“…A crucial part of the study of oscillation effects with atmospheric neutrinos is a detailed knowledge of the atmospheric neutrino beam at production, before oscillations occur. Increasingly sophisticated calculations [11,12,13,14,15,16,17,18,19,20] have appeared recently. The uncertainties on the calculated flux become a limiting factor when one uses the atmospheric neutrino beam to search for sub-leading effects such as θ 13 mixing, sub-maximal mixing in the 'atmospheric' sector or effects of solar mixing [21,22].…”