NEVOD-DECOR: Cosmic-Ray Detector

• NEVOD-DECOR is a surface-based cosmic-ray installation that combines a Cherenkov water calorimeter with a DECOR tracking system to study muon bundles in extensive air showers.
• It integrates a 2000 m³ water detector and multiple supermodules for precise calorimetric energy measurement and angular resolution of muon trajectories.
• The system employs local muon density spectra analysis to characterize cosmic-ray spectral features like the ‘second knee’ and to investigate the muon puzzle.

Searching arXiv for NEVOD-DECOR papers to ground the article in the latest and directly relevant literature. Tool unavailable in this environment. Proceeding with the provided arXiv records and details. NEVOD-DECOR is a surface-based cosmic-ray installation at MEPhI (Moscow) built around the NEVOD Cherenkov water calorimeter and the DECOR coordinate-tracking detector. In the published literature, it functions as a hybrid system for the study of inclined muon bundles in extensive air showers, local muon density spectra (LMDS), calorimetric energy deposits in water, near-horizontal and upward-going albedo muons, and large-scale cosmic-ray anisotropy; later analyses extend the reconstructed primary-energy coverage to approximately $2\,\mathrm{PeV}$–$3\,\mathrm{EeV}$ (Bogdanov et al., 7 Aug 2025).

1. Configuration of the experimental complex

The NEVOD complex is centered on a Cherenkov water detector at ground level in the MEPhI campus. The water calorimeter has an active volume of $2000\,\mathrm{m^3}$, corresponding to a $$26\,\mathrm{m}\times 9\,\mathrm{m}\times 9\,\mathrm{m}$$ tank, and is instrumented with 91 quasi-spherical measuring modules arranged on 25 vertical strings. Each quasi-spherical module contains six FEU-200 photomultipliers oriented along the coordinate axes, providing near-isotropic sensitivity to Cherenkov light. The two-dynode readout extends the dynamic range from 1 to $10^5$ photoelectrons (Bogdanov et al., 2022).

Around the water volume, DECOR is deployed as eight vertical supermodules mounted in the surrounding galleries. In the NEVOD descriptions used for LMDS analyses, each supermodule comprises eight vertical planes of streamer-tube chambers with orthogonal strip readout and an effective area of $8.4\,\mathrm{m^2}$ per supermodule; the full DECOR acceptance for muon bundles is approximately $70\,\mathrm{m^2\,sr}$, with angular resolution better than $0.8^\circ$. Other technical descriptions give each supermodule as $3.1\times 2.7\,\mathrm{m^2}$, again with eight planes and spatial and angular resolutions at the $\lesssim 1\,\mathrm{cm}$ and $3\,\mathrm{EeV}$0 level, respectively (Kokoulin et al., 2017).

Several auxiliary subsystems have been integrated into the complex. The Calibration Telescope System (CTS) consists of two horizontal planes of 40 plastic scintillation counters each, arranged in a chessboard pattern over an area $3\,\mathrm{EeV}$1 above and below the water volume; after the 2013 upgrade, its bottom plane also recorded the muon component of inclined air showers with an effective angular acceptance peaked at $3\,\mathrm{EeV}$2 for muon bundles (Kokoulin et al., 2017). The broader NEVOD infrastructure also includes the NEVOD-EAS cluster-type array for air-shower size, axis, and direction reconstruction, and the PRISMA-32 en-detector array for simultaneous measurements of hadronic and electromagnetic air-shower components (Shulzhenko et al., 2016, Stenkin et al., 2015).

A recurring design feature is the use of shielding by the water tank itself. In selected azimuth sectors, six of the eight DECOR supermodules are shadowed by the NEVOD water volume, raising the muon detection threshold to approximately $3\,\mathrm{EeV}$3 and suppressing electromagnetic and hadronic contamination in inclined-bundle measurements (Bogdanov et al., 2022).

2. Detection principles and core observables

In DECOR, a muon bundle is defined as a group of spatially and temporally correlated muon tracks reconstructed in one or more supermodules. Bundle multiplicity $3\,\mathrm{EeV}$4 is the number of muon tracks in the event. In analyses of inclined bundles, DECOR reconstructs individual tracks in each supermodule, imposes a parallelism cut within a $3\,\mathrm{EeV}$5 cone, and determines the bundle direction $3\,\mathrm{EeV}$6 from a global straight-line fit to the track segments (Kokoulin et al., 2017).

The calorimetric observable is supplied by NEVOD. The detector records the total Cherenkov-light yield, written either as $3\,\mathrm{EeV}$7 or as $3\,\mathrm{EeV}$8, across all photomultipliers. Since muon energy loss in water follows

$3\,\mathrm{EeV}$9

the total light yield is, to first order, proportional to the sum of muon energies and to the total energy deposit of the bundle in water (Bogdanov et al., 2022, Bogdanov et al., 2016).

The principal density observable is the local muon density. In the 2017 LMDS formulation it is defined as

$2000\,\mathrm{m^3}$0

where $2000\,\mathrm{m^3}$1 is the reconstructed multiplicity and $2000\,\mathrm{m^3}$2 is the effective detection area projected into the shower front. Later NEVOD-DECOR papers write the same quantity as

$2000\,\mathrm{m^3}$3

or, in the bias-corrected form used for energy-deposit studies,

$2000\,\mathrm{m^3}$4

where $2000\,\mathrm{m^3}$5 accounts for the bias from Poisson fluctuations and the integral slope $2000\,\mathrm{m^3}$6 of the density spectrum (Kokoulin et al., 2017, Bogdanov et al., 2022, Bogdanov et al., 2016).

For calorimetric studies of bundles, the specific deposit is introduced to remove the trivial scaling with multiplicity and acceptance. Two equivalent notations appear in the literature: $2000\,\mathrm{m^3}$7 These observables are used as proxies for the average muon energy in the bundle after detector-response calibration with Geant4 (Bogdanov et al., 2022, Bogdanov et al., 2016).

CTS implements a different but related counting principle. There, muon bundles are recorded as coincidences of hit scintillation counters in the bottom plane, and the hit-counter multiplicity $2000\,\mathrm{m^3}$8 is used as a proxy for bundle size. In the CTS analyses, the effective bundle angle $2000\,\mathrm{m^3}$9 is taken from the measured muon-angular distribution proportional to $$26\,\mathrm{m}\times 9\,\mathrm{m}\times 9\,\mathrm{m}$$0 (Kokoulin et al., 2017).

3. Local muon density spectra methodology

The LMDS method is the central analysis framework of NEVOD-DECOR. At fixed zenith angle, the differential local muon density spectrum is assumed to follow a power law,

$$26\,\mathrm{m}\times 9\,\mathrm{m}\times 9\,\mathrm{m}$$1

with spectral slope $$26\,\mathrm{m}\times 9\,\mathrm{m}\times 9\,\mathrm{m}$$2 obtained from fits of $$26\,\mathrm{m}\times 9\,\mathrm{m}\times 9\,\mathrm{m}$$3 versus $$26\,\mathrm{m}\times 9\,\mathrm{m}\times 9\,\mathrm{m}$$4 in a specified density interval (Kokoulin et al., 2017).

In the later notation, the measured quantity is the event flux per unit density, per unit solid angle, and per unit time,

$$26\,\mathrm{m}\times 9\,\mathrm{m}\times 9\,\mathrm{m}$$5

A phenomenological reference form,

$$26\,\mathrm{m}\times 9\,\mathrm{m}\times 9\,\mathrm{m}$$6

with $$26\,\mathrm{m}\times 9\,\mathrm{m}\times 9\,\mathrm{m}$$7, $$26\,\mathrm{m}\times 9\,\mathrm{m}\times 9\,\mathrm{m}$$8, and $$26\,\mathrm{m}\times 9\,\mathrm{m}\times 9\,\mathrm{m}$$9, is fitted to the joint $10^5$0 distribution by maximum likelihood. The observed LMDS in each $10^5$1 cell is then obtained from the ratio $10^5$2 multiplied by the reference spectrum, where $10^5$3 comes from a full Monte Carlo simulation of detector response including Poisson fluctuations and track-masking effects (Bogdanov et al., 7 Aug 2025).

The theoretical LMDS is constructed by convolving a primary spectrum with simulated muon lateral distribution functions from CORSIKA. In one form used for bundle-intensity modeling,

$10^5$4

where $10^5$5 is the probability that a shower of primary energy $10^5$6 and zenith $10^5$7 produces a local density between $10^5$8 and $10^5$9 at the observation point. In the continuum formulation of the 2025 analysis, the integral LMDS is written as

$8.4\,\mathrm{m^2}$0

with $8.4\,\mathrm{m^2}$1 determined from the muon lateral distribution function $8.4\,\mathrm{m^2}$2 by solving $8.4\,\mathrm{m^2}$3 (Bogdanov et al., 2022, Bogdanov et al., 7 Aug 2025).

The mapping from local density to primary energy is simulation-based. In the 2017 reconstruction, full CORSIKA ($8.4\,\mathrm{m^2}$4) simulations of the shower muon component for pure proton and iron primaries, using the QGSJET model, yield an approximate calibration curve

$8.4\,\mathrm{m^2}$5

with $8.4\,\mathrm{m^2}$6–$8.4\,\mathrm{m^2}$7. In the anisotropy analysis, a more explicit empirical estimator is used: $8.4\,\mathrm{m^2}$8 with energies in GeV and $8.4\,\mathrm{m^2}$9 in $70\,\mathrm{m^2\,sr}$0 (Kokoulin et al., 2017, Trinchero et al., 2022).

The simulation backbone has evolved with time. The published analyses employ CORSIKA $70\,\mathrm{m^2\,sr}$1, $70\,\mathrm{m^2\,sr}$2, $70\,\mathrm{m^2\,sr}$3, and $70\,\mathrm{m^2\,sr}$4; hadronic-model comparisons include QGSJET, QGSJET-II-04, SIBYLL-2.3, SIBYLL-2.3c, EPOS-LHC, and later EPOS LHC-R, QGSJET-III-01, and SIBYLL-2.3e. The 2025 study also uses two-dimensional muon LDFs to account for geomagnetic-induced asymmetries (Kokoulin et al., 2017, Bogdanov et al., 2016, Bogdanov et al., 2022, Bogdanov et al., 7 Aug 2025).

4. Spectral features: the knee, the second knee, and composition-sensitive trends

One of the best-known NEVOD-DECOR results is the observation of a steepening in the LMDS around a primary energy of about $70\,\mathrm{m^2\,sr}$5. In the 2017 analysis, DECOR reconstructed differential LMDS for effective zenith angles $70\,\mathrm{m^2\,sr}$6, $70\,\mathrm{m^2\,sr}$7, and $70\,\mathrm{m^2\,sr}$8, while CTS measured the near-vertical region at $70\,\mathrm{m^2\,sr}$9. In both subsystems, two power-law fits were performed in intervals corresponding to $0.8^\circ$0–$0.8^\circ$1 and $0.8^\circ$2, and in both cases the slope increased above the characteristic density mapped to $0.8^\circ$3 (Kokoulin et al., 2017).

Measurement	Low-$0.8^\circ$4 integral slope	High-$0.8^\circ$5 integral slope / change
DECOR combined	$0.8^\circ$6	$0.8^\circ$7, $0.8^\circ$8
CTS	$0.8^\circ$9	$3.1\times 2.7\,\mathrm{m^2}$0, $3.1\times 2.7\,\mathrm{m^2}$1

For DECOR, the change in slope was reported as $3.1\times 2.7\,\mathrm{m^2}$2, corresponding to $3.1\times 2.7\,\mathrm{m^2}$3. For CTS, $3.1\times 2.7\,\mathrm{m^2}$4, corresponding to $3.1\times 2.7\,\mathrm{m^2}$5, with additional systematic uncertainties from the 1.3 correction factor for apparent density enhancement and from the assumed angular distribution contributing $3.1\times 2.7\,\mathrm{m^2}$6 to $3.1\times 2.7\,\mathrm{m^2}$7 (Kokoulin et al., 2017).

The paper interprets this “second knee” as evidence that the muon-density spectrum steepens near $3.1\times 2.7\,\mathrm{m^2}$8, indicating a change in the primary cosmic-ray composition and/or interaction characteristics above approximately $3.1\times 2.7\,\mathrm{m^2}$9. It explicitly notes that, in rigidity-dependent acceleration models, such a feature may correspond to the cutoff of the heaviest Galactic components or to the onset of extragalactic protons. The same paper states that the concordance of DECOR and CTS measurements across $\lesssim 1\,\mathrm{cm}$0–$\lesssim 1\,\mathrm{cm}$1 zenith angles and $\lesssim 1\,\mathrm{cm}$2–$\lesssim 1\,\mathrm{cm}$3 provides robust experimental evidence for this feature in the muon sector, complementary to electron-size measurements by KASCADE-Grande, Tunka-133, and IceTop (Kokoulin et al., 2017).

The longer-baseline 2012–2023 analysis extends these composition-sensitive inferences. Using LMDS from $\lesssim 1\,\mathrm{cm}$4 to $\lesssim 1\,\mathrm{cm}$5, NEVOD-DECOR reconstructs an all-particle spectrum from $\lesssim 1\,\mathrm{cm}$6 to $\lesssim 1\,\mathrm{cm}$7, recovering the knee at $\lesssim 1\,\mathrm{cm}$8–$\lesssim 1\,\mathrm{cm}$9, a slight flattening identified as a “second knee” near $3\,\mathrm{EeV}$00, and points approaching the ankle region near $3\,\mathrm{EeV}$01. In the same analysis, the WHISP-defined $3\,\mathrm{EeV}$02-parameter rises from $3\,\mathrm{EeV}$03–0.4 at $3\,\mathrm{EeV}$04 to $3\,\mathrm{EeV}$05–1.0 near $3\,\mathrm{EeV}$06 under the stated modeling assumptions, which the paper describes as an extremely heavy composition (Bogdanov et al., 7 Aug 2025).

5. Muon-bundle calorimetry and the “muon puzzle”

A distinct but closely related NEVOD-DECOR result concerns the discrepancy between observed muon-bundle intensities and the predictions of widely used hadronic interaction models. In the 2022 inclined-bundle analysis, data from May 2012 to March 2021 were selected with $3\,\mathrm{EeV}$07, yielding $3\,\mathrm{EeV}$08 events for $3\,\mathrm{EeV}$09 over $3\,\mathrm{EeV}$10 and $3\,\mathrm{EeV}$11 events for $3\,\mathrm{EeV}$12 over $3\,\mathrm{EeV}$13. LMDS were measured in nine zenith intervals from $3\,\mathrm{EeV}$14 to $3\,\mathrm{EeV}$15 and compared with CORSIKA $3\,\mathrm{EeV}$16 calculations using QGSJET-II-04, SIBYLL-2.3c, and EPOS-LHC for pure proton and pure iron primaries (Bogdanov et al., 2022).

At moderate angles, corresponding to $3\,\mathrm{EeV}$17, the data follow the light-composition proton curves. At the largest angles, corresponding to $3\,\mathrm{EeV}$18, the data lie close to or exceed the iron curves in all three interaction models. The same analysis maps the measurements to the WHISP $3\,\mathrm{EeV}$19-scale,

$3\,\mathrm{EeV}$20

and reports that $3\,\mathrm{EeV}$21 rises steadily above $3\,\mathrm{EeV}$22, reaching $3\,\mathrm{EeV}$23–1.0 around $3\,\mathrm{EeV}$24 in all three models. Under those assumptions, the required composition is described as “extremely heavy” (Bogdanov et al., 2022).

The contradiction with fluorescence measurements of $3\,\mathrm{EeV}$25, which favor light primaries with $3\,\mathrm{EeV}$26–4 at $3\,\mathrm{EeV}$27, is identified as the “muon puzzle.” The NEVOD-DECOR papers formulate the problem in explicitly model-comparison terms: either modern interaction models under-produce high-energy muons, or additional processes become important at laboratory energies $3\,\mathrm{EeV}$28 (Bogdanov et al., 2022).

NEVOD-DECOR addresses this discrepancy not only through counting but also through calorimetry. Using the Geant4 $3\,\mathrm{EeV}$29 detector model, tuned on single near-horizontal muons with $3\,\mathrm{EeV}$30, the response to artificial bundles of known energy and density is established. With the normalized specific deposit, the average muon energy is extracted as

$3\,\mathrm{EeV}$31

The measured $3\,\mathrm{EeV}$32 at fixed density increases from approximately $3\,\mathrm{EeV}$33 at $3\,\mathrm{EeV}$34 to approximately $3\,\mathrm{EeV}$35–$3\,\mathrm{EeV}$36 near $3\,\mathrm{EeV}$37. For $3\,\mathrm{EeV}$38, the quoted values are approximately $3\,\mathrm{EeV}$39 at $3\,\mathrm{EeV}$40, $3\,\mathrm{EeV}$41 at $3\,\mathrm{EeV}$42, $3\,\mathrm{EeV}$43 at $3\,\mathrm{EeV}$44, and $3\,\mathrm{EeV}$45 at $3\,\mathrm{EeV}$46. Above $3\,\mathrm{EeV}$47, the measured $3\,\mathrm{EeV}$48 exceeds model predictions by $3\,\mathrm{EeV}$49–$3\,\mathrm{EeV}$50 in the last four points (Bogdanov et al., 2022).

An earlier energy-deposit study had already reported a milder precursor of the same tendency. For $3\,\mathrm{EeV}$51, corresponding to $3\,\mathrm{EeV}$52, the specific deposit $3\,\mathrm{EeV}$53 showed an approximately $3\,\mathrm{EeV}$54–20% upward deviation from CORSIKA $3\,\mathrm{EeV}$55 plus SIBYLL-2.3 expectations, although the last density bins had limited statistics ($3\,\mathrm{EeV}$56–49) (Bogdanov et al., 2016). This suggests continuity between the earlier bundle-calorimetry anomaly and the later high-statistics formulation of the muon puzzle.

6. Complementary programs and subsystem extensions

NEVOD-DECOR has also been used for measurements of albedo muons, defined as atmospheric muons scattered in the ground into the upper hemisphere after traversing tens of meters of soil. These were studied in the zenith range $3\,\mathrm{EeV}$57 using coincident triggers in two oppositely mounted DECOR supermodules. Two data sets, $3\,\mathrm{EeV}$58 in 2002–2004 and $3\,\mathrm{EeV}$59 in 2011–2015, were combined for a total live time of about $3\,\mathrm{EeV}$60. Across both runs, $3\,\mathrm{EeV}$61 near-horizontal muons were recorded, of which 5,717 were identified as albedo muons in the interval $3\,\mathrm{EeV}$62–$3\,\mathrm{EeV}$63. Comparison with Monte Carlo transport through soil showed that the point-nucleus Molière model overestimates the flux by up to approximately 50% near $3\,\mathrm{EeV}$64, whereas the finite-nucleus model tracks the data within statistical errors across the full $3\,\mathrm{EeV}$65–$3\,\mathrm{EeV}$66 range (Khokhlov et al., 2017).

The complex has also been adapted for anisotropy studies using muon bundles as directional tracers of primary cosmic rays. For 2012–2022, about 14 million events in the local zenith-angle range $3\,\mathrm{EeV}$67–$3\,\mathrm{EeV}$68 were accumulated. The published method corrects the bundle rate for meteorological modulation through

$3\,\mathrm{EeV}$69

with $3\,\mathrm{EeV}$70 and $3\,\mathrm{EeV}$71. After correction, the run-to-run rms spread in bundle rate is reduced from approximately 5–7% to approximately 1–2%. Rayleigh fits in right ascension then give a first-harmonic amplitude $3\,\mathrm{EeV}$72 at $3\,\mathrm{EeV}$73 and $3\,\mathrm{EeV}$74 at $3\,\mathrm{EeV}$75, with phases broadly consistent with the Galactic-center direction within the stated uncertainties (Trinchero et al., 2022).

Two associated detector developments broaden the physical reach of the NEVOD-DECOR site. PRISMA-32, constructed in February 2012 on the fourth floor, uses 32 ZnS(Ag)+$3\,\mathrm{EeV}$76LiF scintillation en-detectors to measure prompt electromagnetic signals and delayed thermal-neutron captures. Its thermal-neutron lateral distribution is fitted by a double exponential with scales $3\,\mathrm{EeV}$77 and $3\,\mathrm{EeV}$78, while the mean neutron arrival-time distribution is described by two exponentials with $3\,\mathrm{EeV}$79 and $3\,\mathrm{EeV}$80 (Stenkin et al., 2015). NEVOD-EAS, deployed in 2015–2016 as a cluster array over approximately $3\,\mathrm{EeV}$81, reconstructs shower size, core position, and arrival direction from scintillation detector stations; the central part achieved an arrival-direction resolution of $3\,\mathrm{EeV}$82, preliminary core-position resolution of order $3\,\mathrm{EeV}$83, and shower-size resolution of order 10% (Shulzhenko et al., 2016).

In the 2025 synopsis, these developments are linked to further expansion of the inclined-bundle program. The paper states that future upgrades, specifically the TREK drift-chamber tracker with approximately $3\,\mathrm{EeV}$84 area and $3\,\mathrm{EeV}$85 two-track resolution, together with enhanced NEVOD water calorimetry, are intended to extend the energy range, improve muon counting precision, and enable measurement of muon energy deposits in support of ongoing work on the muon puzzle and extensive-air-shower physics (Bogdanov et al., 7 Aug 2025).