The neutrino masses are at least six orders of magnitude smaller than the masses of all other charged fermions of the Standard Model. The exchange of weakly interacting particles of low mass creates an interaction potential with a high interaction radius, which can affect the structure of neutron stars. Since neutrinos are fermions, they can participate in long-range two-body interactions through the exchange of neutrino pairs. The neutrino-pair exchange potential is similar to the van der Waals potential resulting from the exchange of two photons.
The infrared instability of long-range multiparticle neutrino interactions in neutron stars has been the subject of discussion for a long time [1-3]. For regularization of neutrino-induced interactions in the infrared range, it was proposed to limit neutrino masses from below to a value of the order of one electron volt, which is remarkably close to the current neutrino mass constraints derived from tritium β-decay experiments and cosmological models.
In this paper, it is demonstrated that the infrared divergences discussed so far in the literature are absent in each individual term of the decomposition of the thermodynamic potential by powers of neutron matter density. Moreover, for both massless and massive neutrinos, all the terms vanish except for the interaction of two neutrons, which is negligible. As a result, long-range multiparticle neutrino interactions have no observable effect on the structure and stability of neutron stars.

[1] E. Fischbach, Long-Range Forces and Neutrino Mass, Ann. Phys. (N.Y.) 247, 213 (1996).
      [2] As. Abada, M.B. Gavela, O. Pinea, To rescue a star, Phys. Lett. B 387, 315-319 (1996).
      [3] E. Fischbach, D.E. Krause, Quan Le Thien and C. Scarlett, Implications of Recent KATRIN Results for Lower-Limits on Neutrino Masses, arXiv:2208.03790v1 [hep-ph] 7 Aug 2022.

M.I. Krivoruchenko
JETP Letters 117, issue 2 (2023)