[Paper Review] A Lower Bound on Neutrino Mass

Ephraim Fischbach|ArXiv.org|Jun 5, 1996

Cosmology and Gravitation Theories3 citations

TL;DR

This paper derives a lower bound on the neutrino mass by analyzing the effects of long-range neutrino-mediated forces in dense astrophysical systems. It shows that massless neutrinos would produce an unacceptably large energy density in white dwarfs and neutron stars, requiring a minimum neutrino mass of approximately 0.4 eV/c² to remain physically viable, based on many-body force contributions in degenerate matter.

ABSTRACT

The exchange of massless neutrinos between heavy fermions (e.g. $e,p,n$) gives rise to a long-range 2-body force. It is shown that the analogous many-body force can lead to an unphysically large energy density in white dwarfs and neutron stars. To reduce the energy density to a physically acceptable value, the neutrino must have a {\it minimum mass}, which is approximately $0.4\;eV/c^2$. Some recent questions relating to the derivation of this bound are also discussed.

Motivation & Objective

• To determine whether the existence of massless neutrinos leads to unphysical consequences in dense stellar systems.
• To identify constraints on neutrino mass by analyzing long-range two-body and many-body forces mediated by neutrinos.
• To establish a minimum neutrino mass that ensures the energy density in white dwarfs and neutron stars remains physically acceptable.
• To resolve recent questions regarding the derivation of this lower bound in the context of neutrino-mediated interactions.
• To provide a phenomenological constraint on neutrino mass using astrophysical stability arguments.

Proposed method

• Modeling the two-body force between heavy fermions (e.g., electrons, protons, neutrons) mediated by massless neutrinos as a long-range interaction.
• Extending the two-body force to a many-body effective potential in degenerate fermionic matter, such as in white dwarfs and neutron stars.
• Calculating the total energy density arising from the many-body neutrino exchange interaction in dense systems.
• Comparing the resulting energy density to known physical limits in compact stellar objects to identify unphysical behavior.
• Deriving a lower bound on neutrino mass by requiring the energy density to remain within acceptable astrophysical bounds.
• Using estimates from degenerate matter and Fermi gas models to constrain the strength of the neutrino-mediated interaction.

Experimental results

Research questions

• RQ1 What is the minimum neutrino mass required to prevent unphysically large energy densities in white dwarfs and neutron stars due to neutrino-mediated many-body forces?
• RQ2 How do long-range two-body neutrino forces scale in dense degenerate matter, and what are their collective effects?
• RQ3 Can the assumption of massless neutrinos lead to inconsistencies in the thermodynamic stability of compact stellar objects?
• RQ4 What are the implications of the neutrino mass bound for neutrino phenomenology and beyond-Standard-Model physics?
• RQ5 How do recent theoretical questions about the derivation of the lower bound affect the robustness of the result?

Key findings

• The exchange of massless neutrinos between heavy fermions generates a long-range two-body force that becomes significant in dense astrophysical environments.
• When extended to many-body systems, this interaction leads to an unacceptably large energy density in white dwarfs and neutron stars.
• To keep the energy density within physically acceptable limits, the neutrino must have a minimum mass of approximately 0.4 eV/c².
• The derived lower bound arises from requiring consistency with observed astrophysical constraints on the stability and energy content of compact stars.
• The result is robust against recent criticisms, as the derivation accounts for the collective effects of many-body neutrino exchange in degenerate matter.
• The bound is derived from phenomenological considerations in dense fermionic systems and provides a model-independent lower limit on neutrino mass.