Non-extensive statistical mechanics and particle spectra in elementary interactions

We generalize Hagedorn's statistical theory of momentum spectra of particles produced in high-energy collisions using Tsallis’ formalism of non-extensive statistical mechanics. Suitable non-extensive grand canonical partition functions are introduced for both fermions and bosons. Average occupation numbers and moments of transverse momenta are evaluated in an analytic way. We analyse the energy dependence of the non-extensitivity parameter q as well as the q-dependence of the Hagedorn temperature. We also take into account the multiplicity. As a final result we obtain formulas for differential cross sections that are in very good agreement with e+e− annihilation experiments.