• Mathematical representation of our emprirical model (( PDF (December 10th 2006))

The energy fluxes of the downgoing atmospheric muon bundles at the IceCube depth. The muon propagation was calculated by JULIeT. The solid angle integration was made. The expected intensities of the GZK-originated muons and taus are also shown for comparison. Thick Blown upper curve: Our New model in a bundle with alpha = 1.99. This is favored by the IC9 2006 data. The attenuation seen around 108 GeV is due to the GZK cutoff. The effects of the EAS cascade fluctuation was taken into account by Corsika muon simulation. Thick Blown lower curve: Same with alpha = 1.96, which is also consistent with the present IceCube 9 string data. It indicates range of the flux suggested by the IceCube 2006 EHE measurement.
The integral fluxes of the atmospheric muon bundles at the IceCube depth as a function of zenith angles. The muon propagation was calculated by JULIeT. Thick Blown: Our New model prediction.
The differential VERTICAL muon bundle flux at sea level, converted from the flux at the IceCube depth. The intensity is approximately two orders of magnitude higher than the conventional muon flux calculated by Thunman et al (Atropart.Phys. 1996) and a factor of 10 larger than the possible prompt muon flux modeled by Bugaev et al (PRD 1998), although the theoretical upper bound of the prompt muon flux obtained by Zas (Atropart.Phys 1993) is still approximately 10 times higher than this result.

Intoduction of Elert model to Corsika (Saori)