New approach to the 3-momentum regularization of the in-medium one- and two-fermion line integrals with applications to cross sections in the Nambu-Jona-Lasinio model

We propose the 3 -momentum sphere intersection regularization applied to the one- and two-fermion line integrals at finite temperature and chemical potential. The quark-antiquark polarization function in this new regularization approach is equivalent to the usual 3 -momentum regularization, when the absolute value of the external 3 -momentum of the polarization is zero. Additionally, it respects the particle -antiparticle symmetry of meson states in the Nambu-Jona-Lasinio (NJL) model for all values of temperature and chemical potential. Without this symmetry, in -medium cross sections calculated in the 3 -momentum regularized NJL model are not consistent. To demonstrate the difference between the usual 3 -momentum regularization with the one proposed in this work, we study the quark -quark and quark-antiquark cross sections in both regularization schemes. To this end we use the standard SU(3) NJL model, with four- and six -quark interactions. We observe major quantitative and qualitative differences when comparing quark -quark cross sections in both schemes. The quark-antiquark cross sections, on the other hand, are very similar in both regularizations, owning to the equivalence between the regularizations when the absolute value of the external 3 -momentum is zero.