Hadron–hadron interactions at high energy via Rademacher functions

Charged particles multiplicity distributions for hadron–hadron interactions at high energy have been studied. Two cases are considered: the proton–proton (p–p) and the pion–proton (π–p) interactions. The parton two-fireball model based on an impact parameter is adopted. The overlapping functions, known to be complicated and nonlinear, are approximated employing a series of Rademacher functions. The analysis has been facilitated, since Rademacher functions are linear, analytic and mathematically simple. The accuracy of the approximation is tunable through the order of the employed Rademacher functions. Theoretical expressions for inelastic cross-sections and the charged multiplicity distributions have been derived employing the proposed representation. Figures are provided to demonstrate good agreement between theoretical calculations and experimental data at different energies. Formulae for the change of some important parameters with the variation of high energy have been derived employing least square curve fitting techniques.