Calculation of muon yields, response functions, and sea level integral energy spectrum using recent accelerator data and Feynman scaling

We calculate the number of muons of energy greater than Eµ due to a primary nucleon of energy E0 for Eµ ≳ 10 GeV. The yields have been calculated (assuming normal parentage for the muons) by solving the atmospheric diffusion equation governing the pion flux in the atmosphere and determining the corresponding muon production spectrum and hence the muon yields. This method assures that muons from pions many generations removed from the primary are included and, in addition, takes account of the effect of pion decay on the multiplication of the pion flux in the atmosphere. The basic input to the equation is the inclusive cross sections for the processes pp → π± + (anything) and πp → π + (anything) as determined from recent accelerator data (including intersecting storage ring (ISR) data for proton-proton (pp) interactions). These production spectra are extrapolated as necessary by use of the Feynman scaling hypothesis. We find a median primary energy ranging from about 15Eµ at Eµ ∼ 10 GeV to about 11Eµ at Eµ ∼ 1000 GeV. The derived sea level integral muon energy spectrum is in good agreement with the observed spectrum.