Vacuum energy and configuration energy for a massive neutrino propagating in a neutron star
Abstract
The configuration energy of neutrons due to neutrino exchange at the one-loop level leads to an unphysically large energy in neutron stars when calculated under the constraints of the current Standard Model of massless neutrinos. However, the configuration energy can be made finite by endowing the three neutrino flavors with a minimum mass. The mass exponentially decreases the range of interaction among the neutrons in the star in the same manner as a Yukawa force is reduced. As the mass of the neutrino is increased the configuration energy of the neutron star is reduced to a physically acceptable value. A minimum neutrino mass can be determined from this calculation. We next contrast the configuration energy with the vacuum energy. The vacuum energy is obtained by computing the energy to all orders of a neutrino propagating in an external neutron field in the one-loop approximation. The vacuum energy does not include interactions among the neutrons themselves, it is the energy the vacuum itself acquires in the presence of the neutron field. The vacuum energy can be understood to be equivalent to the energy of the neutrino condensate that forms in the neutron star. We show that the vacuum energy or equivalently condensate energy increases as the neutrino mass increases. This occurs because massive neutrinos/antineutrinos increase the Fermi momentum which allows more particles to be trapped. Contrast this with the configuration energy which decreases as the neutrino mass is increased. We compute the vacuum energy to all orders and show its equivalence to the condensate energy. From this, it is demonstrated that both neutrinos and antineutrinos are trapped in a neutron medium. Also importantly, we show using a different formalism than Schwinger's logarithmic expansion how to compute the configuration energy of a neutron star. This new method of obtaining the configuration energy employs generalized derivative expansions. These higher-derivatives yield results identical to those obtained by Schwinger's formula. We point out that, previously unknown, the four-body configuration energy also has a dependence on rc (the size of the neutron).
Degree
Ph.D.
Advisors
Fischbach, Purdue University.
Subject Area
Particle physics|Astronomy|Astrophysics
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