Overview

Atmospheric muon flux

When a cosmic particle hits our Earth’s atmosphere, secondary particles are produced in cascades. Depending on the energy of the primary particle, these cascades are large and produce not only one but several particles. These cascades are called extensive air showers. Since most of the produced particles are unstable, on Earth’s surface mainly neutrinos and muons are detected. The amount of muons arising per area per time interval per solid angle and per energy is called muon flux. This muon flux is divided into two different components, depending on their spectral index \(\gamma\), defined by

\[\begin{equation} \frac{dN}{dE} \propto \Phi_0 \cdot E^{-\gamma} \; . \end{equation}\]

One is the conventional component with a spectral index \(\gamma = 3.7\). This flux contains muons arising from pions and kaons, which are the particles produced the most in the first interactions, because they are the lightest hadrons. The other part is build by the prompt component, which are in general all other muons that originate not from pions and kaons. The flux has a spectral index \(\gamma = 2.7\). Thus, it is shifted to higher energies in comparison to the conventional flux. In other words, the prompt spectrum is flatter than the conventional one. The prompt produced particles have short lifetimes which lead in first order to an immediate decay. Hence, the muon energy correlates stronger to the primary particle energy. Instead, the conventional pions and kaons live long enough to interact with the atmosphere. These re-interactions in the atmosphere cause energy losses which reduces the energy successively. This leads to the resulting muons having lower energy as well. Conventional muons dominate below \(1\,\mathrm{PeV}\) and prompt muons dominate above. Figure Fig. 1 shows the different components of the atmospheric muon flux created with MCEq. More information to the hadronic interaction model SIBYLL used to create these spectra are provided here.

Fig. 1 : The atmospheric muon and muon neutrino flux calculated with MCEq is shown.

Previous analyses

Due to the fact, the resulting muon flux follows a power law, the low statistics at high energies are a challenge to detect the prompt component. In the past, three analyses were performed focused on high energetic muons arising from our Earth’s atmosphere by Thomasz Fuchs, Patrick Berghaus and Hans-Peter Bretz. In Tomasz’s thesis, which included an unfolding of the energy spectrum with one year of experimental data, the analysis was limited by MC statistics. This caused the analysis to result in a prompt normalization that is compatible with zero. In Patrick’s thesis, a mismatch between MC and data was found in the \(\cos(\theta)\) distribution. This issue leads to systematic uncertainties resulting the final significance of the detection of the prompt component to be lower than \(3.5 \sigma\). Hans-Peter performed an analysis with three years of data, but a final muon spectrum as a function of the actual muon energy has never been derived.

The links to the analyses can be found here.

New analysis

Our new analysis aims for two goals. On the one hand, we want to detect the prompt component of the atmospheric muon flux significantly. This will be performed by a forward fit of the prompt normalization. On the other hand, an unfolding of the muon energy spectrum will be done.

In the previous analyses, the true information whether a muon is prompt or conventional was not available. To classify a muon as prompt, the type of the parent particle needs to be known (see prompt definition). This information was never saved in the way the CORSIKA simulations have been run in IceCube. The additional information needs more disk storage and for neutrino source searches, these information are not valuable. Hence, it was not important to save the parent particles.

To include the parent and grandparent particles of a muon in the I3MCTree, the EXTENDED HISTORY option needs to be set in CORSIKA. We have started to run simulations with this option, which enables the possibility to divide the atmospheric muon spectrum in a prompt and conventional component. Thus, the spectrum can be adjusted by applying a scalar to scale the amount of prompt and conventional particles. This scalar is the normalization which is measured in the final forward fit. Since the runtime of CORSIKA simulations at high energies is on the order of magnitude of months to create sufficient statistics, this scaling method allows a forward fit without running several CORSIKA simulations in which the hadronic interaction models are adjusted. This has two advantages. First, it saves time and resources. Second, tuning the hadronic interaction models is not simply to do and requires a close collaboration with the model builders. Hence, the scaling method is a good way to measure the prompt component.