On the Accuracy of Underground Muon Intensity Calculations

Abstract

Cosmic ray muons detected by deep underground or underwater detectors have served as an information source on the high-energy cosmic ray spectrum and hadronic interactions in air showers for almost a century. The theoretical interest in underground muons has nearly faded because space-borne experiments probe the cosmic ray spectrum more directly, and accelerators provide precise measurements of hadron yields. However, underground muons probe unique hadron interaction energies and phase space, which are still inaccessible to present accelerator experiments. The cosmic ray nucleon energies reach the hundred-TeV and PeV ranges, which are barely accessible with space-borne experiments. Our new calculation combines two modern computational tools, mceq, for surface muon fluxes, and proposal, for underground transport. We demonstrate excellent agreement with measurements of cosmic ray muon intensities underground within estimated errors. Beyond that, the precision of historical data turns out to be significantly smaller than our error estimates. This result shows that the sources of high-energy atmospheric lepton flux uncertainties at the surface or underground can be significantly constrained without taking more data or building new detectors. The reduction of uncertainties can be expected to impact data analyses at large-volume neutrino telescopes and for the design of future ton-scale direct dark matter detectors.

Data-driven hadronic interaction model for atmospheric lepton flux calculations

“…A difference of ∼ 20% to HKKMS is somewhat larger than expected. The description of fluxes in the TeV range by MCEq and DDM has been recently studied for underground muon intensities [44], and found to be in good agreement with vertical intensity data, and the error estimation of muon fluxes in DDM has been demonstrated to be realistic.…”

“…4, the caveat is that only 20−30% of muons observed at large depths originate from kaon decays (see Fig. 5 in [44]) in contrast to almost 80% of observed muon neutrinos. Under some soft model dependence, data-driven constraints from underground muons on very high energy conventional neutrino fluxes will have much lower uncertainties than estimates (such as [27]) that imply the complete absence of data from accelerators.…”

“…Fig. 7 in [44]). Flux "calibration" applications (such as [26,31]) would profit from underground muon rates measured as a function of the zenith angle and the slant depth in km.w.e., even if only a few bins are populated.…”

“…To cover the IceCube energy range, the required muon energy at the surface is > 1 TeV. More related are muon fluxes or rates observed in deep underground detectors, which are known to much better precision than the few TeV-range measurements at the surface [44]. While there is full overlap between the deep underground contours in Fig.…”

“…As previously discussed, good collider constraints would come from air-shower specific measurements at LHCb in proton-oxygen runs [38]. An alternative source of constrains are atmospheric inclusive muons [26,31], deep underground muons [44,[60][61][62], seasonal variations [63,64] and atmospheric neutrinos [65].…”