Nonextensive effects in the Nambu-Jona-Lasinio model of QCD

We present a nonextensive version of the QCD-based Nambu-Jona-Lasinio (NJL) model of a many-body field theory describing the behavior of strongly interacting matter. It is based on the nonextensive generalization of Boltzmann-Gibbs (BG) statistical mechanics used in the NJL model, which was taken in the form proposed by Tsallis characterized by a dimensionless nonextensivity parameter q (for q -> 1 one recovers the usual BG case). This new phenomenological parameter accounts summarily for all possible effects resulting in a departure from the conditions required by the application of the BG approach, and allows for a simple phenomenological check of the sensitivity of the usual NJL model to such effects (in particular to fluctuations of temperature and correlations in a system of quarks). As an example, we discuss the sensitivity of such a q-NJL model to the departures from the NJL form, both for q > 1 and q < 1 cases, for such observables as the temperature dependences of chiral symmetry restoration, masses of pi and sigma mesons and characteristic features of spinodal decomposition.