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 $\text{SU}\left(3\right)$ 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.

• Received 10 October 2023
• Revised 3 December 2023
• Accepted 5 January 2024

DOI:https://doi.org/10.1103/PhysRevC.109.025206

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Published by the American Physical Society