Phase I Near-Detector Complex

• Phase I Near-Detector Complex is a suite of detectors positioned near neutrino sources to measure unoscillated beams and reduce systematic uncertainties.
• It employs modular architectures with precision trackers, calorimeters, and magnet systems to optimize vertex reconstruction, charge identification, and flux normalization.
• Implementations in DUNE, ESSnuSB, and Neutrino Factory highlight its role in target-matched measurements and advanced neutrino interaction studies.

A Phase I Near-Detector Complex is the baseline, early-running ensemble of detectors deployed close to an intense neutrino source in order to characterize the unoscillated beam, measure interaction rates and topologies on the relevant target material, and reduce the dominant systematic uncertainties in far-detector oscillation analyses. Across the configurations discussed for DUNE, ESSnuSB, and Neutrino Factory studies, the defining functions are flux normalization and spectral measurement, target-matched cross-section constraints, topology and vertex reconstruction, charge-sign separation in magnetized systems, and control of neutral-particle systematics; in mature implementations such as T2K ND280, surrounding calorimetry additionally provides photon reconstruction, particle identification, and hermeticity (Martin-Albo, 2016, Burgman et al., 2021, Matev et al., 2011, Allan et al., 2013).

1. Scientific role and near–far extrapolation

The central task of a Phase I near detector is to constrain the ingredients entering the far-detector event prediction. In the notation used by the cited studies, event rates follow

$$N = \int \Phi(E)\,\sigma(E)\,N_{\text{targets}}\,\epsilon(E)\,dE,$$

or, when detector response is made explicit,

$$N_{\text{obs}}(E_{\text{rec}})\approx \int \Phi_\nu(E_{\text{true}})\,\sigma_\nu(E_{\text{true}})\,\epsilon(E_{\text{true}},E_{\text{rec}})\,N_{\text{targets}}\,dE_{\text{true}}.$$

Phase I complexes are therefore designed to constrain both $\Phi(E)$ and $\sigma(E)$, while also calibrating the migration from true to reconstructed kinematics (Martin-Albo, 2016, Burgman et al., 2021, Matev et al., 2011).

A recurring simplification is that near detectors serve only as flux monitors. In the cited designs, that is incomplete. DUNE’s argon-based near-detector program directly targets final-state interactions (FSI), multinucleon $(2p2h)$ processes, hadronization, and soft-pion production on argon, because the far detector is a liquid-argon TPC and the near–far extrapolation must be anchored in the same nucleus (Martin-Albo, 2016). ESSnuSB uses a water-Cherenkov near detector matched to a water-Cherenkov far detector specifically to extract the electron-neutrino interaction cross section on water and to control CCQE-like modeling uncertainties in oxygen (Burgman et al., 2021). Neutrino Factory studies extend the role further to charm production, $\tau$ appearance, and absolute flux normalization through pure leptonic channels (Matev et al., 2011).

This target matching is not, by itself, sufficient. The ESSnuSB and DUNE studies both treat topology reconstruction, neutral-particle recovery, and detector-response calibration as essential parts of the same systematic-control problem. A plausible implication is that “Phase I” denotes not merely a first installation stage, but the first configuration capable of delivering a quantitatively usable near–far transfer of flux, interaction model, and detector response (Burgman et al., 2021, Emberger et al., 2018).

2. Canonical subsystem architecture

Phase I complexes are typically modular rather than monolithic. The DUNE program considers a magnetized high-pressure gaseous argon TPC, often denoted ND-GAr or HPgTPC, surrounded by an electromagnetic calorimeter inside a dipole magnet, and complemented in separate studies by a movable liquid-argon detector operated in PRISM mode (Martin-Albo, 2016, Gouvêa et al., 2019). ESSnuSB adopts a kiloton-scale water-Cherenkov near detector with 30% PMT coverage, a Super-FGD–based fine-grained tracker block of $(1.4\times1.4\times0.5)\,\mathrm{m}^3$, and an emulsion option still under investigation in the 2021 conceptual design (Burgman et al., 2021).

Neutrino Factory studies present an explicitly layered complex: a high-granularity silicon vertex detector, a high-resolution low-$Z$ tracker, and a downstream muon catcher. In the most mature simulated option, the tracker is a scintillating-fiber detector in a $0.5\,\mathrm{T}$ dipole field; an alternative HiResM$\nu$-inspired straw-tube tracker is also described, with transition-radiation radiators, surrounding Pb/scintillator ECAL, and a muon range detector in the return yoke (Matev et al., 2011, Matev, 2011).

A mature operational reference is the T2K ND280 ECal, which surrounds the Pi-0 Detector and tracker inside the refurbished UA1/NOMAD dipole magnet operating at $$N_{\text{obs}}(E_{\text{rec}})\approx \int \Phi_\nu(E_{\text{true}})\,\sigma_\nu(E_{\text{true}})\,\epsilon(E_{\text{true}},E_{\text{rec}})\,N_{\text{targets}}\,dE_{\text{true}}.$$0. Its role is not only calorimetric containment but neutral-particle reconstruction, photon tagging, and charged-particle identification around the tracking core (Allan et al., 2013).

These architectures share a stable logic. A low-density or fine-grained inner detector provides precise vertexing and charged-particle kinematics; magnetization supplies curvature-based momentum and charge-sign measurement; surrounding calorimetry restores neutral energy flow and hermeticity; and specialized subsystems such as emulsion, silicon vertexing, or muon catchers address backgrounds that would otherwise dominate the far-detector error budget (Emberger et al., 2018, Matev et al., 2011).

3. Magnetized gaseous tracking in DUNE Phase I

The DUNE HPgTPC concept is a large argon gas TPC of square cross section, about $$N_{\text{obs}}(E_{\text{rec}})\approx \int \Phi_\nu(E_{\text{true}})\,\sigma_\nu(E_{\text{true}})\,\epsilon(E_{\text{true}},E_{\text{rec}})\,N_{\text{targets}}\,dE_{\text{true}}.$$1, with drift perpendicular to the beam and parallel to the floor, housed in a cylindrical pressure vessel of approximately $$N_{\text{obs}}(E_{\text{rec}})\approx \int \Phi_\nu(E_{\text{true}})\,\sigma_\nu(E_{\text{true}})\,\epsilon(E_{\text{true}},E_{\text{rec}})\,N_{\text{targets}}\,dE_{\text{true}}.$$2 and holding about $$N_{\text{obs}}(E_{\text{rec}})\approx \int \Phi_\nu(E_{\text{true}})\,\sigma_\nu(E_{\text{true}})\,\epsilon(E_{\text{true}},E_{\text{rec}})\,N_{\text{targets}}\,dE_{\text{true}}.$$3 tonne of argon at $$N_{\text{obs}}(E_{\text{rec}})\approx \int \Phi_\nu(E_{\text{true}})\,\sigma_\nu(E_{\text{true}})\,\epsilon(E_{\text{true}},E_{\text{rec}})\,N_{\text{targets}}\,dE_{\text{true}}.$$4 bar. A dipole magnet provides a uniform field $$N_{\text{obs}}(E_{\text{rec}})\approx \int \Phi_\nu(E_{\text{true}})\,\sigma_\nu(E_{\text{true}})\,\epsilon(E_{\text{true}},E_{\text{rec}})\,N_{\text{targets}}\,dE_{\text{true}}.$$5 perpendicular to the beam, and a lead–plastic scintillator ECAL surrounds the active TPC volume (Martin-Albo, 2016).

Its performance targets are explicitly tied to the near–far systematics problem: point resolution better than $$N_{\text{obs}}(E_{\text{rec}})\approx \int \Phi_\nu(E_{\text{true}})\,\sigma_\nu(E_{\text{true}})\,\epsilon(E_{\text{true}},E_{\text{rec}})\,N_{\text{targets}}\,dE_{\text{true}}.$$6, two-track separation better than $$N_{\text{obs}}(E_{\text{rec}})\approx \int \Phi_\nu(E_{\text{true}})\,\sigma_\nu(E_{\text{true}})\,\epsilon(E_{\text{true}},E_{\text{rec}})\,N_{\text{targets}}\,dE_{\text{true}}.$$7, momentum resolution better than $$N_{\text{obs}}(E_{\text{rec}})\approx \int \Phi_\nu(E_{\text{true}})\,\sigma_\nu(E_{\text{true}})\,\epsilon(E_{\text{true}},E_{\text{rec}})\,N_{\text{targets}}\,dE_{\text{true}}.$$8 for $$N_{\text{obs}}(E_{\text{rec}})\approx \int \Phi_\nu(E_{\text{true}})\,\sigma_\nu(E_{\text{true}})\,\epsilon(E_{\text{true}},E_{\text{rec}})\,N_{\text{targets}}\,dE_{\text{true}}.$$9 tracks, and charge-sign determination from curvature. The curvature relation is written as

$\Phi(E)$0

with the momentum resolution split into measurement and multiple-scattering terms,

$\Phi(E)$1

The explicit motivation for gas rather than liquid argon is that lower density suppresses multiple scattering and lowers tracking thresholds for soft final-state particles (Martin-Albo, 2016).

The same low density is the basis of the detector’s vertex-physics program. Pressurizing argon gas to about $\Phi(E)$2 bar retains a much lower density than liquid argon while providing enough target mass and containment volume for near-detector rates. In the paper’s proton-range study, the threshold kinetic energy for registering an approximately $\Phi(E)$3 proton track is substantially lower in gas than in liquid. This gives sensitivity to low-energy nucleons, soft pions, and conversion or ejection products at the interaction vertex, precisely where FSI and nuclear correlations distort kinematics and where far-detector energy reconstruction is most sensitive to bias (Martin-Albo, 2016).

The detector is therefore not merely a spectrometer. It is an argon-specific exclusive and semi-inclusive cross-section instrument intended to constrain FSI, $\Phi(E)$4, and soft hadron production on the same nucleus used in the far detector. Because charge-sign discrimination separates $\Phi(E)$5 and $\Phi(E)$6 charged-current samples via the lepton sign, it also refines flavor-composition constraints and improves flux unfolding (Martin-Albo, 2016).

4. High-granularity calorimetry and neutral-particle recovery

In DUNE’s HPgTPC option, the tracker’s low density suppresses photon conversions and neutron energy deposition, so a granular ECAL becomes central rather than ancillary. The simulated concept uses alternating absorber and plastic scintillator layers, with default absorber Cu $\Phi(E)$7, active layers of $\Phi(E)$8 plastic scintillator tiles directly coupled to SiPMs, tile sizes studied from $\Phi(E)$9 to $\sigma(E)$0 with a default of $\sigma(E)$1, and a total depth of $\sigma(E)$2 layers, about $\sigma(E)$3 (Emberger et al., 2018).

The calorimeter is optimized for photon pointing, $\sigma(E)$4 association, and neutron sensitivity. For the default configuration without vessel material, the single-photon energy resolution is parameterized by

$\sigma(E)$5

with $\sigma(E)$6, $\sigma(E)$7, and $\sigma(E)$8. The angular resolution is parameterized as

$\sigma(E)$9

with $(2p2h)$0, $(2p2h)$1, and $(2p2h)$2. For $(2p2h)$3 kinetic energy $(2p2h)$4, the default design achieves a decay-vertex resolution of $(2p2h)$5–$(2p2h)$6, improving by more than a factor of $(2p2h)$7 over pure geometric pointing (Emberger et al., 2018).

Granularity is not uniformly valuable throughout the depth. The study finds that finer segmentation in the first approximately $(2p2h)$8 layers yields the largest pointing gain, whereas granularity beyond approximately $(2p2h)$9 layers has marginal impact on pointing. The explicit Phase I recommendation is therefore to use tiles of at most $\tau$0 in the first approximately $\tau$1 layers, with $\tau$2–$\tau$3 tiles or crossed strips deeper in the stack to control channel count and cost (Emberger et al., 2018).

Mechanical integration is a major design tension. If the pressure vessel is placed between tracker and ECAL, the added $\tau$4–$\tau$5 degrades low-energy photon energy resolution notably; $\tau$6 stainless steel is substantially worse than $\tau$7 titanium, and thin ribbed shells are preferred to homogeneous thick shells. The strong recommendation is to place the ECAL inside the HPgTPC pressure vessel wherever possible (Emberger et al., 2018).

An operational precedent for this surrounding-calorimeter logic is T2K ND280. Its ECal consists of $\tau$8 modules around the tracker and P0D, provides approximately $\tau$9 in the barrel and approximately $(1.4\times1.4\times0.5)\,\mathrm{m}^3$0 downstream, and achieved high layer efficiencies in situ: $(1.4\times1.4\times0.5)\,\mathrm{m}^3$1 for the Ds-ECal, $(1.4\times1.4\times0.5)\,\mathrm{m}^3$2 for barrel double-ended layers, and $(1.4\times1.4\times0.5)\,\mathrm{m}^3$3 for single-ended layers. Track or shower timing reaches about $(1.4\times1.4\times0.5)\,\mathrm{m}^3$4 after calibration, and the optimized P0D-ECal photon tagging efficiency exceeds $(1.4\times1.4\times0.5)\,\mathrm{m}^3$5 for photons above $(1.4\times1.4\times0.5)\,\mathrm{m}^3$6 (Allan et al., 2013). This demonstrates that a near-detector ECAL can function simultaneously as a neutral-particle instrument, a PID device, and a hermetic outer envelope.

5. Water-target Phase I design in ESSnuSB

The 2021 ESSnuSB conceptual design defines a Phase I near-detector complex at $(1.4\times1.4\times0.5)\,\mathrm{m}^3$7 from the neutrino production point. Its baseline comprises a cylindrical water-Cherenkov near detector aligned with the beam, of length $(1.4\times1.4\times0.5)\,\mathrm{m}^3$8 and radius $(1.4\times1.4\times0.5)\,\mathrm{m}^3$9, corresponding to an active water volume of approximately $Z$0, instrumented with $Z$1-inch PMTs at $Z$2 inner-surface coverage. Reconstruction is performed with fiTQun and simulation with WCSim (Burgman et al., 2021).

This WC-ND is complemented by a Super-FGD–like fine-grained detector of about $Z$3 plastic scintillator cubes in a $Z$4 block, providing fully active three-dimensional granularity for pion and proton tagging, $Z$5 background control, and acceptance modeling. A NINJA-like emulsion subsystem is under investigation to add micrometric vertexing and exclusive-channel capability (Burgman et al., 2021).

The beam conditions determine the reconstruction problem. The proton driver is a $Z$6 $Z$7 beam at kinetic energy $Z$8 and repetition rate $Z$9, with compressed spill length about $0.5\,\mathrm{T}$0. At the near detector, most neutrinos are between $0.5\,\mathrm{T}$1 and $0.5\,\mathrm{T}$2 and peak around $0.5\,\mathrm{T}$3; the unoscillated flavor composition is $0.5\,\mathrm{T}$4, with the remainder dominated by $0.5\,\mathrm{T}$5 (Burgman et al., 2021).

The water-Cherenkov selection performance is quoted explicitly. For charged leptons reconstructed with fiTQun, the electron selection efficiency is $0.5\,\mathrm{T}$6 with muon-to-electron misidentification of $0.5\,\mathrm{T}$7, and the muon selection efficiency is $0.5\,\mathrm{T}$8 with electron-to-muon misidentification of $0.5\,\mathrm{T}$9. For neutrino samples after full cuts, the positive-horn electron-like sample contains $\nu$0 $\nu$1 e-ID events and $\nu$2 misidentified $\nu$3 e-like events, corresponding to $\nu$4 and triggered $\nu$5 acceptance of about $\nu$6; the negative-horn configuration reaches $\nu$7 with triggered $\nu$8 acceptance of about $\nu$9 (Burgman et al., 2021).

Energy reconstruction uses the quasi-elastic estimator

$$N_{\text{obs}}(E_{\text{rec}})\approx \int \Phi_\nu(E_{\text{true}})\,\sigma_\nu(E_{\text{true}})\,\epsilon(E_{\text{true}},E_{\text{rec}})\,N_{\text{targets}}\,dE_{\text{true}}.$$00

with $$N_{\text{obs}}(E_{\text{rec}})\approx \int \Phi_\nu(E_{\text{true}})\,\sigma_\nu(E_{\text{true}})\,\epsilon(E_{\text{true}},E_{\text{rec}})\,N_{\text{targets}}\,dE_{\text{true}}.$$01 for $$N_{\text{obs}}(E_{\text{rec}})\approx \int \Phi_\nu(E_{\text{true}})\,\sigma_\nu(E_{\text{true}})\,\epsilon(E_{\text{true}},E_{\text{rec}})\,N_{\text{targets}}\,dE_{\text{true}}.$$02 in the ESSnuSB studies. The quoted RMS of $$N_{\text{obs}}(E_{\text{rec}})\approx \int \Phi_\nu(E_{\text{true}})\,\sigma_\nu(E_{\text{true}})\,\epsilon(E_{\text{true}},E_{\text{rec}})\,N_{\text{targets}}\,dE_{\text{true}}.$$03 is approximately $$N_{\text{obs}}(E_{\text{rec}})\approx \int \Phi_\nu(E_{\text{true}})\,\sigma_\nu(E_{\text{true}})\,\epsilon(E_{\text{true}},E_{\text{rec}})\,N_{\text{targets}}\,dE_{\text{true}}.$$04 for $$N_{\text{obs}}(E_{\text{rec}})\approx \int \Phi_\nu(E_{\text{true}})\,\sigma_\nu(E_{\text{true}})\,\epsilon(E_{\text{true}},E_{\text{rec}})\,N_{\text{targets}}\,dE_{\text{true}}.$$05 and $$N_{\text{obs}}(E_{\text{rec}})\approx \int \Phi_\nu(E_{\text{true}})\,\sigma_\nu(E_{\text{true}})\,\epsilon(E_{\text{true}},E_{\text{rec}})\,N_{\text{targets}}\,dE_{\text{true}}.$$06 for $$N_{\text{obs}}(E_{\text{rec}})\approx \int \Phi_\nu(E_{\text{true}})\,\sigma_\nu(E_{\text{true}})\,\epsilon(E_{\text{true}},E_{\text{rec}})\,N_{\text{targets}}\,dE_{\text{true}}.$$07 in positive horn, and approximately $$N_{\text{obs}}(E_{\text{rec}})\approx \int \Phi_\nu(E_{\text{true}})\,\sigma_\nu(E_{\text{true}})\,\epsilon(E_{\text{true}},E_{\text{rec}})\,N_{\text{targets}}\,dE_{\text{true}}.$$08 for $$N_{\text{obs}}(E_{\text{rec}})\approx \int \Phi_\nu(E_{\text{true}})\,\sigma_\nu(E_{\text{true}})\,\epsilon(E_{\text{true}},E_{\text{rec}})\,N_{\text{targets}}\,dE_{\text{true}}.$$09 and $$N_{\text{obs}}(E_{\text{rec}})\approx \int \Phi_\nu(E_{\text{true}})\,\sigma_\nu(E_{\text{true}})\,\epsilon(E_{\text{true}},E_{\text{rec}})\,N_{\text{targets}}\,dE_{\text{true}}.$$10 for $$N_{\text{obs}}(E_{\text{rec}})\approx \int \Phi_\nu(E_{\text{true}})\,\sigma_\nu(E_{\text{true}})\,\epsilon(E_{\text{true}},E_{\text{rec}})\,N_{\text{targets}}\,dE_{\text{true}}.$$11 in negative horn (Burgman et al., 2021).

The significance of this Phase I design lies in the combination rather than any single subsystem. Water matching minimizes material extrapolation uncertainty, the WC detector provides large mass and ring PID, and the fine-grained tracker restores hadronic topology information needed to control NC $$N_{\text{obs}}(E_{\text{rec}})\approx \int \Phi_\nu(E_{\text{true}})\,\sigma_\nu(E_{\text{true}})\,\epsilon(E_{\text{true}},E_{\text{rec}})\,N_{\text{targets}}\,dE_{\text{true}}.$$12 backgrounds, sub-threshold muons, and nuclear-effect biases in $$N_{\text{obs}}(E_{\text{rec}})\approx \int \Phi_\nu(E_{\text{true}})\,\sigma_\nu(E_{\text{true}})\,\epsilon(E_{\text{true}},E_{\text{rec}})\,N_{\text{targets}}\,dE_{\text{true}}.$$13 (Burgman et al., 2021).

6. Flux standards, movable detectors, and electroweak reach

Phase I near-detector complexes can also operate as precision flux and electroweak instruments. In DUNE-PRISM, the detector analyzed is a $$N_{\text{obs}}(E_{\text{rec}})\approx \int \Phi_\nu(E_{\text{true}})\,\sigma_\nu(E_{\text{true}})\,\epsilon(E_{\text{true}},E_{\text{rec}})\,N_{\text{targets}}\,dE_{\text{true}}.$$14 ton fiducial-mass LArTPC located $$N_{\text{obs}}(E_{\text{rec}})\approx \int \Phi_\nu(E_{\text{true}})\,\sigma_\nu(E_{\text{true}})\,\epsilon(E_{\text{true}},E_{\text{rec}})\,N_{\text{targets}}\,dE_{\text{true}}.$$15 from the production target and moved perpendicular to the beam in discrete $$N_{\text{obs}}(E_{\text{rec}})\approx \int \Phi_\nu(E_{\text{true}})\,\sigma_\nu(E_{\text{true}})\,\epsilon(E_{\text{true}},E_{\text{rec}})\,N_{\text{targets}}\,dE_{\text{true}}.$$16 steps from $$N_{\text{obs}}(E_{\text{rec}})\approx \int \Phi_\nu(E_{\text{true}})\,\sigma_\nu(E_{\text{true}})\,\epsilon(E_{\text{true}},E_{\text{rec}})\,N_{\text{targets}}\,dE_{\text{true}}.$$17 to $$N_{\text{obs}}(E_{\text{rec}})\approx \int \Phi_\nu(E_{\text{true}})\,\sigma_\nu(E_{\text{true}})\,\epsilon(E_{\text{true}},E_{\text{rec}})\,N_{\text{targets}}\,dE_{\text{true}}.$$18 off-axis. With a $$N_{\text{obs}}(E_{\text{rec}})\approx \int \Phi_\nu(E_{\text{true}})\,\sigma_\nu(E_{\text{true}})\,\epsilon(E_{\text{true}},E_{\text{rec}})\,N_{\text{targets}}\,dE_{\text{true}}.$$19 beam and seven years of running, split equally between neutrino and antineutrino modes and between on-axis and off-axis positions, the study projects a determination of $$N_{\text{obs}}(E_{\text{rec}})\approx \int \Phi_\nu(E_{\text{true}})\,\sigma_\nu(E_{\text{true}})\,\epsilon(E_{\text{true}},E_{\text{rec}})\,N_{\text{targets}}\,dE_{\text{true}}.$$20 at low momentum transfer with about $$N_{\text{obs}}(E_{\text{rec}})\approx \int \Phi_\nu(E_{\text{true}})\,\sigma_\nu(E_{\text{true}})\,\epsilon(E_{\text{true}},E_{\text{rec}})\,N_{\text{targets}}\,dE_{\text{true}}.$$21 precision (Gouvêa et al., 2019).

The methodological point is that on-axis to off-axis flux ratios are tightly constrained by meson decay kinematics even when absolute normalization carries $$N_{\text{obs}}(E_{\text{rec}})\approx \int \Phi_\nu(E_{\text{true}})\,\sigma_\nu(E_{\text{true}})\,\epsilon(E_{\text{true}},E_{\text{rec}})\,N_{\text{targets}}\,dE_{\text{true}}.$$22–$$N_{\text{obs}}(E_{\text{rec}})\approx \int \Phi_\nu(E_{\text{true}})\,\sigma_\nu(E_{\text{true}})\,\epsilon(E_{\text{true}},E_{\text{rec}})\,N_{\text{targets}}\,dE_{\text{true}}.$$23 uncertainties. The analysis selects neutrino–electron scattering with $$N_{\text{obs}}(E_{\text{rec}})\approx \int \Phi_\nu(E_{\text{true}})\,\sigma_\nu(E_{\text{true}})\,\epsilon(E_{\text{true}},E_{\text{rec}})\,N_{\text{targets}}\,dE_{\text{true}}.$$24 and bins in $$N_{\text{obs}}(E_{\text{rec}})\approx \int \Phi_\nu(E_{\text{true}})\,\sigma_\nu(E_{\text{true}})\,\epsilon(E_{\text{true}},E_{\text{rec}})\,N_{\text{targets}}\,dE_{\text{true}}.$$25, exploiting the kinematic limit $$N_{\text{obs}}(E_{\text{rec}})\approx \int \Phi_\nu(E_{\text{true}})\,\sigma_\nu(E_{\text{true}})\,\epsilon(E_{\text{true}},E_{\text{rec}})\,N_{\text{targets}}\,dE_{\text{true}}.$$26. Angular resolution at the level of about $$N_{\text{obs}}(E_{\text{rec}})\approx \int \Phi_\nu(E_{\text{true}})\,\sigma_\nu(E_{\text{true}})\,\epsilon(E_{\text{true}},E_{\text{rec}})\,N_{\text{targets}}\,dE_{\text{true}}.$$27 is central to background rejection; energy resolution has a minor impact on the $$N_{\text{obs}}(E_{\text{rec}})\approx \int \Phi_\nu(E_{\text{true}})\,\sigma_\nu(E_{\text{true}})\,\epsilon(E_{\text{true}},E_{\text{rec}})\,N_{\text{targets}}\,dE_{\text{true}}.$$28 spectrum. Neutrino trident production is then used to lift the residual $$N_{\text{obs}}(E_{\text{rec}})\approx \int \Phi_\nu(E_{\text{true}})\,\sigma_\nu(E_{\text{true}})\,\epsilon(E_{\text{true}},E_{\text{rec}})\,N_{\text{targets}}\,dE_{\text{true}}.$$29 degeneracies that remain in $$N_{\text{obs}}(E_{\text{rec}})\approx \int \Phi_\nu(E_{\text{true}})\,\sigma_\nu(E_{\text{true}})\,\epsilon(E_{\text{true}},E_{\text{rec}})\,N_{\text{targets}}\,dE_{\text{true}}.$$30–e scattering alone (Gouvêa et al., 2019).

Neutrino Factory studies pursue an analogous flux-standard-candle strategy with a compact magnetized scintillating-fiber tracker. The reference detector is placed about $$N_{\text{obs}}(E_{\text{rec}})\approx \int \Phi_\nu(E_{\text{true}})\,\sigma_\nu(E_{\text{true}})\,\epsilon(E_{\text{true}},E_{\text{rec}})\,N_{\text{targets}}\,dE_{\text{true}}.$$31 downstream of the straight section, has roughly $$N_{\text{obs}}(E_{\text{rec}})\approx \int \Phi_\nu(E_{\text{true}})\,\sigma_\nu(E_{\text{true}})\,\epsilon(E_{\text{true}},E_{\text{rec}})\,N_{\text{targets}}\,dE_{\text{true}}.$$32 dimensions, a total mass of about $$N_{\text{obs}}(E_{\text{rec}})\approx \int \Phi_\nu(E_{\text{true}})\,\sigma_\nu(E_{\text{true}})\,\epsilon(E_{\text{true}},E_{\text{rec}})\,N_{\text{targets}}\,dE_{\text{true}}.$$33 tons, and operates in a $$N_{\text{obs}}(E_{\text{rec}})\approx \int \Phi_\nu(E_{\text{true}})\,\sigma_\nu(E_{\text{true}})\,\epsilon(E_{\text{true}},E_{\text{rec}})\,N_{\text{targets}}\,dE_{\text{true}}.$$34 dipole field. It consists of $$N_{\text{obs}}(E_{\text{rec}})\approx \int \Phi_\nu(E_{\text{true}})\,\sigma_\nu(E_{\text{true}})\,\epsilon(E_{\text{true}},E_{\text{rec}})\,N_{\text{targets}}\,dE_{\text{true}}.$$35 modules, each with a tracker station based on orthogonal $$N_{\text{obs}}(E_{\text{rec}})\approx \int \Phi_\nu(E_{\text{true}})\,\sigma_\nu(E_{\text{true}})\,\epsilon(E_{\text{true}},E_{\text{rec}})\,N_{\text{targets}}\,dE_{\text{true}}.$$36 scintillating-fiber layers and a calorimeter section of scintillator bars with embedded WLS fibers (Matev, 2011, Matev et al., 2011).

In full simulation, this detector achieves approximately Gaussian and unbiased angular resolution with $$N_{\text{obs}}(E_{\text{rec}})\approx \int \Phi_\nu(E_{\text{true}})\,\sigma_\nu(E_{\text{true}})\,\epsilon(E_{\text{true}},E_{\text{rec}})\,N_{\text{targets}}\,dE_{\text{true}}.$$37 for both muons and electrons, and muon momentum resolution reaching about $$N_{\text{obs}}(E_{\text{rec}})\approx \int \Phi_\nu(E_{\text{true}})\,\sigma_\nu(E_{\text{true}})\,\epsilon(E_{\text{true}},E_{\text{rec}})\,N_{\text{targets}}\,dE_{\text{true}}.$$38 at the highest energies. The key analysis channels are inverse muon decay and neutrino–electron elastic scattering, whose theoretically clean cross sections enable absolute flux normalization. The studies report that cut-based and template-based procedures improve signal-to-background from about $$N_{\text{obs}}(E_{\text{rec}})\approx \int \Phi_\nu(E_{\text{true}})\,\sigma_\nu(E_{\text{true}})\,\epsilon(E_{\text{true}},E_{\text{rec}})\,N_{\text{targets}}\,dE_{\text{true}}.$$39 to $$N_{\text{obs}}(E_{\text{rec}})\approx \int \Phi_\nu(E_{\text{true}})\,\sigma_\nu(E_{\text{true}})\,\epsilon(E_{\text{true}},E_{\text{rec}})\,N_{\text{targets}}\,dE_{\text{true}}.$$40–$$N_{\text{obs}}(E_{\text{rec}})\approx \int \Phi_\nu(E_{\text{true}})\,\sigma_\nu(E_{\text{true}})\,\epsilon(E_{\text{true}},E_{\text{rec}})\,N_{\text{targets}}\,dE_{\text{true}}.$$41, and conclude that the neutrino flux normalization can be measured with an uncertainty of order $$N_{\text{obs}}(E_{\text{rec}})\approx \int \Phi_\nu(E_{\text{true}})\,\sigma_\nu(E_{\text{true}})\,\epsilon(E_{\text{true}},E_{\text{rec}})\,N_{\text{targets}}\,dE_{\text{true}}.$$42 (Matev, 2011, Matev et al., 2011).

These examples clarify a broader point about Phase I design. A near-detector complex is not limited to supplying nuisance-parameter constraints for oscillation fits. When the detector combines precise angular reconstruction, charge identification, and strong control of hadronic activity, it can also perform low-$$N_{\text{obs}}(E_{\text{rec}})\approx \int \Phi_\nu(E_{\text{true}})\,\sigma_\nu(E_{\text{true}})\,\epsilon(E_{\text{true}},E_{\text{rec}})\,N_{\text{targets}}\,dE_{\text{true}}.$$43 electroweak measurements, absolute flux standardization through pure leptonic channels, and background measurements for charm and $$N_{\text{obs}}(E_{\text{rec}})\approx \int \Phi_\nu(E_{\text{true}})\,\sigma_\nu(E_{\text{true}})\,\epsilon(E_{\text{true}},E_{\text{rec}})\,N_{\text{targets}}\,dE_{\text{true}}.$$44 processes that directly condition the oscillation program (Gouvêa et al., 2019, Matev et al., 2011).