Hadron–hadron interactions at high energy via Rademacher functions Tarek I. Haweel a, * , Mahmoud Y. El-Bakry b, * , Khaled A. El-Metwally c a Department of Electrical Engineering, Assiut University, Egypt b Department of Physics, Faculty of Education, Salalah 211, P.O. Box 2908, Oman c Electrical Engineering, Sultan Qaboos University, P.O. Box 33, Muscat 123, Oman Abstract 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 (p–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 demon- strate 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. Ó 2003 Published by Elsevier Science Ltd. 1. Introduction Particle physics action modeling is an interesting and growing field in theoretical high-energy physics. Mathematical modeling is usually adopted along with statistical and environmental assumptions to investigate such high-energy in- teractions. The validity of the mathematical treatment and assumptions comes from the agreement between the the- oretical results and corresponding outcomes from experimental measurements. The closest is this agreement the successful is a certain modeling. Models are provided for the hadron structure [1–3]. These include the three-fireball model [4], quark models [5], fragmentation model [6,7] and many others. Multi-particle production can be also modeled and described efficiently by studying the multiplicity distribution [8]. Several methods exists which investigate the multiplicity distribution of particles at high-energy [9–12]. Among these are the multiplicity scaling [9,10], partially coherent laser distribution [11], the statistical bootstrap model [12], the negative binomial distribution [13], the two sources model [14], Monte Carlo studies of pion distributions from heavy ion collisions [15], and many others. An efficient approach to study hadron–hadron interaction is to employ the parton two-fireball model [16,17]. In this model, the hadrons are composed of quarks and gluons which, as a collection, may be considered as point-like particles called partons [18]. This nucleon structure has been used in different mathematical models [19] along with other assumptions to describe hadron–hadron interaction. The partons behave as free point-like particles in high-energy * Corresponding authors. E-mail addresses: tarekih@hotmail.com (T.I. Haweel), yasseenl@omantel.net.om (M.Y. El-Bakry). 0960-0779/03/$ - see front matter Ó 2003 Published by Elsevier Science Ltd. doi:10.1016/S0960-0779(02)00581-7 Chaos, Solitons and Fractals 18 (2003) 159–168 www.elsevier.com/locate/chaos