On particle production for high energy neutrino beams

Analytical formulae for the calculation of secondary particle yields in p-A interactions are given. These formulae can be of great practical importance for fast calculations of neutrino fluxes and for designing new neutrino beam-lines. The formulae are based on a parameterization of the inclusive invariant cross sections for secondary particle production measured in p-Be interactions. Data collected in different energy ranges and kinematic regions are used. The accuracy of the fit to the data with the empirical formulae adopted is within the experimental uncertainties. Prescriptions to extrapolate this parameterization to finite targets and to targets of different materials are given. The results obtained are then used as an input for the simulation of neutrino beams. We show that our approach describes well the main characteristics of measured neutrino spectra at CERN. Thus it may be used in fast simulations aiming at the optimisation of the long-baseline neutrino beams at CERN and FNAL. In particular we will show our predictions for the CNGS beam from CERN to Gran Sasso.