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A 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

Authors: Renan Câmara Pereira; Pedro Costa; Constança Providência;João Moreira

Ref.: Phys. Rev. C 109, 025206-57 (2024)

Abstract: 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. In order 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)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.

DOI: 10.1103/PhysRevC.109.025206

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