromagnetic Calorimeter

• LDMX Electromagnetic Calorimeter is a high-granularity silicon–tungsten sampling detector designed to precisely measure electromagnetic showers and serve as the primary missing-energy trigger.
• It utilizes fine segmentation, low MIP sensitivity, and advanced machine-learning techniques to achieve efficient photon rejection and robust shower-shape discrimination.
• The evolving design—from simulation with 34 sensing layers to a final 32-layer configuration—optimizes recoil-electron measurement and seamless integration with the tracker and hadronic calorimeter.

The LDMX electromagnetic calorimeter (ECal) is the forward, high-granularity silicon–tungsten sampling calorimeter of the Light Dark Matter eXperiment, positioned downstream of the target and recoil tracker and upstream of the hadronic calorimeter. Within LDMX it is simultaneously a precision electromagnetic detector, the primary missing-energy trigger element, and a central veto instrument against rare Standard Model processes that can mimic missing momentum or missing energy. Across the detector-design, photon-veto, 8 GeV performance, and broader-physics studies, the ECal is consistently described as a compact Si–W imaging calorimeter derived from CMS High Granularity Calorimeter technology and optimized for recoil-electron measurement, photon rejection, minimum-ionizing-particle sensitivity, and integration with tracker- and HCal-based veto logic (Åkesson et al., 2018, Åkesson et al., 2019, Åkesson et al., 2023, Appert et al., 15 Aug 2025).

1. System role in the LDMX detector

In the standard LDMX missing-momentum configuration, a thin tungsten target of thickness $0.1\,X_0$ sits between an upstream tagging tracker and a downstream recoil tracker in a $1.5$ T dipole/fringe field. The recoil electron is then measured in the ECal, while the HCal surrounds the ECal on all sides except the beam-facing side. This placement makes the ECal the first downstream detector that can test whether the apparent energy loss inferred from the trackers is truly invisible or is instead carried by ordinary electromagnetic or hadronic secondaries (Åkesson et al., 2023).

The ECal has several concurrent functions. First, it provides the primary missing-energy trigger. In the 8 GeV study, the trigger uses only the first 20 ECal layers, on the argument that signal recoil-electron showers are largely contained in the front of the calorimeter; the online requirement is that the energy in the first 20 layers be less than $3160$ MeV, corresponding to a missing-energy requirement of $4840$ MeV. Second, offline, the full ECal is used for a stricter total-energy veto. Third, the ECal topology is used to identify non-electromagnetic or multi-object activity accompanying the recoil electron, especially hard bremsstrahlung photons that undergo photo-nuclear or muon-conversion processes rather than ordinary electromagnetic showering (Åkesson et al., 2023).

The detector-wide trigger logic is also expressed as

$$E_{\text{miss}} = nE_{\text{beam}} - E_{\text{ECal}},$$

with $n$ provided by the trigger scintillator. In that sense the ECal is not ancillary to the missing-energy concept; it is the detector subsystem that directly instantiates it online (Appert et al., 15 Aug 2025).

A recurring theme in the LDMX literature is subsystem complementarity. The recoil tracker establishes the outgoing electron momentum and trajectory, the ECal measures visible electromagnetic energy and local shower topology, and the HCal vetoes neutral hadrons, penetrating hadrons, and muons that are only weakly constrained by electromagnetic calorimetry. The 8 GeV photon-rejection study emphasizes that the ECal is especially strong for identifying anomalous activity near and inside the calorimeter volume, whereas the HCal is indispensable for neutral-hadron rejection and the recoil tracker is particularly effective for target-originating extra charged particles (Åkesson et al., 2023).

Beyond the baseline dark-matter program, the ECal is also treated as part of a forward nearly hermetic spectrometer for electron–nucleus scattering. In that context, LDMX is described as having near $2\pi$ azimuthal acceptance from the forward beam axis out to $\sim 40^\circ$, and the ECal contributes to simultaneous access to the scattered electron, photons, and low-energy hadrons in the forward cone most relevant to DUNE-like kinematics (Ankowski et al., 2019).

2. Technology, geometry, and design evolution

Across the design documents, the ECal is consistently described as a silicon–tungsten high-granularity sampling calorimeter based on technology and designs developed for the CMS High Granularity Calorimeter. The detector is selected for high granularity, radiation hardness, compactness, speed, fast readout, and MIP sensitivity, with tungsten as absorber and silicon as active medium (Ankowski et al., 2019, Åkesson et al., 2019, Appert et al., 15 Aug 2025).

Several published descriptions correspond to different stages of the LDMX design:

Source	Configuration described	Key stated numbers
Initial design study (Åkesson et al., 2018)	Initial and evolving concepts	42-layer study geometry; later 32 layers and $40\,X_0$ under study
Photon-veto study (Åkesson et al., 2019)	Detailed Si–W ECal concept	17 double layers, 34 sensing layers, $40\,X_0$, pad area $1.5$0
Design report (Appert et al., 15 Aug 2025)	Simulation and final-design distinction	studies used 34 layers in 17 doublelayers; final design 32 layers in 16 doublelayers, still $1.5$1

The 2019 photon-veto paper gives the most explicit early hardware summary. It states that the ECal consists of 17 double layers, each containing two Si–W layers, for 34 sensing layers total. Tungsten absorber thicknesses vary from about 1 mm to 7 mm, with 14 cm total tungsten corresponding to $1.5$2 total depth. The calorimeter fits in a cube of roughly 55 cm side length, with 1–1.5 mm air gaps between double layers. Each sensing layer uses hexagonal modules in a “flower” pattern, with six modules surrounding a core module; each module has 432 sensing pads of area $1.5$3 (Åkesson et al., 2019).

The later design report retains the same basic Si–W architecture but records an engineering evolution from the 34-layer simulation geometry to a final design with 32 silicon layers paired in 16 doublelayers, achieved by increasing absorber in the deepest layers with no anticipated change in performance. In that report, each silicon plane contains seven hexagonal modules; the detector has $1.5$4 radiation lengths total depth, an active detection volume roughly $1.5$5, a full system envelope of $1.5$6 transverse by 65 cm deep, and a mass of about 825 kg. It quotes standard-cell area as $1.5$7 in the ECal overview and $1.5$8 in the sensor subsection, explicitly noting both values in the report. The same document gives 3024 channels per layer and 96,768 silicon channels for the final 32-layer detector (Appert et al., 15 Aug 2025).

The mechanical design emphasizes avoidance of projective dead regions. The 2025 report describes continuous absorber sheets, offset sensor planes across a doublelayer, and module staggering; on opposite sides of a doublelayer, the sensor planes are offset by half a pad size. The same report gives an estimated inter-module dead region of about 1.5 mm and a Molière radius of about 2.5 cm, while quoting a radius containing 68% of electromagnetic shower energy in the first $1.5$9 layers of less than 1 cm. The earlier photon-veto study quotes a simulated Molière radius of $3160$0 mm and notes that the shower starts much narrower, about 3 mm laterally in the earliest layers (Åkesson et al., 2019, Appert et al., 15 Aug 2025).

A further distinction concerns silicon thickness. The initial design study considered 500 or 700 $3160$1m silicon, emphasizing improved signal charge and MIP detectability relative to CMS sensor thicknesses (Åkesson et al., 2018). The later design report states that 400 $3160$2m sensors are being considered for use in LDMX and quotes channel capacitance of about 20 pF for those high-density sensors (Appert et al., 15 Aug 2025). This indicates an engineering evolution rather than a change in calorimetric principle.

3. Triggering, response, and reconstruction observables

The ECal is the primary physics-trigger detector in LDMX. At 4 GeV, the photon-veto study defines the trigger by summing energy in the first 20 ECal layers and requiring reconstructed energy below $3160$3 GeV, corresponding to at least $3160$4 GeV of missing energy. Offline, the total ECal energy over the full depth is also required to be below $3160$5 GeV (Åkesson et al., 2019). At 8 GeV, the same front-calorimeter logic is retained with a threshold of $3160$6 MeV in the first 20 layers; offline, events with more than $3160$7 MeV in the full ECal are rejected (Åkesson et al., 2023).

The design report gives a more general trigger-performance summary. It states that a missing-energy trigger at 1 kHz rate can be achieved with

$3160$8

with efficiency exceeding 90% for true $3160$9 MeV. It also lists an example single-electron trigger menu item, $4840$0 MeV (Appert et al., 15 Aug 2025).

The ECal energy resolution is parameterized in the 2025 design report as

$4840$1

For electrons at normal incidence, the detector-level fit gives $4840$2, $4840$3, and $4840$4. The same report summarizes this as a constant term of about $4840$5 and a stochastic term of about $4840$6. The earlier photon-veto paper similarly states that the ECal resolution is dominated by a stochastic term of $4840$7 (Appert et al., 15 Aug 2025, Åkesson et al., 2019).

The ECal is also explicitly designed for high MIP sensitivity. The design report gives required signal-to-noise ratios of at least 5 for MIPs in central core modules of layers 5–10 and at least 10 outside that region, while stating that 400 $4840$8m silicon is expected to yield $4840$9. It also specifies pad-threshold requirements of at least $$E_{\text{miss}} = nE_{\text{beam}} - E_{\text{ECal}},$$0 inside the shower-max region and at least $$E_{\text{miss}} = nE_{\text{beam}} - E_{\text{ECal}},$$1 outside, a hit-timing requirement better than about 1 ns, and a trigger-primitive latency below 1 $$E_{\text{miss}} = nE_{\text{beam}} - E_{\text{ECal}},$$2s (Appert et al., 15 Aug 2025).

In analysis, the ECal is typically used through hit-level or containment-based variables rather than a full collider-style clustering model. The 8 GeV study states that it works directly with calorimeter hits and energy sums in geometrically defined regions relative to expected trajectories. The central reconstruction construct is a layer-dependent containment radius defined as the radius containing on average 68% of a signal electron’s shower energy in that layer; those radii depend on recoil-electron momentum and angle at the ECal face, with phase space split into four categories to capture shower-shape changes (Åkesson et al., 2023).

The principal shower observables used in LDMX ECal analyses include total deposited energy, total isolated energy, energy-weighted average layer index, overall lateral spread, deepest layer with a hit, number of readout hits, highest energy in a single cell, transverse RMS, energy in the back ECal, and energy or hit multiplicity outside containment regions around the projected electron and photon trajectories. The longitudinal and transverse granularity is therefore used not only for energy measurement but for a track-informed topological description of the full event (Åkesson et al., 2018, Åkesson et al., 2019, Åkesson et al., 2023).

Calibration strategy in the 2025 design report is unusually extensive because trigger miscalibration can move ordinary EM events into the missing-energy region. The report describes about 3 days of cosmic-ray precalibration per module, daily pedestal and noise runs, HGCROC charge-injection calibration, in-situ intercalibration using muon-conversion events at about 7500/day, and a dedicated beam-dump calibration target consisting of a 15 cm tungsten block, about $$E_{\text{miss}} = nE_{\text{beam}} - E_{\text{ECal}},$$3, capable of producing an illustrative $$E_{\text{miss}} = nE_{\text{beam}} - E_{\text{ECal}},$$4 EoT sample in a day (Appert et al., 15 Aug 2025).

4. Photon rejection, shower-shape discrimination, and machine learning

The LDMX ECal is driven by the need to reject hard bremsstrahlung backgrounds in which the photon does not simply shower electromagnetically but undergoes rare photo-nuclear or muon-conversion processes. The 4 GeV photon-veto study states that roughly $$E_{\text{miss}} = nE_{\text{beam}} - E_{\text{ECal}},$$5 multi-GeV photon events must be rejected in a $$E_{\text{miss}} = nE_{\text{beam}} - E_{\text{ECal}},$$6 EoT run and concludes that the proposed sampling calorimetry can achieve better than $$E_{\text{miss}} = nE_{\text{beam}} - E_{\text{ECal}},$$7 rejection of few-GeV photons, specifically a rejection factor of $$E_{\text{miss}} = nE_{\text{beam}} - E_{\text{ECal}},$$8 for photons with an energy of 2.8 GeV to 4 GeV (Åkesson et al., 2019).

At 4 GeV, the ECal veto chain proceeds from trigger and offline energy cuts to a single recoil-track requirement, an ECal multivariate veto using shower features, HCal vetoing, and finally ECal MIP-track vetoing. The ECal boosted decision tree is trained on ECal photo-nuclear background and mixed signal samples. Its inputs include global shower variables and containment-based variables defined with respect to the projected recoil-electron and inferred photon trajectories. The paper states that requiring the BDT discriminator to be greater than 0.99 retains approximately 85–99% of the signal, depending on mediator mass, while rejecting more than 99.9% of photo-nuclear reactions occurring in the ECal. After the HCal veto, which rejects 99.9924% of the remaining ECal photo-nuclear background while preserving 99% of the signal, the final ECal MIP-track veto rejects all remaining simulated backgrounds (Åkesson et al., 2019).

The 8 GeV study explicitly tests whether the same ECal strategy remains valid after the beam-energy upgrade. Its main conclusion is affirmative: the same 42 ECal shower-shape variables and the same overall veto logic are retained, with analysis-side adjustments rather than hardware changes. The BDT is trained on $$E_{\text{miss}} = nE_{\text{beam}} - E_{\text{ECal}},$$9 signal events, with equal populations of four dark-photon masses, and $n$0 ECal photo-nuclear events. The threshold is chosen to preserve 85% signal efficiency for the most difficult benchmark, $n$1 MeV; at that working point, the ECal photo-nuclear background efficiency is $n$2, about a factor of three lower than at 4 GeV for the same 1 MeV signal efficiency (Åkesson et al., 2023).

Several ECal variables are singled out in the 8 GeV study as especially discriminating: total isolated energy, average layer index, transverse RMS of hit positions, energy in the back ECal, and total energy outside four containment radii around the electron and photon trajectories. These variables encode the fact that photo-nuclear backgrounds tend to have more isolated energy, deposit energy deeper, and exhibit larger lateral spread than a single recoil-electron electromagnetic shower (Åkesson et al., 2023).

The quantitative cutflow at 8 GeV makes the ECal contribution explicit. For samples scaled to $n$3 EoT, the trigger leaves $n$4 ECal photo-nuclear events; requiring total ECal energy below $n$5 MeV reduces this to $n$6; the single recoil-track requirement leaves $n$7; and the ECal BDT reduces that to $n$8. After the HCAL veto only about 2 ECal photo-nuclear events remain in the scaled sample, and the final ECAL MIP-tracking step removes the remainder so that no simulated background survives. The headline result is that all simulated photon-induced backgrounds are rejected for at least $n$9 EoT at 8 GeV, supporting the planned initial $2\pi$0 EoT exposure (Åkesson et al., 2023).

The ECal MIP-tracking stage is especially important for charged secondaries from photonuclear reactions and for $2\pi$1 backgrounds. At 8 GeV it is applied after the BDT and HCal vetoes and searches for axial and non-axial short tracks in the calorimeter. The efficiency impact is strongly mass dependent: around 90% for $2\pi$2 GeV but only about 50% for $2\pi$3 MeV, because highly collinear electron/photon topologies generate fake tracks in the recoil-electron shower (Åkesson et al., 2023). This is one of the clearest documented tradeoffs between rare-background rejection and signal efficiency.

Later overview studies extend the ECal-based analysis program to newer machine-learning architectures. A 2025 conference summary reports a BDT using ECal shower and hit features, an ECal internal-tracking requirement $2\pi$4, and a final HCal veto $2\pi$5, yielding about 2 background events at the target exposure with final signal efficiencies of 49.9%, 64.3%, 68.3%, and 59.3% for $2\pi$6, 10, 100, and 1000 MeV, respectively. The same summary also reports a ParticleNet graph-neural-network approach using ECal hit information; after $2\pi$7 and the HCal veto, the background is estimated as $2\pi$8 events at $2\pi$9 EoT, with final signal efficiencies of 87.6%, 89.7%, 89.4%, and 75.7% for the same four mass points (Vami, 10 Nov 2025).

5. Broader physics uses of the ECal

Although the ECal was designed for the dark-matter missing-momentum program, the detector literature assigns it broader roles. In the electron–nucleus scattering study relevant to DUNE, the ECal is treated as one of the key reasons the LDMX detector is unusually well suited for precision measurements of final-state electrons, photons, pions, protons, and neutrons. In that program the ECal measures electromagnetic showers from the scattered electron and photons, assists in charged-particle identification together with the recoil tracker via $\sim 40^\circ$0, helps distinguish neutral hadrons from charged hadrons by vetoing aligned charged tracks and minimum-ionizing signatures, and contributes to the forward hermeticity needed to infer hadronic energy flow and missing-energy components relevant to neutrino calorimetry (Ankowski et al., 2019).

For that application, the paper states electron energy resolution of 5%–10%, electron transverse-momentum resolution $\sim 40^\circ$1 MeV, and electron kinetic-energy thresholds of approximately 60 MeV; charged pions and protons are assigned similar thresholds and resolutions. The detector is described as having near $\sim 40^\circ$2 azimuthal coverage in the forward region out to $\sim 40^\circ$3, and the inclusive measurement reach is summarized as

$\sim 40^\circ$4

with expected event counts $\sim 40^\circ$5 per bin (Ankowski et al., 2019). In this use case the ECal is not a standalone spectrometer; it is part of a coordinated tracker–ECal–HCal system for multiply differential electron–nucleus measurements.

A second extension is the “ECal as Target” search, which uses the calorimeter itself as an active production medium for dark bremsstrahlung during early running. That study emphasizes that the ECal contains approximately $\sim 40^\circ$6 of material, far larger than the $\sim 40^\circ$7 nominal thin target, and therefore provides a substantial secondary target mass. In this mode the signal is a single electromagnetic shower with anomalously low visible energy rather than a full missing-momentum topology based on a recoil-track measurement (Collaboration et al., 11 Aug 2025).

The ECal-as-target analysis uses a limited variable set deliberately tailored to early data. For a 4 GeV beam the trigger requires $\sim 40^\circ$8 GeV, and for 8 GeV $\sim 40^\circ$9 GeV, where $40\,X_0$0 is the reconstructed energy in the first 20 ECal layers. Offline, tighter full-calorimeter cuts are applied: $40\,X_0$1

$40\,X_0$2

These are combined with an HCal veto $40\,X_0$3 and an ECal transverse shower-width requirement $40\,X_0$4 mm. Under $40\,X_0$5 EoT early-running conditions, the study projects sensitivity down to approximately $40\,X_0$6 in $40\,X_0$7 for $40\,X_0$8 MeV and $40\,X_0$9 for $40\,X_0$0 MeV (Collaboration et al., 11 Aug 2025).

These broader uses underscore a persistent feature of the LDMX ECal: the same hardware is repeatedly repurposed as trigger device, veto detector, topological classifier, semiexclusive final-state detector, and, in the early-search proposal, even as an active target.

6. Modeling assumptions, caveats, and open questions

The ECal performance claims in the LDMX literature are strongly simulation-driven. The dedicated photon-rejection studies use customized Geant4-based simulations, with version 10.02.p03 stated explicitly in both the 4 GeV and 8 GeV work. Signal production is generated with MadGraph/MadEvent and propagated through Geant4; rare backgrounds are generated in Geant4 with biasing to make the requisite Monte Carlo samples tractable. At 8 GeV, the photo-nuclear cross section is enhanced by a factor 550, and muon conversion by factors 10000 in the target and 30000 in the ECal, with event weights applied to preserve total rates (Åkesson et al., 2019, Åkesson et al., 2023).

Hadronic and rare-photon interaction modeling is a documented systematic concern. The 4 GeV photon-veto paper states that the default Bertini photo-nuclear model overpopulated single- and di-neutron reactions and cumulative backscattered hadrons while underpopulating single-pion and single-kaon final states, prompting corrections, many later adopted in official Geant4 versions. The same paper also replaces the default Geant4 treatment of $40\,X_0$1 with a modified implementation using the full dimuon phase-space distribution from the cited Tsai expression (Åkesson et al., 2019). The initial design study likewise notes that unphysical backward-hadron reflections in nominal Geant4 samples made early ECal optimization conservative and suboptimal (Åkesson et al., 2018).

The 8 GeV study is explicit about remaining limitations. It states that the biased ECal photo-nuclear sample corresponds to $40\,X_0$2 EoT and that further efforts are required to reach a $40\,X_0$3 EoT sample, as expected for the full 8 GeV run. It also states that no detailed systematic-uncertainty budget is presented for ECal response, shower modeling, or BDT robustness, and that crucial hardware and reconstruction details are inherited from earlier design reports rather than restated in the paper (Åkesson et al., 2023).

Design evolution is another source of apparent ambiguity. The 2018 initial design study discusses both a 42-layer geometry and a later 32-layer, $40\,X_0$4 option (Åkesson et al., 2018). The 2019 photon-veto paper describes 17 double layers and 34 sensing layers (Åkesson et al., 2019). The 2025 design report states that simulation studies used 34 layers in 17 doublelayers but that the final design will have 32 layers in 16 doublelayers with no anticipated change in performance (Appert et al., 15 Aug 2025). These documents therefore record an evolving engineering baseline rather than a single frozen mechanical definition.

A final caveat concerns efficiency tradeoffs in the most aggressive ECal-based veto steps. The 8 GeV study shows that the final ECal MIP-track veto can reduce signal efficiency to about 50% for the $40\,X_0$5 MeV benchmark because overlapping electron/photon geometries generate fake tracks (Åkesson et al., 2023). The ECal’s fine granularity is thus a source of both rejection power and analysis complexity.

The common conclusion across the LDMX literature is stable despite these caveats. The ECal is not treated as a conventional forward electromagnetic calorimeter whose task ends with energy measurement. It is the detector subsystem through which LDMX operationalizes low-energy triggering, shower-topology analysis, rare-photon rejection, MIP-like secondary identification, and several of the experiment’s most distinctive auxiliary measurements (Åkesson et al., 2019, Åkesson et al., 2023, Appert et al., 15 Aug 2025).