LHAASO water detector precisely measures atmospheric muon spectrum

Deep beneath the shower fronts of cosmic ray cascades, muons race through the atmosphere carrying a record of the most violent processes in the universe and the most subtle details of particle interactions in air. A team of Russian and Chinese physicists has now shown that one of the world’s most productive gamma-ray observatories can double as a precision instrument for studying these particles. In a study published in the journal Experimental Astronomy, researchers led by Yu. V. Stenkin of the Institute for Nuclear Research of the Russian Academy of Sciences demonstrated that the Water Cherenkov Detector Array (WCDA) of the LHAASO experiment, without any modification or reconstruction, can serve as an optimal “pair-meter” to measure the energy spectrum of near-horizontal atmospheric muons with energies beyond approximately 10 teraelectronvolts.

LHAASO, the Large High Altitude Air Shower Observatory, sits at an altitude of about 4,400 meters on Haizi Mountain in Sichuan Province, China. It was conceived as a multi-purpose facility for gamma-ray astronomy and cosmic ray physics, combining an extensive array of surface detectors with the WCDA, a vast pool-based Cherenkov detector designed primarily to catch the faint blue light emitted by charged particles traversing purified water. The new work extends the observatory’s scientific portfolio in a direction its designers never originally intended. The authors argue that the task list of LHAASO “will undoubtedly be extended in future,” and the muon spectrum measurement they propose is a concrete step in that direction, obtained essentially for free from an instrument already running.

The physical principle behind the proposal is the pair-meter technique, a method with a long pedigree in high-energy cosmic ray physics. When a sufficiently energetic muon passes through a dense medium, it occasionally interacts electromagnetically with the Coulomb field of an atomic nucleus and radiates a high-energy photon, which promptly converts into an electron-positron pair. The number of such pairs produced per unit length, and the energy carried by them, are statistically related to the energy of the parent muon. Historically, pair-meters were built as dedicated multi-layer calorimeters with ionization chambers or scintillator sheets stacked in depth, used by groups in experimental campaigns from the 1970s onward to measure the high-energy muon spectrum at sea level. The technique’s advantage is that it directly measures energy deposition rather than merely counting particles, giving it access to a range of muon energies that magnet spectrometers struggle to reach.

What the new study shows is that the WCDA naturally behaves like such a pair-meter. The detector consists of thousands of water cells, each viewed by a photomultiplier tube (PMT), arranged in large pools. A near-horizontal muon crossing the detector travels through several meters of water, producing Cherenkov light along its track and, intermittently, bremsstrahlung photons that convert into electron-positron pairs, each of which generates its own burst of Cherenkov light. The pattern of light flashes across the cell grid therefore encodes both the trajectory of the muon and the stochastic history of its energy losses. By counting and characterizing these bursts, the detector can reconstruct the muon’s energy in much the same way a classical pair-meter would.

The research is a careful simulation-driven feasibility study rather than a measurement. The authors modeled the response of the WCDA to the Cherenkov light produced by high-energy muons and their accompanying electromagnetic showers, taking into account the detailed geometry of the cell configuration, the possibility of optical crosstalk between neighboring cells, and the response characteristics of the photomultiplier tubes. Event simulations were performed with the GEANT4 toolkit, the standard Monte Carlo package for transporting particles through matter, while the theoretical muon fluxes and energy-loss processes were treated with the analytical machinery developed over decades by the Moscow school of muon physics, including cross-section calculations for bremsstrahlung, pair production and nuclear interactions following the work of Kelner, Kokoulin and Petrukhin.

This attention to detector detail matters because the energy estimation relies on rare, large energy-loss events. A 10 TeV muon traversing water loses energy mostly through ionization, which is nearly constant and carries little energy information; the fluctuating radiative losses are what carry the signal. The study had to confirm that the granularity of the WCDA cells is fine enough, and the PMT dynamic range and single-photoelectron response good enough, to distinguish a catastrophic bremsstrahlung burst from the steady glow of ionization light. Crosstalk, in which light leaks between adjacent cells, was found to be manageable within the existing configuration. The conclusion of the analysis is emphatic: WCDA without any reconstruction can serve as an optimal pair-meter for the task.

The scientific payoff of such a measurement is considerable. The atmospheric muon spectrum above 10 TeV is a sensitive probe of the composition of primary cosmic rays in the “knee” region, around a few petaelectronvolts, where the all-particle spectrum steepens and the origin of the break remains one of the oldest open questions in astrophysics. Muons at these energies are produced high in the atmosphere by primaries whose identities, protons or heavier nuclei, are imprinted in the muon flux and its angular distribution. Measurements of the muon charge ratio and spectrum at high energy also constrain models of hadronic interactions at center-of-mass energies inaccessible to fixed-target accelerators, a matter of practical importance for neutrino astronomy, since atmospheric muons and the neutrinos accompanying them form the dominant background for detectors such as IceCube.

Indeed, the study situates itself explicitly in a lineage of large-volume water and ice detectors used for muon physics, citing the measurements performed with the Moscow MSU detector and by the IceCube Collaboration, and pointing to related efforts by the HAWC experiment, which has pursued muon studies with its own water Cherenkov array. The LHAASO team’s contribution is to show that the necessary pair-meter capability is already latent in the WCDA design. In earlier publications, the group had argued for the relevance of extensive air shower muon studies and outlined the possibility in principle; the new paper delivers the full detector-response analysis, including figures quantifying light collection after muon passage and comparisons of simulated data with actual WCDA data processed by the collaboration.

The division of labor documented in the paper illustrates the breadth of the effort. Stenkin wrote the main manuscript; Butkevich calculated muon fluxes and made key estimations; Shchegolev carried out the GEANT4 event simulations; Kurinov processed WCDA data for comparison with simulations; Karpikov analyzed data from the KM2A, LHAASO’s other surface array, to assess its possible use in the program; Kuleshov simulated the detector response to extensive air showers; Maliy simulated light collection following muon passage; Ma analyzed data and discussed results; and Yao is responsible for the stable operation and data taking of the WCDA itself. The work was supported by the Russian Ministry of Science and Higher Education and by the National Natural Science Foundation of China, a concrete example of Russian-Chinese cooperation in fundamental physics.

For the observatory itself, the result is strategically attractive because it requires no new construction and no downtime. The WCDA already records gigabytes of data per second, and muon events arriving near horizontally are a well-defined subset of its data stream that can be selected offline. Every high-energy muon that punches through the water volume becomes a data point on the cosmic ray spectrum, effectively converting the world’s most sensitive gamma-ray detector at ultra-high energies into a second instrument of equal ambition. If the planned analysis proceeds to a full spectrum measurement, it would extend direct knowledge of the atmospheric muon spectrum into a region where only sparse and sometimes discrepant data exist, and it would do so with an instrument whose calibration, stability and throughput are already proven by years of gamma-ray observations.

The study also carries a broader lesson for experimental design in particle astrophysics: multi-purpose detectors can yield physics well beyond their original specifications when their response is understood in sufficient detail. The WCDA was built to detect the isotropic Cherenkov glow of air shower particles sweeping across its surface, not the sparse tracks of single high-energy muons. Yet the same PMTs, the same water volumes and the same electronics that serve gamma-ray astronomy turn out to be precisely the apparatus a pair-meter demands. As the authors put it, the experiment’s task number will be extended in future, and with this work, the atmospheric muon spectrum, a quantity sought by cosmic ray physicists since the pioneering pair-meter experiments of the 1970s, now has a new, unusually powerful route to measurement at the roof of the world.