On the transport equations of cosmic neutrinos passing through Earth and secondary νμ fluxes

The convergence of the iterative solutions of the transport equations of cosmic muon and tau neutrinos propagating through Earth is studied and analyzed. For achieving a fast convergence of the iterative solutions of the coupled transport equations of ντ , ν̄τ and the associated τ ± fluxes, a new semi–analytic input algorithm is presented where the peculiar τ–decay contributions are implemented already in the initial zeroth order input. Furthermore, the common single transport equation for muon neutrinos is generalized by taking into account the contributions of secondary νμ and ν̄μ fluxes due to the prompt τ–decay τ → νμ initiated by the associated tau flux. Differential and total nadir angle integrated upward–going μ + μ+ event rates are presented for underground neutrino telescopes and compared with the muon rates initiated by the primary νμ, ντ and τ fluxes.