High energy cosmic ray physics with underground muons in MACRO. II. Primary spectra and composition

Multimuon data from the MACRO experiment at Gran Sasso have been analyzed using a new method, which allows one to estimate the primary cosmic ray fluxes. The estimated all-particle spectrum is higher and flatter than the one obtained from direct measurements but is consistent with EAS array measurements. The spectral indexes of the fitted energy spectrum are 2.56$\pm$0.05 for $E<\mathrm{}$500 TeV and 2.9$\pm$0.3 for $E>\mathrm{}$5000 TeV with a gradual change at intermediate energies. The average mass number shows little dependence on the primary energy below 1000 TeV, with a value of 10.1$\pm$2.5 at 100 TeV. At higher energies the best fit average mass shows a mild increase with energy, even though no definite conclusion can be reached taking into account errors. The fitted spectra cover a range from $\sim$ 50 TeV up to several thousand TeV.