aa r X i v : . [ nu c l - e x ] S e p Muon Production in Relativistic Cosmic-Ray Interactions
Spencer R. Klein
Nuclear Science Division, LBNL, Berkeley, CA, 94720 USA and the Physics Department, University of California,Berkeley, 94720 USA
Abstract
Cosmic-rays with energies up to 3 × eV have been observed. The nuclear composition ofthese cosmic rays is unknown but if the incident nuclei are protons then the corresponding centerof mass energy is √ s nn =
700 TeV. High energy muons can be used to probe the composition ofthese incident nuclei. The energy spectra of high-energy ( > x partons in the incident nucleus and low- x partons in the nitrogen / oxygentargets. Muon measurements can complement the central-particle data collected at colliders.This paper will review muon production data and discuss some non-perturbative (soft) modelsthat have been used to interpret the data. I will show measurements of TeV muon transversemomentum ( p T ) spectra in cosmic-ray air showers from MACRO, and describe how the IceCubeneutrino observatory and the proposed Km3Net detector will extend these measurements to ahigher p T region where perturbative QCD should apply. With a 1 km surface area, the fullIceCube detector should observe hundreds of muons / year with p T in the pQCD regime.
1. Introduction
Surface air shower arrays and air-fluorescence detectors have observed cosmic-ray showerswith energies up to 3 × eV. However, despite decades of e ff ort (the first 10 eV showerswere seen in the 1960’s [1]), we still know very little about these particles.At energies below 10 eV, direct measurements by balloon and satellite detectors have shownthat cosmic rays include nuclei, from hydrogen to iron with a sprinkling of heavier elements. Thisis consistent with the composition that is expected from supernovae [2], a likely source for lowerenergy cosmic rays. However, at higher energies the composition is poorly known.Higher energy fluxes are too low for direct measurements so we must use indirect approaches,with much larger terrestrial detectors that observe the shower particles created when the cosmic-ray interacts in the atmosphere. The atmosphere is 28 radiation lengths (11 hadronic interactionlengths) thick, so measuring the cosmic-ray composition is akin to doing particle identificationfrom the back of a calorimeter. Detectors measure the total energy, not the energy per particle.The challenge is to distinguish a 10 eV proton (for example) from a 10 eV (total) iron nucleus,with A =
56. As A rises, the initial energy is spread among more particles and the showerdevelops faster, reaching its maximum particle count higher in the atmosphere.Shower development has been studied by air fluorescence detectors, which observe nitrogenfluorescence induced by charged particles moving through the atmosphere. These measurements Preprint submitted to Nuclear Physics A May 28, 2018 re calorimetric, so they provide a fairly direct measure of the total shower energy of the shower.One can also observe the shower development as it progresses through the atmosphere, andthereby probe the composition.Shower particles that reach the surface are studied with air shower arrays, grids of scintillatoror water / ice Cherenkov sampling detectors which sample the electrons and photons which reachthe ground. These arrays can cover up to 3000 km . They measure the shower arrival direction(using timing), energy (via particle density measurements), and lateral spread, with the lateralspread being somewhat sensitive to composition. Co-located muon detectors measure muonsfrom pion and kaon decay. Most of these muons have energies of a few GeV. The ratio ofmuons to electromagnetic energy is also composition sensitive, with heavier nuclei producingmore muons. Unfortunately, the inferred energy and composition are dependent on the hadronicinteraction model used to simulate the showers.
2. TeV Muons
The LEP experiments have used magnetic spectrometers to study cosmic-ray muons withenergies up 3 TeV / c [3]. TeV muons can also be studied by putting a detector underneath akilometer or more of rock or ice. These muons are produced early in the shower, and so aresomewhat more directly sensitive to the initial ion composition. However, a very large detector,(10 to 10 m ) is needed to get good statistics. For example, the 72 m by 12 m MACROexperiment in the Gran Sasso Laboratory lay below 1500 meters of water equivalent (mwe) ofrock shielding [4].These experiments have measured the muon energy spectra and multiplicities, and also thelateral separation (decoherence). These distributions are compared with models with varyingcosmic-ray compositions. Unfortunately, the choice of hadronic interaction model can have asignificant a ff ect on the inferred composition. MACRO also took data in coincidence with theEASTOP air shower array. More recently, the SPASE air shower array at the South Pole andAMANDA in-ice detector took data in coincidence. These combined datasets have reduced, butstill significant sensitivity to the choice of hadronic model. Because these muons are predomi-nantly produced from low p T pions and kaons, these models are necessarily quite phenomeno-logical [5].Figure 1 shows the SPASE / AMANDA composition measurement [6]. The x axis shows thesurface energy measured by SPASE, while the the y axis shows the aggregate muon energy inAMANDA. The blue shading shows the expectation for all-proton and all-iron simulations. Thedata (points) are in-between, indicating an intermediate composition.
3. High p T Muon in Air Showers
High p T muons will allow perturbative QCD (pQCD) to be used to interpret the data andinfer composition. Since TeV muons are created high in the atmosphere, the high p T muons areisolated from the bundle of predominantly lower p T muons. The lateral separation d from theshower core at the Earths surface is d = h p T E µ (1)where h is the interaction height and E µ is the muon energy. For a typical interaction height of25 km, a 500 GeV muon with p T = / c will be 200 m from the shower core. The MACRO2 S30) log1 1.5 2 2.5 3 3.5 ( K ) l og -1-0.500.511.5 E * A * p r o t o n s i r o n } c a li b . b i n -2 -1 E ff i c i e n cy MACRO-fitLIGHT modelHEAVY modelEfficiency in Ref. (7,8)
Figure 1: (left) Combined data from the SPASE-II south polar array and the AMANDA underground muon detector. S30is a measure of the surface energy, while K50 is a measure of the light produced by muons in the underground array. Ironshowers produce more muons. The data prefers a mixed composition [6]. (right) The muon decoherence (separation)function measured by MACRO, from 0 to 50 m separation, compared with the results of a light and a heavy compositionmodel. The data is intermediate between the two models [4]. collaboration has measured muon pair decoherence (separations) out to 50 meters, as in Fig. 1(right), and compared them to di ff erent models. They also used detailed simulations, shown inFig. 2 (left) to relate separation to mean p T . In MACRO, 50 m corresponds to a mean p T of 1.2GeV, not fully in the pQCD regime.With a 1 km surface area, the IceCube detector and IceTop surface array will be able to mea-sure muons out to much larger separation distances, where pQCD holds robustly. Rate estimatesfor charmed quarks and for pions and kaons in jets depend on the minimum accessible E µ and d , but the complete IceTop / IceCube should observe hundreds of high p T muons each year. Mostof these muons are from charmed particle decays, with a smaller number from pions and kaonsin jets. The composition has a large e ff ect on the muon p T spectra, especially near the kinematiclimits. There are many more 10 eV partons in a 10 eV proton than in a 10 eV iron nucleus,at any Q .Figure 2 (right) shows one event found by IceCube, showing an isolated muon about 400 mfrom the shower core. The collaboration has also observed near-horizontal muon pairs. Thesemuons have a initial energies of at least several TeV [8]. The proposed Km3Net detector couldmake similar studies.The measured muon decoherence spectrum can be compared with predictions based onpQCD and di ff erent composition models. In the longer run, one can also use this data to probeshadowing at low Bjorken − x . Because of the fixed-target geometry, the observed muons areproduced in the far-forward region, and come from the collision of a high − x parton in the inci-dent particle with a low- x parton in the N or O target. The data will therefore be sensitive toshadowing in nitrogen or oxygen. The accessible kinematic range will depend on the minimumobservable muon-core distance, but it may reach below x = − [9].3 P t ( G e V / c ) run 107866 event 2586581 z , m
200 4000250500-2500-2000-1500-1000-500
Figure 2: (left) The relationship between p T and separation determined by MACRO [4]. (right) An interesting eventobserved by IceCube. An air shower hits the 11 stations in the IceTop surface array, and light is seen in 96 buried opticalmodules. 84 of the modules are on 4 strings near the extrapolated air shower core. The remaining 12 modules are onanother string about 400 meters from the projection [7].
4. Conclusions
TeV muons can be used to probe cosmic-ray interactions at energies above 1 PeV, where,despite decades of e ff ort we do not understand the incident cosmic-ray composition. The Ice-Cube detector, now being built at the South Pole, will be large enough to study high p T muonproduction in air showers. This o ff ers the possibility to study the composition in the context of apQCD model. It also o ff ers nuclear physicists the opportunity to study production of far forwardmuons, potentially probing nuclear shadowing at very small x . Acknowledgments.
I thank my IceCube and STAR Collaborators for useful comments onthis work. Lisa Gerhardt has contributed greatly to this study of high p T muons. This work wassupported in part by the National Science Foundation under Grant 0653266 and the Departmentof Energy under Contract DE-AC-02-05CH11231. References [1] J. Linsley, Phys. Rev. Lett. , 146 (1963).[2] J. R. Horandel, Adv. Space Res. , 442 (2008) [arXiv:astro-ph / et al. , Phys. Rev. D60 , 032001 (1999).[5] T. Pierog and K. Werner, arXiv:0905.1198; T. Pierog et al. , arXiv:0802.1262; R. Engel et al. , AIP Conf. Proc. , 65 (2009).[6] K. Andeen, C. Song and K. Rawlins for the SPASE2 and IceCube Collaborations, in arXiv:0711.0353.[7] S. Klein and D. Chirkin for the IceCube Collaboration, in arXiv:0711.0353.[8] L. Gerhardt and S. Klein for the IceCube Collaboration, presented at the 31st Intl. Cosmic Ray Conf.[9] S. Klein, preprint astro-ph /0612051.