Finite-size effects on multibody neutrino exchange

Abstract

The effect of multibody massless neutrino exchanges between neutrons inside a finite-size neutron star is studied. We use an effective Lagrangian, which incorporates the effect of the neutrons on the neutrinos. Following Schwinger, it is shown that the total interaction energy density is computed by comparing the zero point energy of the neutrino sea with and without the star. It has already been shown that in an infinite-size star the total energy due to neutrino exchange vanishes exactly. The opposite claim that massless neutrino exchange would produce a huge energy is due to an improper summation of an infrared-divergent quantity. The same vanishing of the total energy has been proved exactly in the case of a finite star in a one-dimensional toy model. Here we study the three-dimensional case. We first consider the effect of a sharp star border, assumed to be a plane. We find that there is a non- vanishing of the zero point energy density difference between the inside and the outside due to the refraction index at the border and the consequent non-penetrating waves. An analytical and numerical calculation for the case of a spherical star with a sharp border confirms that the preceding border effect is the dominant one. The total result is shown to be infrared-safe, thus confirming that there is no need to assume a neutrino mass. The ultraviolet cut-offs, which correspond in some sense to the matching of the effective theory with the exact one, are discussed. Finally the energy due to long distance neutrino exchange is of the order of $10^{-8}--10^{-13}GeVperneutron$, i.e. negligible with respect to the neutron mass density.

Latex file (Revtex), 34 pages, 8 postscripted figures

References in corpus (5)

• Neutrino self-energy and pair creation in neutron stars
• Neutrino ground state in a dense star
• Multibody neutrino exchange in a neutron star: neutrino sea and border effects
• Neutrino-Exchange Interactions in 1-, 2-, and 3-Dimensions
• CP-Violating Reflection of High Energy Fermions during a first order Phase Transition

Cited by in corpus (7)

• Neutrino ground state in a dense star
• Neutrino forces in neutrino backgrounds
• On the short-range behavior of neutrino forces beyond the Standard Model: from $1/r^5$ to $1/r^4$, $1/r^2$, and $1/r$
• The neutrino force in neutrino backgrounds: Spin dependence and parity-violating effects
• Neutrino forces and the Sommerfeld enhancement
• Neutrino force at all length scales
• Addendum to Finite-size effects on multibody neutrino exchange