Muon Spectrum Research Articles

Observing the second knee in the PCR spectrum in the region of 1017 eV using the method of local muon density spectra

The results from measuring EAS local muon density spectra at ultrahigh energies of primary particles are reported. These spectra are recorded by two instruments at the NEVOD experimental complex (MEPhI, Moscow). Muon bundles in inclined EAS at zenith angles exceeding 55° are registered by the DECOR coordinate detector. Mostly near-vertical muon bundles are registered at the bottom plane of scintillation counters in the calibration telescope system positioned underwater at a depth of approximately 9 m. The results from fitting the local muon density spectra measured by both instruments at primary particle energies below and above 1017 eV confirm the presence of the second knee (an increase in the slope) in the energy spectrum of cosmic rays in this region.

Delivering the world’s most intense muon beam

A new muon beamline, muon science innovative channel (MuSIC), was set up at the Research Centre for Nuclear Physics (RCNP), Osaka University, in Osaka, Japan, using the 392 MeV proton beam impinging on a target. The production of an intense muon beam relies on the efficient capture of pions, which subsequently decay to muons, using a novel superconducting solenoid magnet system. After the pion-capture solenoid the first $36^\circ$ of the curved muon transport line was commissioned and the muon flux was measured. In order to detect muons, a target of either copper or magnesium was placed to stop muons at the end of the muon beamline. Two stations of plastic scintillators located upstream and downstream from the muon target were used to reconstruct the decay spectrum of muons. In a complementary method to detect negatively-charged muons, the X-ray spectrum yielded by muonic atoms in the target were measured in a germanium detector. Measurements, at a proton beam current of 6 pA, yielded $(10.4 \pm 2.7) \times 10^5$ muons per Watt of proton beam power ($\mu^+$ and $\mu^-$), far in excess of other facilities. At full beam power (400 W), this implies a rate of muons of $(4.2 \pm 1.1) \times 10^8$ muons s$^{-1}$, amongst the highest in the world. The number of $\mu^-$ measured was about a factor of 10 lower, again by far the most efficient muon beam produced. The set up is a prototype for future experiments requiring a high-intensity muon beam, such as a muon collider or neutrino factory, or the search for rare muon decays which would be a signature for phenomena beyond the Standard Model of particle physics. Such a muon beam can also be used in other branches of physics, nuclear and condensed matter, as well as other areas of scientific research.

Testing of the VENUS 4.12, DPMJET 2.55, QGSJET II-03 and SIBYLL 2.3 hadronic interaction models via help of the atmospheric vertical muon spectra

Uncertainties of the model energy spectra of the most energetic secondary π± -mesons (and K ± -mesons) are discussed. Computer simulations of the partial energy spectra of the atmospheric vertical muons induced by primary cosmic particles with various fixed energies in interval 102 −107 GeV in terms of the VENUS 4.12, DPMJET 2.55, QGSJET II-03 and SIBYLL 2.3 models had been carried out with help of CORSIKA package. These partial spectra should be convoluted with the contemporary spectra of the primary cosmic particles. Results of simulations are compared with the contemporary atmospheric vertical muon flux data. Comparison shows that all models underestimate production of secondary π± -mesons (and K ± -mesons) by factor of ∼ 2 at the most high energies. This underestimation induces more rapid development of extensive air showers in the atmosphere and results in uncertainties in estimates of energy and composition of the primary cosmic particles.

Search for the rare decays K+ → μ+X in E949 experiment

The existence of a heavy neutrino, , in the decays was tested using the E949 experimental data with an exposure of 1.70 × 1012 stopped kaons. The allowed heavy neutrino mass region for the analysis is from 175 MeV/c2 to 300 MeV/c2. With major background from the radiative decay understood and suppressed, the preliminary new upper limits (90% C.L.) on the neutrino mixing matrix element between muon and heavy neutrino, |UμH|2, were set at the level of 10−8 to 10−9. New limit on the branching ratio assuming Standard Model muon spectrum is set to be 2.4 × 10−6.

Sensitivity of EAS measurements to the energy spectrum of muons

We have studied how the energy spectrum of muons at production affects some of the most common measurements related to muons in extensive air shower studies, namely, the number of muons at the ground, the slope of the lateral distribution of muons, the apparent muon production depth, and the arrival time delay of muons at ground. We found that by changing the energy spectrum by an amount consistent with the difference between current models (namely EPOS-LHC and QGSJet-II.04), the muon surface density at ground increases 5% at 20° zenith angle and 17% at 60° zenith angle. This effect introduces a zenith angle dependence on the reconstructed number of muons which might be experimentally observed. The maximum of the muon production depth distribution at 40° increases ∼ 10 g/cm2 and ∼ 0 g/cm2 at 60°, which, from pure geometrical considerations, increases the arrival time delay of muons. There is an extra contribution to the delay due to the subluminal velocities of muons of the order of ∼ 3 ns at all zenith angles. Finally, changes introduced in the logarithmic slope of the lateral density function are less than 2%.

A cosmic Ray Muon Experiment: a Way to Teach Standard Model of Particles at Community Colleges

This experiment is an example of research for early undergraduate students and of its benefits and challenges as an accessible strategy for community colleges, in the spirit of the report on improving undergraduate STEM education from the US President's Council of Advisors on Science and Technology. The goals of this project include measuring average low- energy muon flux, day/night flux difference, time dilation, energy spectra of electrons and muons in arbitrary units, muon decay curve, average lifetime of muons. From the lifetime data we calculate the weak coupling constant gw, electric charge e and the Higgs energy density.

K + → μ + ν μ ν ν ¯ $$ {\mathrm{K}}^{+}\to {\mu}^{+}{\nu}_{\mu}\nu \overline{\nu} $$ and K + → e + ν e ν ν ¯ $$ {\mathrm{K}}^{+}\to {\mathrm{e}}^{+}{\nu}_{\mathrm{e}}\nu \overline{\nu} $$ decays within the Chiral Perturbation Theory

Decays $K^{+} \rightarrow \mu^{+}\nu_{\mu} \nu \bar \nu$ and $K^{+}\rightarrow e^{+}\nu_{e} \nu \bar \nu$ are examined to the leading order in momenta in the framework of Chiral Perturbation Theory. Predictions of the Standard Model for the muon and electron differential energy spectra and branching ratios of $K_{\mu 3 \nu}$ and $K_{e 3 \nu}$ are presented.

Search for the rare decayK+→μ+νν¯ν

Evidence of the K+→μ+νν¯ν decay was searched for using E949 (Brookhaven National Laboratory, USA) experimental data with an exposure of 1.70×1012 stopped kaons. The data sample is dominated by the background process K+→μ+νμγ. An upper limit on the decay rate Γ(K+→μ+νν¯ν)<2.4×10−6Γ(K+→all) at 90% confidence level was set assuming the standard model muon spectrum. The data are presented in such a way as to allow calculation of rates for any assumed μ+ spectrum.Received 29 June 2016DOI:https://doi.org/10.1103/PhysRevD.94.032012© 2016 American Physical SocietyPhysics Subject Headings (PhySH)Research AreasRare decaysParticles & Fields

The knee in the cosmic ray energy spectrum from the simultaneous EAS charged particles and muon density spectra

In this work we examine with the help of Monte Carlo simulation whether a consistent primary energy spectrum of cosmic rays emerges from both the experimentally observed total charged particles and muon size spectra of cosmic ray extensive air showers considering primary composition may or may not change beyond the knee of the energy spectrum. It is found that EAS-TOP observations consistently infer a knee in the primary energy spectrum provided the primary is pure unchanging iron whereas no consistent primary spectrum emerges from simultaneous use of the KASCADE observed total charged particle and muon spectra. However, it is also found that when primary composition changes across the knee the estimation of spectral index of total charged particle spectrum is quite tricky, depends on the choice of selection of points near the knee in the size spectrum.

Analysis of muon and electron neutrino charged current interactions in the T2K near detectors

We present the updated measurement of the muon neutrino interaction rates and spectrum at the T2K near detector complex, ND280, located at the JPARC accelerator facility in Tokai, Japan, 280 meters downstream from the target. The measurements are obtained using all the data collected until 2014. The momentum-angle spectrum of muons from νμ charged current (CC) interactions measured at ND280 off-axis detector constrains the flux and cross-section uncertainties in the T2K oscillation analysis. This spectrum was also used to measure a differential cross-section measurement of muon neutrinos on carbon. Similarly the νe contamination of the T2K beam was measured to verify this intrinsic background for the electron neutrino appearance and provide the first electron neutrino cross-section result since the Gargamelle experiment. The νμ CC inclusive events selected in the on-axis detector (INGRID) at 280 m and originally used for monitoring the T2K beam stability were also used to measure the CC interaction cross sections on carbon and iron. The selections and results for both ND280 and INGRID will be presented in this paper as well as future prospects for both detectors.

A case study of using cosmic ray muons to monitor supercritical CO2 migration in geological formations

In carbon dioxide (CO2) geological storage, the monitoring of the injected CO2 migration in underground storage is essential to understanding storage process and ensuring storage safety. An effective monitoring system will be required for decades into the future during storage phase to indicate the location where the injected fluids have extended to. A novel radiographic probing technique using naturally occurring cosmic ray muon radiations was introduced in recent years as a promising continuous and cost-effective candidate method. This method utilizes the ability of different materials to attenuate muons as the detection property. The feasibility of this technique still needs to be investigated in terms of higher simulation accuracy, the intrinsic spatial resolution, and response sensitivity for storage with impurities. In this study, simulations are performed to understand the sensitivity of this method in responding to the presence of the injected fluids in saline aquifer formations. The energy spectrum of the cosmic ray muons for different zenith angles at sea level is sampled according to the modified Gaisser’s formula. The muon propagation process has been simulated with high fidelity by detailed description of different materials involved in the deployed geological model. The muon attenuation along different paths carries information on the interior of a monitored region and the muon scattering effect may lower the accuracy to locate the fluids. The intrinsic spatial resolution of this method is thus analyzed and found to be at a scale of several meters. This method aims to provide the basis for understanding the injected fluids behavior. The simulations show that the method is feasible and the injected fluids in saline aquifers can be identified with a high sensitivity.

Characterization of the atmospheric muon flux in IceCube

Muons produced in atmospheric cosmic ray showers account for the by far dominant part of the event yield in large-volume underground particle detectors. The IceCube detector, with an instrumented volume of about a cubic kilometer, has the potential to conduct unique investigations on atmospheric muons by exploiting the large collection area and the possibility to track particles over a long distance. Through detailed reconstruction of energy deposition along the tracks, the characteristics of muon bundles can be quantified, and individual particles of exceptionally high energy identified. The data can then be used to constrain the cosmic ray primary flux and the contribution to atmospheric lepton fluxes from prompt decays of short-lived hadrons.In this paper, techniques for the extraction of physical measurements from atmospheric muon events are described and first results are presented. The multiplicity spectrum of TeV muons in cosmic ray air showers for primaries in the energy range from the knee to the ankle is derived and found to be consistent with recent results from surface detectors. The single muon energy spectrum is determined up to PeV energies and shows a clear indication for the emergence of a distinct spectral component from prompt decays of short-lived hadrons. The magnitude of the prompt flux, which should include a substantial contribution from light vector meson di-muon decays, is consistent with current theoretical predictions.The variety of measurements and high event statistics can also be exploited for the evaluation of systematic effects. In the course of this study, internal inconsistencies in the zenith angle distribution of events were found which indicate the presence of an unexplained effect outside the currently applied range of detector systematics. The underlying cause could be related to the hadronic interaction models used to describe muon production in air showers.

Discovering sterile neutrinos lighter thanMWat the LHC

We study the purely leptonic $W$ decays $W^+ \to e^+ \mu^- e^+ \nu_e$ and $W^+ \to e^+ e^+ \mu^- \bar \nu_\mu$ (or their charge conjugates) produced at the LHC, induced by sterile neutrinos with mass below $M_W$ in the intermediate state. While the first mode is induced by both Dirac or Majorana neutrinos, the second mode is induced only by Majorana neutrinos, as it violates lepton number. We find that, even when the final (anti-)neutrino goes undetected, one could distinguish between these two processes, thus distinguishing the Dirac or Majorana character of the sterile neutrinos, by studying the muon spectrum in the decays.

Testing model energy spectra of charged particles produced in hadron interactions on the basis of atmospheric muons

An original method for calculating the spectrum of atmospheric muons with the aid of the CORSIKA 7.4 code package and numerical integration is proposed. The first step consists in calculating the energy distribution of muons for various fixed energies of primary-cosmic-ray particles and within several chosen hadron-interaction models included in the CORSIKA 7.4 code package. After that, the spectrum of atmospheric muons is calculated via integrating the resulting distribution densities with the chosen spectrum of primary-cosmic-ray particles. The atmospheric-muon fluxes that were calculated on the basis of the SIBYLL 2.1, QGSJET01, and QGSJET II-04 models exceed the predictions of the wellknown Gaisser approximation of this spectrum by a factor of 1.5 to 1.8 in the range of muon energies between about 103 and 104 GeV.Under the assumption that, in the region of extremely highmuon energies, a dominant contribution to the muon flux comes from one to two generations of charged π± and K ± mesons, the production rate calculated for these mesons is overestimated by a factor of 1.3 to 1.5. This conclusion is confirmed by the results of the LHCf and TOTEM experiments.

Altitude profile of atmospheric muons in a location with relatively high cut-off rigidity

We have investigated the differential and integrated muon fluxes, muon charge ratios and the zenith angle dependence of the integrated muon intensities at sea level and various depths in the atmosphere of Tsukuba, Japan, for muons with momenta below 400GeV/c using the Geant4 simulation package. The simulated sea level muon spectrum and charge ratio have been seen to be in good agreement, throughout the momentum interval of the interest, with those from the measurements made by the BESS-TeV spectrometer. Integrated muon intensities have been found to increase as the atmospheric depth decreases up to slightly above 200g/cm2, and then they have a trend to decrease at lower atmospheric depths. Muon charge ratios at each of the atmospheric depth of interest have been shown to have a very similar behavior with the one at sea level. Simulation results for the zenith angle dependence of muon intensity have been quite compatible with the existing information in the literature for sea level. It has also been shown that the zenith angular dependence of muon intensity has a tendency to disappear (to obey the secθ distribution) as the atmospheric depth decreases for muons with relatively low (high) momenta.

Atmospheric neutrino flux calculation using the NRLMSISE-00 atmospheric model

In this paper, we extend the calculation of the atmospheric neutrino flux~\cite{hkkm2004,hkkms2006,hkkm2011} to the sites in polar and tropical regions. In our earliest full 3D-calculation~\cite{hkkm2004}, we used DPMJET-III~\cite{dpm} for the hadronic interaction model above 5~GeV, and NUCRIN~\cite{nucrin} below 5~GeV. We modified DPMJET-III as in Ref.~\cite{hkkms2006} to reproduce the experimental muon spectra better, mainly using the data observed by BESS group~\cite{BESSTeVpHemu}. In a recent work~\cite{hkkm2011}, we introduced JAM interaction model for the low energy hadronic interactions. JAM is a nuclear interaction model developed with PHITS (Particle and Heavy-Ion Transport code System)~\cite{phits}. In Ref.~\cite{hkkm2011}, we could reproduce the observed muon flux at the low energies at balloon altitude with DPMJET-III above 32 GeV and JAM below that better than the combination of DPMJET-III above 5~GeV and NUCRIN below that. Besides the interaction model, we have also improved the calculation scheme according to the increase of available computational power, such as the "virtual detector correction" introduced in Ref.~\cite{hkkms2006} and the optimization of it in Ref.~\cite{hkkm2011}. The statistics of the Monte Carlo simulation is also improved at every step of the work.

Constraints of hadronic interaction models from the cosmic muon observations

A simple method of the vertical muon energy spectrum simulations has been suggested. These calculations have been carried out in terms of various models of hadronic interactions. The most energetic π ± -mesons and K ± -mesons produced in hadron interactions contribute mainly to this energy spectrum of muons due to the very steep energy spectrum of the primary particles. So, some constraints on the hadronic interaction models may be set from a comparison of calculated results with cosmic data on the vertical muon energy spectrum. This comparison showed that the most energetic secondary particles production is too high in the case of the QGSJET II-04 model and rather low in the case of the QGSJET II-03 model. These conclusion have been supported by the LHC data. The longitudinal development of extensive air showers (EAS), in particular, the depth Xmax of its maximum, is determined by the rate of fragmentation of energy E0 of the primary particle. This rate depends on the interaction cross sections of shower particles, and on the energy spectra of secondary particles are generated in interactions. Obviously, if the probability of particle production with energies close to the energy of the incident particle is high then the development of the cascade slows down. Conversely, in the case of rapid fragmentation of the incident energy cascades develop rather rapidly. The depth Xmax of shower maximum in many studies is the main parameter for determining the composition of primary cosmic radiation (PCR) at ultra-high energies. It should also be noted that in the case of the slow rate of development cascade and hence large values of depth Xmax the lateral distribution of the shower particles at the observation level becomes narrower. Therefore, the values of signals in the surface and underground detectors located at large distances from the shower core are decreased. It must be taken into account when determining the density of muons at large distances from the shower core and the composition of the PCR found from the muon lateral distribution. Studies of the composition and characteristics of the energy spectrum of the PCR are important components of theories of the origin of cosmic rays at ultra-high energies. Interpretation of experimental data on the depth of the shower maximum Xmax and the observed fraction of muons at a fixed distance from the shower core are carried out in terms of different hadronic

Test of hadron interaction models in the most important energy range of secondary particles in spectra of atmospheric muons

A simple method has been proposed for testing hadron interaction models, which are used to simulate extensive air showers, in observed spectra of atmospheric muons. It has been shown that muon flux intensities in the energy range of 102–104 GeV that are calculated within the SIBYLL 2.1, QGSJETII-04, and QGSJET01 models exceed the data of the classical experiments L3 + Cosmic, MACRO, and LVD on the spectra of atmospheric muons by a factor of 1.5–2. It has been concluded that these tested models overestimate the generation of secondary particles with the highest energies in elementary events of interaction between hadrons in agreement with the LHCf and TOTEM accelerator experiments.

Impact of secondary acceleration on the neutrino spectra in gamma-ray bursts

We discuss the acceleration of secondary muons, pions, and kaons in gamma-ray bursts within the internal shock scenario, and their impact on the neutrino fluxes. We introduce a two-zone model consisting of an acceleration zone (the shocks) and a radiation zone (the plasma downstream the shocks). The acceleration in the shocks, which is an unavoidable consequence of the efficient proton acceleration, requires efficient transport from the radiation back to the acceleration zone. On the other hand, stochastic acceleration in the radiation zone can enhance the secondary spectra of muons and kaons significantly if there is a sufficiently large turbulent region. Overall, it is plausible that neutrino spectra can be enhanced by up to a factor of two at the peak by stochastic acceleration, that an additional spectral peaks appears from shock acceleration of the secondary muons and pions, and that the neutrino production from kaon decays is enhanced. Depending on the GRB parameters, the general conclusions concerning the limits to the internal shock scenario obtained by recent IceCube and ANTARES analyses may be affected by up to a factor of two by secondary acceleration. Most of the changes occur at energies above 10^7 GeV, so the effects for next-generation radio-detection experiments will be more pronounced. In the future, however, if GRBs are detected as high-energy neutrino sources, the detection of one or several pronounced peaks around 10^6 GeV or higher energies could help to derive the basic properties of the magnetic field strength in the GRB.

Variations of muon flux in the atmosphere during thunderstorms

The variations of muon flux that are occasionally registered by ground-based scintillation detectors during thunderstorms are investigated. The variations are mainly negative (deficit) and originate due to the electric field of thunderclouds. They last from several minutes up to several hours and demonstrate minor (up to a few percent) deviations against the background. We develop an appropriate theoretical model to describe this phenomenon by investigating the two processes responsible for it: (i) the transformation of an energetic spectrum of muons in the electric field due to their acceleration or deceleration, and (ii) the decay of muons conditioned by a short life span. The change of muon flux near the ground is derived at a given altitudinal distribution (profile) of the electric field. Two possible opposite cases of an altitudinal profile of a two-layered electric field are considered: (i) upward directed in the lower layer of the cloud and downward directed in the upper layer and (ii) vice versa. We find that in case (i), the deficit of muon fluxes is observed by the detector at any threshold energy. It emerges due to a decrease of the flux of positive muons decelerated in the lower layer of a thundercloud. The corresponding increase of the flux of accelerated muons turns out to be smaller because of their partial decaying. As a result, an uncompensated decrease of total flux of muons is formed near the ground. However, in case (ii), the deficit is smaller, and it may become positive when it is observed by detectors with a threshold energy larger than $\ensuremath{\sim}300\text{ }\mathrm{MeV}$. The results may help estimate the height and electric field of thunderclouds by analyzing the records of muon detectors with different energy thresholds.