A new approach to derive atmospheric muon fluxes

Abstract

Hadron diffusion equations are solved using an alternative analytical method based on depth-like ordered exponential operators, similar to those used by Feynman. With this method, these equations are solvable for any form of the primary spectrum (an improvement compared with other methods). The muon fluxes generated by these hadronic showers are then obtained for zenith angles covering 0°–89°. A comparison of our calculations for the vertical and horizontal muon fluxes with experimental data and with another theoretical calculation is made. The agreement between them is in general very good, greater than 90%.

An operator method to solve transport equations of atmospheric neutrinos

“…In order to solve the transport equations for atmospheric neutrinos, we need to perform numerical methods to get these fluxes. All the necessary parameters to do that are fully described in a series of papers published by us in this decade [4]. Thus, we now present our results and compare them with theoretical, experimental and simulated results found in the literature.…”

“…In order to obtain the neutrino fluxes and the ν/ν ratio, it is important to know the meson fluxes. The π ± and K ± fluxes were already obtained in previous papers [4]. But we need to know the solutions for the K 0 L component, since it is an important source of neutrinos as well.…”

“…where (BR) M represents the branching ratio for the (M → ν j ) decay and M(t, E 0 , θ * ) corresponds to the meson fluxes given by pions taken from the second paper of [4] and kaons from equation ( 34).…”

“…In the above equation, the index j means the neutrino (or anti-neutrino) kind and the index s represents the muon helicity (LH or RH). The secondary spectra f µ ± s →ν j are given by Lipari [5] and the muon spectra are taken from the second paper of [4]. In function f µ we have two terms: one that includes the muon polarization and another one without polarization, which allows us to investigate the effect of the muon polarization on the neutrino fluxes.…”

“…One of these methods consists in the use of the Feynman-like procedure of ordered exponential operators to solve them [3]. Some papers were published by us based on this specific method [4]. Here, we extend these same techniques to obtain neutrino fluxes.…”