WCDA Detector of the Lhaaso Experiment as a Pair-Meter to Measure Atmospheric Muon Spectrum

WCDA Detector of the Lhaaso Experiment as a Pair-Meter to Measure Atmospheric Muon Spectrum | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article WCDA Detector of the Lhaaso Experiment as a Pair-Meter to Measure Atmospheric Muon Spectrum Yu. V. Stenkin, A. V. Butkevich, I. S. Karpikov, K. O. Kurinov, and 4 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-6998918/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 22 Apr, 2026 Read the published version in Experimental Astronomy → Version 1 posted 9 You are reading this latest preprint version Abstract The LHAASO (Large High Altitude Air Shower Observatory) experiment is a multi-purpose experiment for gamma-ray astronomy, cosmic ray physics and for many other tasks. Its task number will be undoubtedly extended in future. We proposed to use existing WCDA (Water Cherenkov Detector Array being a part of LHAASO) as a pair-meter to measure atmospheric muon energy spectrum. This work confirms that WCDA without any reconstruction can serve as an optimal pair-meter to study near-horizontal atmospheric muons with energy beyond ~ 10 TeV. In this article we study response of the WCDA detector to Cherenkov light produced by high energy muons and its accompanying, taking into account the cells configuration, possible crosstalk between cells, and photomultiplier (PMT) characteristics. Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Introduction Study of atmospheric muon fluxes at highest energies continued for decades but the problem is not still solved. Working worldwide muon detectors does not measure muon energy – only cosmic ray muon flux or muon number in EAS (Extensive Air Shower) or in parallel muon groups. However, muon energy spectrum study has a special interest allowing one to measure primary cosmic ray spectrum at the Earth’s surface or at shallow depths underground, underwater or under ice. Muon magnetic spectrometers, such as MUTRON [ 1 ] and DEIS [ 2 ] used in previous years, had an upper limit to muon energy of ~ 10 TeV due to small deviation of such relativistic muons in the magnetic field. This is why muon spectrum has never been measured above this energy using such technique. Pair-meter technique is free of this limit. Moreover, the higher the muon energy, the higher is accuracy of the method. As known, muon energy losses dE µ /dx = - a - b E µ , where a is slowly changing ionization losses, a ~ 2MeV/(g/cm 2 ) and b = b br + b ph + b pair is sum of fractional energy loss in the three radiation processes. Parameter a/b ≈500 GeV shows when radiation losses dominate and thus well above this energy one can use the energy losses to estimate muon energy E µ . Note that cross-section for electron-positron pair production by muon is high enough and slowly depends on E µ while energy transfer is proportional to E µ . G.T. Zatsepin in Ref. [ 3 ] firstly proposed the idea of the method and the name “pair-meter” was given to the method later [ 4 ]. Some estimations of the pair-meter configuration in water and the method accuracy applied to DUMAND proposal can be found in [ 5 ]. Theory of the muon pair-meter was developed in [ 6 ], where optimal parameters of the “ideal pair-meter” have been estimated. Nevertheless, up to date no one full-scale pair-meter has been constructed anywhere in the world. The reason is that the “ideal pair-meter” should have very big size (~ 1000 rad. lengths or ~ few hundred meters in water), it should be a track (and fully active) detector to measure ionization (or Cherenkov light), i. e. it should be mostly scintillator or Cherenkov media. In a case of WCDA we have water as a fully active transparent registration media. Therefore, Cherenkov light production should be added for all particles, including parent muon, producing significant amount of light only at rather low energy below our measurements range. As we show below, WCDA parameters are very close to “ideal pair-meter”. Moreover, this is already working detector and nothing has to be change there. The WCDA’ detailed description can be found in [ 7 , 8 ]. It is a huge water Cherenkov detector of 260x300x4.5 m 3 size, composed of 3 water pools, each subdivided by light-protected cells of 5x5x4.5 m 3 size. This makes it practically an optimal pair-meter to study atmospheric near horizontal high-energy muons. For WCDA we have track length T in radiation lengths t 0 (36 g/cm 2 for water), depending on the number of passed cells (n) of 13.9 r. l. each, as T = 13.9n ~ 83¸834 r. l. for n = 6¸60. Therefore, relative accuracy of the muon energy reconstruction can be estimated using a formula from [ 6 ] as δ=(137/Τ) 1/2 ≈ 1.28¸0.40 accordingly. Total side area of the Cherenkov detector is about S ≈ 1350 m 2 for zenith angles 80–90 degrees. Moreover, upper water surface area can also be used at angles 70–88 degrees when muon entries the detector through roof or walls thus making real detector much higher (~ 20000 m 2 ). One could compare it with a pair-meter constructed on a base of MUTRON, it had area only S = 7 m 2 and much lower length. Atmospheric muon energy spectrum measuring were performed in a few experiments up to date [ 9 , 10 ] in energy range up to E µ ~ 1 PeV. Authors of Ref. [ 9 ] tried to use existing underground detector BUST (Baksan Underground Scintillator Telescope) [ 11 ] as a pair-meter but its features with only 4 scintillator layers of rather small thickness were far from the optimal pair-meter parameters [ 6 ]. As a result, the data statistical errors did not allow them to give an unambiguous result. IceCube results obtained using alternative methods with the giant neutrino telescope [ 12 ] have rather low statistical errors. Design of this telescope is optimized for neutrino interactions inside the huge ice cube, but it has no subdivision to individual measuring cells and thus it cannot serve as a pair-meter. This is why the authors used another technique for muon energy measurements: muon group multiplicity or measurement of single muon high-energy interactions in ice through other processes (bremsstrahlung or inelastic nuclear interactions). As a result, the authors obtained some unexpected results and they are not sure they considered all systematic errors. For example, it is interesting that the IceCube result agrees well with a pure power law spectrum with slope γ ~ 3.7 at muon energy up to 1.58 PeV (i.e. well beyond so-called “knee” in primary cosmic rays at ~ 5 PeV). The authors explain it by an addition of prompt muons from decays of heavy charmed mesons just in the “knee” region and just in the needed amount. An attempt to study near horizontal muon flux was made by the HAWC collaboration using its large water Cherenkov detector array [ 13 ]. However, there are no muon energy measurements in this experiment. The task of the HAWC group was measuring of muon absorption in rock by selecting muon tracks from a nearby mountain. An example of recorded near horizontal muon is shown there as a track crossing many water Cherenkov tanks [ 13 ]. Sure, similar events do exist in WCDA. Therefore, the situation with muon spectrum measurement is still hot and new experiments needed because muons are produced by cosmic rays through pion, kaon and heavier meson decays in air and both muon energy or muon number spectrum can serve as energy estimators for primary cosmic rays spectrum recovering. Extension of the LHAASO experiment tasks The Large High Altitude Air Shower Observatory is one of the biggest multipurpose and highly informative experiment in the world, running since 2019 [ 7 , 8 ]. It has many aims concentrated mostly in fields of Gamma ray astronomy, Cosmic ray physics, etc. Outstanding results have been already obtained by this experiment [ 13 ] but up to date there were no any tasks connected with neutrino astrophysics or with atmospheric muon energy spectrum measurements. The experiment consists of several independent arrays each having its own tasks: Water Cherenkov Detector Array designed for gamma-ray astronomy and looking as a huge water pool subdivided into many light protected water cells. The latter makes the WCDA being a large track detector at near horizontal directions making it suitable for astrophysical neutrino interactions search, as shown in [ 14 ]. Current proposal is a by-product for the above task, where near horizontal muons produce a background for neutrino event search. This is a ready to use pair-meter detector and nothing has to be changed in its construction. Only special data processing and special trigger could be added. Therefore, one could regard WCDA as a working full-scale track detector having the optimal pair-meter parameters. Angular resolution δΘ for muon trajectory depends on its length and our simple estimation gave δΘ ≈ 0.4 o for muon track length l = 60m. We could mention here that we need not very good angular resolution for this research because we have only to select muons inside the working angular range for near horizontal muons of say 70 ÷ 89 o . Simulations 2.1. Muon tracks simulation To apply the pair-meter method to the LHAASO experiment we made a series of detailed Monte-Carlo simulations, considering all known WDCA Cherenkov detector parameters. First, we made simulations using GEANT4 codes [ 15 ] of the WCDA ionization response to passage of UHE (Ultra High Energy) near horizontal muons [ 16 ]. At the next step of the experiment modeling, using GEANT4, we simulated Cherenkov light produced by relativistic muon in water Cherenkov detector taking into account cells configuration, its possible cross talk, and PMTs positions. The problem is that the cell curtains do not shield full 4πgeometry of the cell and small amount of light can penetrate to neighboring cells. The cell geometry, its size, PMT positions, curtain configuration, PMT’s photo-cathode size and quantum efficiency were taken into account. Figure 1 (left panel) shows a simulated example of UHE (3.16 PeV) near horizontal (88 deg.) muon passage through the detector when entering through the detector building roof. The mean light production recalculated to number of photoelectrons (npe) per cell for this track is equal to 258 npe/cell. As seen, muon track can be identify without any problem thus confirming that the detector performances and cell size are good and this allows us to search for near horizontal muon tracks without any detector changes. Right panel in Fig. 1 shows the same simulated event showing produced light in cells if it exceeds 10 npe. This picture shows the event more clearly removing cells with low energy deposition and, probably cross talk or background cell hits. Applying the lower threshold allows one also removing low energy deposit PMT hits produced mainly by low energy accompanies of the UHE muon passed through air and scattered back to water. Considering fast timing and recorded light in each cell (251 npe/cell in this track example with threshold), we can estimate the muon energy and its direction with acceptable accuracy, when the track length is long enough. The light in the WCDA cells produced separately by only due to Cherenkov light, ionization and pair production process parent muon are shown in Fig. 2 for muons of energy 316 GeV (left) and 10 TeV (right). Only cells with more than 10 npe are shown. Figures legends present full event information including mean npe/cell. Lower threshold for collected Cherenkov light about 10 photo-electrons deposit per cell allows one removing of low energy deposit PMT hits produced mainly by low energy accompanies of the UHE muon passed through air and scattered back to water. Considering fast timing and recorded light in each cell we can estimate the muon energy and its direction with acceptable accuracy, when the track length is long enough. Later we will study these dependences with better accuracy and will try to develop an algorithm for the best muon energy recovering. A question could arise: is number of photo-electrons produced by muon in the detector proportional to its energy or not? Should one separates energy deposit through only pair production or not? To answer this question we simulated all muon interactions in detector’s water and then only by pair production process. Because of these simulations, we have a statistical plot showing how the above processes depend on muon energy, presented in Fig. 3 . As seen, above E µ > ~ 3 TeV pair production prevails and produced light really follows linear function on muon energy. Another question concerns so-called catastrophic muon interactions, i.e. bremsstrahlung and nuclear interactions. These muon energy losses result in almost full energy loss and after such interaction muon track will end with a large energy deposit. Such events would be clearly seen in WCDA and could be rejected or muon energy estimation could be made on the track before such interaction if its length is long enough. Another question concerns the method accuracy. We gave a brief error estimation in Introduction. In addition, we have made special simulations for recorded light distribution in 3000 events for 100 TeV near horizontal muons in WCDA shown in Fig. 4 . As seen the distribution follows well log-normal fit for all muon energies above 100 TeV. We should note here that our aim is to measure muon energy spectrum and we need not to know exactly individual muon energy. It means we need to measure and its systematic errors are small enough. 2.2. Cross talk simulation Cross talk between neighboring cells, if any, can make wrong cell hits close to the trajectory. To check it we made special simulation estimating this effect in Considering real curtains geometry and their sizes and light reflection coefficient R = 0.05, we estimated the light cross talk between the cells as one close to negligible as shown in Fig. 5 , especially if lower threshold for the cell light is applied. Also shown are results with hypothetically modified light protection curtain reflection R and geometry when they are: a) for R = 0 (red line); b) extended up to water-air boundary (green); c) extended down up to the pool bottom (blue) and d) extended both up and down (magneta). As seen, the crosstalk even now (with regular curtains) is as low as ~ 1% for zenith angles 80–88 degrees and it can be excluded by a lower threshold of ~ 10 npe/cell. One can also see that the crosstalk is mostly produced by a gap (~ 0.5 m) between pool bottom and curtain, because this gap is closer to the PMTs situated near the pool bottom. Expected near horizontal muon flux To estimate the expected UHE near horizontal atmospheric muon flux we use the spectrum of conventional (decay) and “prompt” muons calculated in Refs. [ 17 , 18 ], respectively in the energy range 0–10 PeV. The spectra of “direct” muons were estimated within two models for the production of charmed particles. We calculated the expected number of background events per year for both fluxes of the “prompt” muons. In our calculation, we took into account the muon energy losses due to bremsstrahlung [ 19 ], pair production [ 3 ] and nuclear interaction [ 20 ]. Expected atmospheric muon flux depends on trigger conditions applied for muon track selection in the WCDA: zenith angles, track length and/or number of hit cells. Table 1 shows the estimation result: As seen, due to huge the WCDA the pair-meter area, expected muon counting rate is high even for selected minimal track length as high as 70 m involving 14 water cells. This is background muons of energy ~ 10 GeV. We are going to start with much higher muon energy of ~ 10 TeV and we expect of ~ 45 event/day hitting at least 9 cells along track. Expected events rate of our interest (E µ > 500 TeV) is expected to be ~ 100/year. Summary We proposed to study near horizontal atmospheric cosmic ray muon flux using the WCDA water detector as a pair-meter with a huge area and length. Our simulations show that WCDA parameters are close to the best ones needed to serve as a pair-meter. Advantage of the WCDA is its cell structure making it a kind of track detector for near horizontal directions allowing one to apply the pair-meter method even for multiple muon events and to reject any possible background. This would allow us to measure muon spectrum up to the highest energy using existing detectors without any reconstruction. We needed only to add an additional trigger and develop an event separation algorithm to solve the muon problem in the nearest future. The proposal has been accepted by the LHAASO collaboration and the work started in late 2024. Declarations Author Contribution Yu.V. Stenkin wrote the main manuscript textA.V. Butkevich calculated muon fluxes and made some estimationsO.B. Shchegolev made event simulations with GEAN4K.O. Kurinov processed the WCDA data to compare it with the simulationsI.S. Karpikov processed Km2A data to compare with the simulations and estimated its possible usageD.A. Kuleshov simulated detector response to EASI.O. Malii simulated light collection after muon passage through the WCDA (prepared figures 3-5)Xinhua MA analysed the data and discussed the resultsZ.G. Yao is responsible for the WCDA stable work and its data taking Acknowledgments This work is supported by Russian Ministry of Science and Higher Education grant No. 075-15-2024-541 and by the National Natural Science Foundation of China (NSFC, No.12320101005). References Kitamura, T., et al.: // Proc. 14th ICRC, Munich, v. 6, p. 2145. (1975) Allkofer, O.C., Bella, G., Dau, W.D., et al.: Nuclear Phys. B259 , 1–18 (1985) Alekseev, I.S.: and G.T. Zatsepin. High energy µ-mesons, p. 32. ICRC, Moscow (1959). 1 Nakamura, I., Kitamura, T., Mitsui, K., et al.: A measurement of the high energy muon spectrum by pair meter. Proc. 16th ICRC, Kyoto, 10 19–23. (1979) Dau, W.D.: Proc. International DUMAND Simposium. Hawai, v.1, p.271. (1980) Kokoulin, R.P., Petrukhin, A.A.: NIMA2631988. P. 468 Ma, X.-H., Bi, Y.-J., Cao, Z., et al.: Chapter 1. Chin. Phys. C 2022 V 46 , 3, 035001 http://english.ihep.cas/lhaaso/ Bogdanov, A.G., Kokoulin, R.P., et al.: Astropart. Phys. V. 36 (1), 224 (2012) Aartsen, M.G., Abraham, K., et al.: Astropart. Phys. V. 78 , 1 (2016) Alekseeev, E.N., et al.: Proc. 16th ICRC, Kyoto, 10, p.276, (1979) Ahron, S., Barber, D.B., Kieda, Wayne, R., Springer, et al.: Oct. (HAWC Collaboration). PoS(ICRC2017)512; arXiv:1710.04290v1 [astro-ph.HE] 11 (2017) Stenkin, Y.V.: //Journal Experimental Theoretical Phys. 134 (4), 386 (2022) Stenkin, Y.V., Butkevich, A.V., et al.: // Phys. At. Nucl. 87 (2), S314–S318 (2024) GEANT collaboration: REF. Manual, Release 11.2, (2023) Stenkin, Y.V., Butkevich, A.V., et al.: // Bulletin of Russian Academy of Sciences: Physics. V. 89(6), In press. (2025) Butkevich, A.V., Dedenko, L.G., Zheleznykh, I.M.: Sov J. Nucl. Phys. 50 , 90 (1989) Bugaev, E.V., Misaki, A., Naumov, V.A., Sinegovskaya, T.S., Sinegovsky, S.I., Takahashi, N.: Phys. Rev. D. 58 , 054001 (1998) Kelner, S.R., Kokoulin, R.P., Petrukhin, A.A.: Phys. Nucl. 60 , 576 (1997) Butkevich, A.V., Mikheev, S.P.: Zh Eksp. Teor Fiz. 122 , 17 (2002) Additional Declarations No competing interests reported. Cite Share Download PDF Status: Published Journal Publication published 22 Apr, 2026 Read the published version in Experimental Astronomy → Version 1 posted Editorial decision: Revision requested 13 Jan, 2026 Reviews received at journal 11 Dec, 2025 Reviews received at journal 23 Nov, 2025 Reviewers agreed at journal 21 Nov, 2025 Reviewers agreed at journal 21 Nov, 2025 Reviewers invited by journal 12 Aug, 2025 Editor assigned by journal 18 Jul, 2025 Submission checks completed at journal 30 Jun, 2025 First submitted to journal 28 Jun, 2025 You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-6998918","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":499452995,"identity":"68dc5c7d-433b-40ca-a562-5e036db88d4a","order_by":0,"name":"Yu. V. Stenkin","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA8klEQVRIiWNgGAWjYJCCA2CSh7GB4QOQNmAnTosBWAvjDJAWZuIsAmlhYGDmIUaLwY3chwcY/vyRM+c53PbYdo9dtDkz87EPjHsO49GSbnCAsc3A2LK3sd0451ly7s5mtuQZDM/waUljOMDYYJC44Txjm3TOAebcDYd5jIH+I6CF4Y9BPViLxYF6oBb+z0RoYTNIMDjb2CYNVAmyhRmvFskzzxgOJLYZG244c7BNsufAcZBfjBkSDqTj1MJ3PI35w4c/cvIGZ9KfSfw4UJ27nb35McOHA9Y4tSgcABIJGMKYIggg34BHchSMglEwCkYBGAAACfRY4sKnWYoAAAAASUVORK5CYII=","orcid":"","institution":"Institute for Nuclear Research of Russian Academy of Sciences","correspondingAuthor":true,"prefix":"","firstName":"Yu.","middleName":"V.","lastName":"Stenkin","suffix":""},{"id":499452997,"identity":"a227368c-ba36-47e4-a2c9-6901a354e077","order_by":1,"name":"A. V. Butkevich","email":"","orcid":"","institution":"Institute for Nuclear Research of Russian Academy of Sciences","correspondingAuthor":false,"prefix":"","firstName":"A.","middleName":"V.","lastName":"Butkevich","suffix":""},{"id":499452998,"identity":"29a47dde-a491-4a92-8f27-66391c0f5873","order_by":2,"name":"I. S. Karpikov","email":"","orcid":"","institution":"Institute for Nuclear Research of Russian Academy of Sciences","correspondingAuthor":false,"prefix":"","firstName":"I.","middleName":"S.","lastName":"Karpikov","suffix":""},{"id":499452999,"identity":"d1f4d514-7623-4077-9df0-f41d84652b8c","order_by":3,"name":"K. O. Kurinov","email":"","orcid":"","institution":"Institute for Nuclear Research of Russian Academy of Sciences","correspondingAuthor":false,"prefix":"","firstName":"K.","middleName":"O.","lastName":"Kurinov","suffix":""},{"id":499453000,"identity":"8c380540-0295-47dd-8df6-b380cd90cdba","order_by":4,"name":"X. H. Ma","email":"","orcid":"","institution":"Institute for Nuclear Research of Russian Academy of Sciences","correspondingAuthor":false,"prefix":"","firstName":"X.","middleName":"H.","lastName":"Ma","suffix":""},{"id":499453002,"identity":"a776055d-83a1-436a-a780-eac938ff1c78","order_by":5,"name":"I. O. Maliy","email":"","orcid":"","institution":"Institute for Nuclear Research of Russian Academy of Sciences","correspondingAuthor":false,"prefix":"","firstName":"I.","middleName":"O.","lastName":"Maliy","suffix":""},{"id":499453004,"identity":"8f13bb4f-021b-457f-b238-d1aada76ff0f","order_by":6,"name":"O. B. Shchegolev","email":"","orcid":"","institution":"Institute for Nuclear Research of Russian Academy of Sciences","correspondingAuthor":false,"prefix":"","firstName":"O.","middleName":"B.","lastName":"Shchegolev","suffix":""},{"id":499453005,"identity":"a8ef1448-4c4c-4ed9-8c56-53476e94d7cd","order_by":7,"name":"Z. G. Yao","email":"","orcid":"","institution":"Institute of High Energy Physics, Chinese Academy of Sciencies","correspondingAuthor":false,"prefix":"","firstName":"Z.","middleName":"G.","lastName":"Yao","suffix":""}],"badges":[],"createdAt":"2025-06-28 16:08:13","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-6998918/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-6998918/v1","draftVersion":[],"editorialEvents":[{"content":"https://doi.org/10.1007/s10686-026-10045-z","type":"published","date":"2026-04-22T15:59:05+00:00"}],"editorialNote":"","failedWorkflow":false,"files":[{"id":89500453,"identity":"3b093333-6876-4e3a-ba68-65c095661d6d","added_by":"auto","created_at":"2025-08-20 15:53:52","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":57488,"visible":true,"origin":"","legend":"\u003cp\u003eSimulated event of muon track in light intensity (npe) produced in crossing cells without threshold (left panel) and with threshold 10 npe per a cell (right panel).\u003c/p\u003e","description":"","filename":"1.png","url":"https://assets-eu.researchsquare.com/files/rs-6998918/v1/fd6797a02d65e28de6abda93.png"},{"id":89500503,"identity":"461d3922-915a-4638-b790-25bad1ed314c","added_by":"auto","created_at":"2025-08-20 15:53:58","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":78382,"visible":true,"origin":"","legend":"\u003cp\u003eSimulation of Cherenkov light in hit cells with threshold 10 npe, produced by muon separately in different processes: only its own Cherenov light (upper), only by ionization (middle) and only by pair production (bottom) for two muon energy: 316 GeV (left) a 10 TeV (right).\u003c/p\u003e","description":"","filename":"2.png","url":"https://assets-eu.researchsquare.com/files/rs-6998918/v1/a5f2fe33873c7fd9c1275e1a.png"},{"id":89500462,"identity":"d7e0b3c0-eaf0-4b28-9fa6-337ce8b42f92","added_by":"auto","created_at":"2025-08-20 15:53:54","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":39382,"visible":true,"origin":"","legend":"\u003cp\u003eMean light produced by muon in different processes as a function of muon energy: pair production (red), Cherenkov light (yellow), ionization (green) and sum of them (violet).\u003c/p\u003e","description":"","filename":"3.png","url":"https://assets-eu.researchsquare.com/files/rs-6998918/v1/5320ad2130ea99789f3edb1c.png"},{"id":89500464,"identity":"5d15f42f-8535-48fe-9758-100e0d4292ad","added_by":"auto","created_at":"2025-08-20 15:53:54","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":16163,"visible":true,"origin":"","legend":"\u003cp\u003eDistribution of recorded light samples produced by 100 TeV muon crossed 23 cells of WCDA at zenith angle 88 degrees.\u003c/p\u003e","description":"","filename":"4.png","url":"https://assets-eu.researchsquare.com/files/rs-6998918/v1/cf3e9a670bdc0333f790e3d4.png"},{"id":89500465,"identity":"afe2dfd5-6ce0-4b89-bd68-cf6f94daf0af","added_by":"auto","created_at":"2025-08-20 15:53:55","extension":"png","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":34554,"visible":true,"origin":"","legend":"\u003cp\u003eLight crosstalk simulation results showing percentage of light in two neighboring cells in comparison with the main (central) cell where muon passed. R is light reflection coefficient.\u003c/p\u003e","description":"","filename":"5.png","url":"https://assets-eu.researchsquare.com/files/rs-6998918/v1/cd6bbf56ed5a8a7794275e0c.png"},{"id":107927897,"identity":"78c02c05-b18c-4299-ae23-a450abec6330","added_by":"auto","created_at":"2026-04-27 16:06:03","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":387365,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-6998918/v1/597f2683-30f1-4d5d-8eca-17b4060cc73e.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"\u003cp\u003eWCDA Detector of the Lhaaso Experiment as a Pair-Meter to Measure Atmospheric Muon Spectrum\u003c/p\u003e","fulltext":[{"header":"Introduction","content":"\u003cp\u003eStudy of atmospheric muon fluxes at highest energies continued for decades but the problem is not still solved. Working worldwide muon detectors does not measure muon energy \u0026ndash; only cosmic ray muon flux or muon number in EAS (Extensive Air Shower) or in parallel muon groups. However, muon energy spectrum study has a special interest allowing one to measure primary cosmic ray spectrum at the Earth\u0026rsquo;s surface or at shallow depths underground, underwater or under ice. Muon magnetic spectrometers, such as MUTRON [\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e] and DEIS [\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e] used in previous years, had an upper limit to muon energy of ~\u0026thinsp;10 TeV due to small deviation of such relativistic muons in the magnetic field. This is why muon spectrum has never been measured above this energy using such technique. Pair-meter technique is free of this limit. Moreover, the higher the muon energy, the higher is accuracy of the method.\u003c/p\u003e\u003cp\u003eAs known, muon energy losses dE\u003csub\u003e\u0026micro;\u003c/sub\u003e/dx = -\u003cem\u003ea\u003c/em\u003e - \u003cem\u003eb\u003c/em\u003eE\u003csub\u003e\u0026micro;\u003c/sub\u003e, where \u003cem\u003ea\u003c/em\u003e is slowly changing ionization losses, \u003cem\u003ea\u003c/em\u003e\u0026thinsp;~\u0026thinsp;2MeV/(g/cm\u003csup\u003e2\u003c/sup\u003e) and \u003cem\u003eb\u003c/em\u003e\u0026thinsp;=\u0026thinsp;b\u003csub\u003ebr\u003c/sub\u003e + b\u003csub\u003eph\u003c/sub\u003e \u003cb\u003e+\u003c/b\u003e b\u003csub\u003epair\u003c/sub\u003e is sum of fractional energy loss in the three radiation processes. Parameter \u003cem\u003ea/b\u003c/em\u003e \u0026asymp;500 GeV shows when radiation losses dominate and thus well above this energy one can use the energy losses to estimate muon energy E\u003csub\u003e\u0026micro;\u003c/sub\u003e. Note that cross-section for electron-positron pair production by muon is high enough and slowly depends on E\u003csub\u003e\u0026micro;\u003c/sub\u003e while energy transfer is proportional to E\u003csub\u003e\u0026micro;\u003c/sub\u003e. G.T. Zatsepin in Ref. [\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e] firstly proposed the idea of the method and the name \u0026ldquo;pair-meter\u0026rdquo; was given to the method later [\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e]. Some estimations of the pair-meter configuration in water and the method accuracy applied to DUMAND proposal can be found in [\u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e]. Theory of the muon pair-meter was developed in [\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e], where optimal parameters of the \u0026ldquo;ideal pair-meter\u0026rdquo; have been estimated. Nevertheless, up to date no one full-scale pair-meter has been constructed anywhere in the world. The reason is that the \u0026ldquo;ideal pair-meter\u0026rdquo; should have very big size (~\u0026thinsp;1000 rad. lengths or ~\u0026thinsp;few hundred meters in water), it should be a track (and fully active) detector to measure ionization (or Cherenkov light), i. e. it should be mostly scintillator or Cherenkov media. In a case of WCDA we have water as a fully active transparent registration media. Therefore, Cherenkov light production should be added for all particles, including parent muon, producing significant amount of light only at rather low energy below our measurements range. As we show below, WCDA parameters are very close to \u0026ldquo;ideal pair-meter\u0026rdquo;. Moreover, this is already working detector and nothing has to be change there. The WCDA\u0026rsquo; detailed description can be found in [\u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e, \u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e]. It is a huge water Cherenkov detector of 260x300x4.5 m\u003csup\u003e3\u003c/sup\u003e size, composed of 3 water pools, each subdivided by light-protected cells of 5x5x4.5 m\u003csup\u003e3\u003c/sup\u003e size. This makes it practically an optimal pair-meter to study atmospheric near horizontal high-energy muons. For WCDA we have track length T in radiation lengths t\u003csub\u003e0\u003c/sub\u003e (36 g/cm\u003csup\u003e2\u003c/sup\u003e for water), depending on the number of passed cells (n) of 13.9 r. l. each, as T\u0026thinsp;=\u0026thinsp;13.9n\u0026thinsp;~\u0026thinsp;83\u0026cedil;834 r. l. for n\u0026thinsp;=\u0026thinsp;6\u0026cedil;60. Therefore, relative accuracy of the muon energy reconstruction can be estimated using a formula from [\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e] as δ=(137/Τ)\u003csup\u003e1/2\u003c/sup\u003e \u0026asymp; 1.28\u0026cedil;0.40 accordingly. Total side area of the Cherenkov detector is about S \u0026asymp; 1350 m\u003csup\u003e2\u003c/sup\u003e for zenith angles 80\u0026ndash;90 degrees. Moreover, upper water surface area can also be used at angles 70\u0026ndash;88 degrees when muon entries the detector through roof or walls thus making real detector much higher (~\u0026thinsp;20000 m\u003csup\u003e2\u003c/sup\u003e ). One could compare it with a pair-meter constructed on a base of MUTRON, it had area only S\u0026thinsp;=\u0026thinsp;7 m\u003csup\u003e2\u003c/sup\u003e and much lower length.\u003c/p\u003e\u003cp\u003eAtmospheric muon energy spectrum measuring were performed in a few experiments up to date [\u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e, \u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e] in energy range up to E\u003csub\u003e\u0026micro;\u003c/sub\u003e\u0026thinsp;~\u0026thinsp;1 PeV. Authors of Ref. [\u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e] tried to use existing underground detector BUST (Baksan Underground Scintillator Telescope) [\u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e] as a pair-meter but its features with only 4 scintillator layers of rather small thickness were far from the optimal pair-meter parameters [\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e]. As a result, the data statistical errors did not allow them to give an unambiguous result. IceCube results obtained using alternative methods with the giant neutrino telescope [\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e] have rather low statistical errors. Design of this telescope is optimized for neutrino interactions inside the huge ice cube, but it has no subdivision to individual measuring cells and thus it cannot serve as a pair-meter. This is why the authors used another technique for muon energy measurements: muon group multiplicity or measurement of single muon high-energy interactions in ice through other processes (bremsstrahlung or inelastic nuclear interactions). As a result, the authors obtained some unexpected results and they are not sure they considered all systematic errors. For example, it is interesting that the IceCube result agrees well with a pure power law spectrum with slope γ\u0026thinsp;~\u0026thinsp;3.7 at muon energy up to 1.58 PeV (i.e. well beyond so-called \u0026ldquo;knee\u0026rdquo; in primary cosmic rays at ~\u0026thinsp;5 PeV). The authors explain it by an addition of prompt muons from decays of heavy charmed mesons just in the \u0026ldquo;knee\u0026rdquo; region and just in the needed amount.\u003c/p\u003e\u003cp\u003eAn attempt to study near horizontal muon flux was made by the HAWC collaboration using its large water Cherenkov detector array [\u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e]. However, there are no muon energy measurements in this experiment. The task of the HAWC group was measuring of muon absorption in rock by selecting muon tracks from a nearby mountain. An example of recorded near horizontal muon is shown there as a track crossing many water Cherenkov tanks [\u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e]. Sure, similar events do exist in WCDA.\u003c/p\u003e\u003cp\u003eTherefore, the situation with muon spectrum measurement is still hot and new experiments needed because muons are produced by cosmic rays through pion, kaon and heavier meson decays in air and both muon energy or muon number spectrum can serve as energy estimators for primary cosmic rays spectrum recovering.\u003c/p\u003e"},{"header":"Extension of the LHAASO experiment tasks","content":"\u003cp\u003eThe Large High Altitude Air Shower Observatory is one of the biggest multipurpose and highly informative experiment in the world, running since 2019 [\u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e, \u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e]. It has many aims concentrated mostly in fields of Gamma ray astronomy, Cosmic ray physics, etc. Outstanding results have been already obtained by this experiment [\u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e] but up to date there were no any tasks connected with neutrino astrophysics or with atmospheric muon energy spectrum measurements. The experiment consists of several independent arrays each having its own tasks: Water Cherenkov Detector Array designed for gamma-ray astronomy and looking as a huge water pool subdivided into many light protected water cells. The latter makes the WCDA being a large track detector at near horizontal directions making it suitable for astrophysical neutrino interactions search, as shown in [\u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e14\u003c/span\u003e]. Current proposal is a by-product for the above task, where near horizontal muons produce a background for neutrino event search. This is a ready to use pair-meter detector and nothing has to be changed in its construction. Only special data processing and special trigger could be added. Therefore, one could regard WCDA as a working full-scale track detector having the optimal pair-meter parameters. Angular resolution δΘ for muon trajectory depends on its length and our simple estimation gave δΘ\u0026thinsp;\u0026asymp;\u0026thinsp;0.4\u003csup\u003eo\u003c/sup\u003e for muon track length l\u0026thinsp;=\u0026thinsp;60m. We could mention here that we need not very good angular resolution for this research because we have only to select muons inside the working angular range for near horizontal muons of say 70\u0026thinsp;\u0026divide;\u0026thinsp;89\u003csup\u003eo\u003c/sup\u003e.\u003c/p\u003e"},{"header":"Simulations","content":"\u003cdiv id=\"Sec3\" class=\"Section2\"\u003e\u003cdiv id=\"Sec4\" class=\"Section3\"\u003e\u003ch2\u003e2.1. Muon tracks simulation\u003c/h2\u003e\u003cp\u003eTo apply the pair-meter method to the LHAASO experiment we made a series of detailed Monte-Carlo simulations, considering all known WDCA Cherenkov detector parameters. First, we made simulations using GEANT4 codes [\u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e] of the WCDA ionization response to passage of UHE (Ultra High Energy) near horizontal muons [\u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e].\u003c/p\u003e\u003cp\u003eAt the next step of the experiment modeling, using GEANT4, we simulated Cherenkov light produced by relativistic muon in water Cherenkov detector taking into account cells configuration, its possible cross talk, and PMTs positions. The problem is that the cell curtains do not shield full 4πgeometry of the cell and small amount of light can penetrate to neighboring cells. The cell geometry, its size, PMT positions, curtain configuration, PMT\u0026rsquo;s photo-cathode size and quantum efficiency were taken into account.\u003c/p\u003e\u003cp\u003eFigure\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e (left panel) shows a simulated example of UHE (3.16 PeV) near horizontal (88 deg.) muon passage through the detector when entering through the detector building roof. The mean light production recalculated to number of photoelectrons (npe) per cell for this track is equal to 258 npe/cell. As seen, muon track can be identify without any problem thus confirming that the detector performances and cell size are good and this allows us to search for near horizontal muon tracks without any detector changes. Right panel in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e shows the same simulated event showing produced light in cells if it exceeds 10 npe. This picture shows the event more clearly removing cells with low energy deposition and, probably cross talk or background cell hits. Applying the lower threshold allows one also removing low energy deposit PMT hits produced mainly by low energy accompanies of the UHE muon passed through air and scattered back to water. Considering fast timing and recorded light in each cell (251 npe/cell in this track example with threshold), we can estimate the muon energy and its direction with acceptable accuracy, when the track length is long enough.\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003eThe light in the WCDA cells produced separately by only due to Cherenkov light, ionization and pair production process parent muon are shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e for muons of energy 316 GeV (left) and 10 TeV (right). Only cells with more than 10 npe are shown. Figures legends present full event information including mean npe/cell. Lower threshold for collected Cherenkov light about 10 photo-electrons deposit per cell allows one removing of low energy deposit PMT hits produced mainly by low energy accompanies of the UHE muon passed through air and scattered back to water. Considering fast timing and recorded light in each cell we can estimate the muon energy and its direction with acceptable accuracy, when the track length is long enough. Later we will study these dependences with better accuracy and will try to develop an algorithm for the best muon energy recovering.\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003eA question could arise: is number of photo-electrons produced by muon in the detector proportional to its energy or not? Should one separates energy deposit through only pair production or not? To answer this question we simulated all muon interactions in detector\u0026rsquo;s water and then only by pair production process. Because of these simulations, we have a statistical plot showing how the above processes depend on muon energy, presented in Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e. As seen, above E\u003csub\u003e\u0026micro;\u003c/sub\u003e\u0026thinsp;\u0026gt;\u0026thinsp;~\u0026thinsp;3 TeV pair production prevails and produced light really follows linear function on muon energy. Another question concerns so-called catastrophic muon interactions, i.e. bremsstrahlung and nuclear interactions. These muon energy losses result in almost full energy loss and after such interaction muon track will end with a large energy deposit. Such events would be clearly seen in WCDA and could be rejected or muon energy estimation could be made on the track before such interaction if its length is long enough.\u003c/p\u003e\u003cp\u003eAnother question concerns the method accuracy. We gave a brief error estimation in Introduction. In addition, we have made special simulations for recorded light distribution in 3000 events for 100 TeV near horizontal muons in WCDA shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e. As seen the distribution follows well log-normal fit for all muon energies above 100 TeV. We should note here that our aim is to measure muon energy spectrum and we need not to know exactly individual muon energy. It means we need to measure\u0026thinsp;\u0026lt;\u0026thinsp;ε\u0026thinsp;\u0026gt;\u0026thinsp;and its systematic errors are small enough.\u003c/p\u003e\u003c/div\u003e\n\u003ch3\u003e2.2. Cross talk simulation\u003c/h3\u003e\n\u003cp\u003eCross talk between neighboring cells, if any, can make wrong cell hits close to the trajectory. To check it we made special simulation estimating this effect in Considering real curtains geometry and their sizes and light reflection coefficient R\u0026thinsp;=\u0026thinsp;0.05, we estimated the light cross talk between the cells as one close to negligible as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e, especially if lower threshold for the cell light is applied. Also shown are results with hypothetically modified light protection curtain reflection R and geometry when they are: a) for R\u0026thinsp;=\u0026thinsp;0 (red line); b) extended up to water-air boundary (green); c) extended down up to the pool bottom (blue) and d) extended both up and down (magneta). As seen, the crosstalk even now (with regular curtains) is as low as ~\u0026thinsp;1% for zenith angles 80\u0026ndash;88 degrees and it can be excluded by a lower threshold of ~\u0026thinsp;10 npe/cell. One can also see that the crosstalk is mostly produced by a gap (~\u0026thinsp;0.5 m) between pool bottom and curtain, because this gap is closer to the PMTs situated near the pool bottom.\u003c/p\u003e"},{"header":"Expected near horizontal muon flux","content":"\u003cp\u003eTo estimate the expected UHE near horizontal atmospheric muon flux we use the spectrum of conventional (decay) and \u0026ldquo;prompt\u0026rdquo; muons calculated in Refs. [\u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e, \u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e18\u003c/span\u003e], respectively in the energy range 0\u0026ndash;10 PeV. The spectra of \u0026ldquo;direct\u0026rdquo; muons were estimated within two models for the production of charmed particles.\u003c/p\u003e\u003cp\u003eWe calculated the expected number of background events per year for both fluxes of the \u0026ldquo;prompt\u0026rdquo; muons. In our calculation, we took into account the muon energy losses due to bremsstrahlung [\u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e], pair production [\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e] and nuclear interaction [\u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e].\u003c/p\u003e\u003cp\u003eExpected atmospheric muon flux depends on trigger conditions applied for muon track selection in the WCDA: zenith angles, track length and/or number of hit cells. Table\u0026nbsp;1 shows the estimation result:\u003c/p\u003e\u003cp\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"584\" height=\"224\"\u003e\u003c/p\u003e\u003cp\u003eAs seen, due to huge the WCDA the pair-meter area, expected muon counting rate is high even for selected minimal track length as high as 70 m involving 14 water cells. This is background muons of energy\u0026thinsp;~\u0026thinsp;10 GeV. We are going to start with much higher muon energy of ~\u0026thinsp;10 TeV and we expect of ~\u0026thinsp;45 event/day hitting at least 9 cells along track. Expected events rate of our interest (E\u003csub\u003e\u0026micro;\u003c/sub\u003e\u0026thinsp;\u0026gt;\u0026thinsp;500 TeV) is expected to be ~\u0026thinsp;100/year.\u003c/p\u003e"},{"header":"Summary","content":"\u003cp\u003eWe proposed to study near horizontal atmospheric cosmic ray muon flux using the WCDA water detector as a pair-meter with a huge area and length. Our simulations show that WCDA parameters are close to the best ones needed to serve as a pair-meter. Advantage of the WCDA is its cell structure making it a kind of track detector for near horizontal directions allowing one to apply the pair-meter method even for multiple muon events and to reject any possible background. This would allow us to measure muon spectrum up to the highest energy using existing detectors without any reconstruction. We needed only to add an additional trigger and develop an event separation algorithm to solve the muon problem in the nearest future. The proposal has been accepted by the LHAASO collaboration and the work started in late 2024.\u003c/p\u003e"},{"header":"Declarations","content":"\u003ch2\u003eAuthor Contribution\u003c/h2\u003e\u003cp\u003eYu.V. Stenkin wrote the main manuscript textA.V. Butkevich calculated muon fluxes and made some estimationsO.B. Shchegolev made event simulations with GEAN4K.O. Kurinov processed the WCDA data to compare it with the simulationsI.S. Karpikov processed Km2A data to compare with the simulations and estimated its possible usageD.A. Kuleshov simulated detector response to EASI.O. Malii simulated light collection after muon passage through the WCDA (prepared figures 3-5)Xinhua MA analysed the data and discussed the resultsZ.G. Yao is responsible for the WCDA stable work and its data taking\u003c/p\u003e\u003ch2\u003eAcknowledgments\u003c/h2\u003e\u003cp\u003eThis work is supported by Russian Ministry of Science and Higher Education grant No. 075-15-2024-541 and by the National Natural Science Foundation of China (NSFC, No.12320101005).\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\u003cli\u003e\u003cspan\u003eKitamura, T., et al.: // Proc. 14th ICRC, Munich, v. 6, p. 2145. (1975)\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eAllkofer, O.C., Bella, G., Dau, W.D., et al.: Nuclear Phys. \u003cb\u003eB259\u003c/b\u003e, 1\u0026ndash;18 (1985)\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eAlekseev, I.S.: and G.T. Zatsepin. High energy \u0026micro;-mesons, p. 32. ICRC, Moscow (1959). 1\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eNakamura, I., Kitamura, T., Mitsui, K., et al.: A measurement of the high energy muon spectrum by pair meter. Proc. 16th ICRC, Kyoto, 10 19\u0026ndash;23. (1979)\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eDau, W.D.: Proc. International DUMAND Simposium. Hawai, v.1, p.271. (1980)\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eKokoulin, R.P., Petrukhin, A.A.: NIMA2631988. P. 468\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eMa, X.-H., Bi, Y.-J., Cao, Z., et al.: Chapter 1. Chin. Phys. C 2022 V \u003cb\u003e46\u003c/b\u003e, 3, 035001\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003e\u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttp://english.ihep.cas/lhaaso/\u003c/span\u003e\u003cspan address=\"http://english.ihep.cas/lhaaso/\" targettype=\"URL\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eBogdanov, A.G., Kokoulin, R.P., et al.: Astropart. Phys. V. \u003cb\u003e36\u003c/b\u003e(1), 224 (2012)\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eAartsen, M.G., Abraham, K., et al.: Astropart. Phys. V. \u003cb\u003e78\u003c/b\u003e, 1 (2016)\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eAlekseeev, E.N., et al.: Proc. 16th ICRC, Kyoto, 10, p.276, (1979)\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eAhron, S., Barber, D.B., Kieda, Wayne, R., Springer, et al.: Oct. (HAWC Collaboration). PoS(ICRC2017)512; arXiv:1710.04290v1 [astro-ph.HE] 11 (2017)\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eStenkin, Y.V.: //Journal Experimental Theoretical Phys. \u003cb\u003e134\u003c/b\u003e(4), 386 (2022)\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eStenkin, Y.V., Butkevich, A.V., et al.: // Phys. At. Nucl. \u003cb\u003e87\u003c/b\u003e(2), S314\u0026ndash;S318 (2024)\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eGEANT collaboration: REF. Manual, Release 11.2, (2023)\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eStenkin, Y.V., Butkevich, A.V., et al.: // Bulletin of Russian Academy of Sciences: Physics. V. 89(6), In press. (2025)\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eButkevich, A.V., Dedenko, L.G., Zheleznykh, I.M.: Sov J. Nucl. Phys. \u003cb\u003e50\u003c/b\u003e, 90 (1989)\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eBugaev, E.V., Misaki, A., Naumov, V.A., Sinegovskaya, T.S., Sinegovsky, S.I., Takahashi, N.: Phys. Rev. D. \u003cb\u003e58\u003c/b\u003e, 054001 (1998)\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eKelner, S.R., Kokoulin, R.P., Petrukhin, A.A.: Phys. Nucl. \u003cb\u003e60\u003c/b\u003e, 576 (1997)\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eButkevich, A.V., Mikheev, S.P.: Zh Eksp. Teor Fiz. \u003cb\u003e122\u003c/b\u003e, 17 (2002)\u003c/span\u003e\u003c/li\u003e\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":true,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"experimental-astronomy","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"expa","sideBox":"Learn more about [Experimental Astronomy](http://link.springer.com/journal/10686)","snPcode":"10686","submissionUrl":"https://submission.nature.com/new-submission/10686/3","title":"Experimental Astronomy","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false},"keywords":"","lastPublishedDoi":"10.21203/rs.3.rs-6998918/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-6998918/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eThe LHAASO (Large High Altitude Air Shower Observatory) experiment is a multi-purpose experiment for gamma-ray astronomy, cosmic ray physics and for many other tasks. Its task number will be undoubtedly extended in future. We proposed to use existing WCDA (Water Cherenkov Detector Array being a part of LHAASO) as a pair-meter to measure atmospheric muon energy spectrum. This work confirms that WCDA without any reconstruction can serve as an optimal pair-meter to study near-horizontal atmospheric muons with energy beyond ~\u0026thinsp;10 TeV. In this article we study response of the WCDA detector to Cherenkov light produced by high energy muons and its accompanying, taking into account the cells configuration, possible crosstalk between cells, and photomultiplier (PMT) characteristics.\u003c/p\u003e","manuscriptTitle":"WCDA Detector of the Lhaaso Experiment as a Pair-Meter to Measure Atmospheric Muon Spectrum","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-08-20 15:53:24","doi":"10.21203/rs.3.rs-6998918/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"decision","content":"Revision requested","date":"2026-01-13T05:26:23+00:00","index":"","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2025-12-11T16:12:59+00:00","index":"hide","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2025-11-23T14:51:55+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"251381065374885575199829895849707023556","date":"2025-11-21T15:44:58+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"24917198256749518822205473733929501376","date":"2025-11-21T05:34:06+00:00","index":"hide","fulltext":""},{"type":"reviewersInvited","content":"","date":"2025-08-12T14:13:59+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2025-07-18T09:11:12+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2025-07-01T03:20:16+00:00","index":"","fulltext":""},{"type":"submitted","content":"Experimental Astronomy","date":"2025-06-28T16:00:58+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"experimental-astronomy","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"expa","sideBox":"Learn more about [Experimental Astronomy](http://link.springer.com/journal/10686)","snPcode":"10686","submissionUrl":"https://submission.nature.com/new-submission/10686/3","title":"Experimental Astronomy","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false}}],"origin":"","ownerIdentity":"62b962ba-db7b-458d-9642-e9fa915035cb","owner":[],"postedDate":"August 20th, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"published-in-journal","subjectAreas":[],"tags":[],"updatedAt":"2026-04-27T16:03:54+00:00","versionOfRecord":{"articleIdentity":"rs-6998918","link":"https://doi.org/10.1007/s10686-026-10045-z","journal":{"identity":"experimental-astronomy","isVorOnly":false,"title":"Experimental Astronomy"},"publishedOn":"2026-04-22 15:59:05","publishedOnDateReadable":"April 22nd, 2026"},"versionCreatedAt":"2025-08-20 15:53:24","video":"","vorDoi":"10.1007/s10686-026-10045-z","vorDoiUrl":"https://doi.org/10.1007/s10686-026-10045-z","workflowStages":[]},"version":"v1","identity":"rs-6998918","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-6998918","identity":"rs-6998918","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}