Addendum to “Finite-size effects on multibody neutrino exchange”

The interaction energy of the neutrons due to massless neutrino exchange in a neutron star has recently been proved, using an effective theory, to be extremely small and infrared safe. Our comment here is of conceptual order: two approaches to compute the total interaction energy density have recently been proposed. Here, we study the connection between these two approaches. From $\mathrm{CP}$ invariance, we argue that the resulting interaction energy has to be even in the parameter $b=-G_F{n}_n/\sqrt{2},$ which expresses the static neutrino potential created by a neutron medium of density $n_n.$