Ephraim Fischbach, Al Overhauser
Physics Department, Purdue University,
West Lafayette, Indiana 47907
Brian Woodahl
Physics Department, North Dakota State University, Fargo, North Dakota 58105
We analyze the decays Phi to K-Kbar utilizing a formulation of transition rates which explicitly exhibits corrections to Fermi's Golden Rule. These corrections arise in systems in which the phase space and/or matrix element varies rapidly with the energy, as happens in Phi to K-Kbar, which is just above threshold. We show that the theoretical corrections resolve a puzzling 5-sigma discrepancy between theory and experiment for the branching ratio Gamma[K+,K-] over Gamma[Ko,Kobar]. ©2002 Elsevier Science.
Fourth-Order Self-Energy of a Neutron Star Due to Massive Neutrino Exchange
Brian Woodahl and Ephraim
Fischbach
Physics Department, Purdue University,
West Lafayette, Indiana 47907
We calculate the self-energy of a neutron star to fourth-order in the Fermi constant Gf, arising from neutrino exchange to one loop. We assume the neutron star is comprised entirely of neutrons and use the low-energy Lagrangian describing the interaction between neutrons and massive Dirac neutrinos. The calculation presented here derives from a more rigorous formalism than that used in previous work on the four-body self-energy, and consequently the results differ slightly. We have determined that the fourth-order self-energy, like the recently calculated second-order self-energy, is positive and dependent on the neutron-neutron hard core radius. Importantly, we also show that the fourth-order contribution is greater than the second order. We further demonstrate that, in contrast with the recently calculated vacuum energy shift in which the neutron field is taken to be external, the four-body self-energy decreases in magnitude as the neutrino mass is increased. This decrease of the self-energy as the neutrino mass increases was also the case in the second-order self-energy. The implications of these new findings are discussed. ©2001 The American Physical Society.
Self-Energy to Lowest Order of a Neutron Star Due to Massive Neutrino Exchange
Brian Woodahl and Ephraim
Fischbach
Physics Department, Purdue University,
West Lafayette, Indiana 47907
We calculate the self-energy to lowest order in the Fermi constant Gf (two-body contribution) of a neutron star due to massive Dirac neutrino exchange. We show that, in contrast to the recently calculated vacuum energy in which the neutron field is considered to be external, the two-body self-energy of the neutron field decreases as the mass of the Dirac neutrino is increased. We also show by direct calculation that the presence of the neutrino condensate has little effect on the two-body self-energy. The implications of these results are discussed in detail. ©2000 The American Physical Society.
Vacuum Energy for a Massive Dirac Neutrino Propagating in a Neutron Medium
Brian Woodahl and Ephraim
Fischbach
Physics Department, Purdue University,
West Lafayette, Indiana 47907
We calculate the energy acquired by the vacuum due to both a massless and massive Dirac neutrino propagating in an external neutron field, utilizing the quantum field theoretic approach of Schwinger. This method computes the vacuum energy to all orders in the coupling, using the interaction Hamiltonian for a neutrino in the presence of an external background of neutrons. To verify our results, we develop heuristic arguments to compute the energy of the neutrino condensate arising from a neutron-induced chiral potential well. The results for the massive case are new, and are discussed in some detail. ©2000 The American Physical Society.
Neutrino-Exchange Interactions in 1-, 2-, and 3-Dimensions
Authors: Brian Woodahl and Ephraim
Fischbach (Purdue University)
Comments: LaTeX, 10 pages
Report-no: PURD-TH-98-02
We examine several recent calculations of the self-energy of a neutron star arising from neutrino-exchange. It is shown that the results of Abada, et al. in 1+1 dimensions have no bearing on a 3-dimensional neutron star, since the criticality parameter (Gf N)/R^2 is always much smaller than unity in 1+1 dimensions. Furthermore, the calculation of Kiers and Tytgat in 3-dimensions is shown to disagree with the lowest order 2-body contribution, which is known exactly.
Authors: Brian Woodahl, et. al. (Purdue
University)
Comments: LaTeX, 8 pages, 2 PostScript
figures
Proceedings of: "Beyond the Desert", Castle
Ringberg, Tegernsee, Germany, 8-14 June 1997
Report-no: PURD-TH-97-07
It has been shown recently that the exchange of virtual neutrino
pairs leads to long-range forces in neutron stars and
white dwarfs. Here we consider the possibility that the presence of trapped low-energy neutrinos (neutrino condensate) can suppress the exchange of the virtual neutrino pairs, thereby suppressing the long-range forces. We show that for the two-body contribution, the resulting suppression is extremely small.
Schleef, et. al.
Physics Department, Purdue University,
West Lafayette, Indiana 47907
A formalism is developed for using geometric probability to evaluate interaction energies arising from radial potentials. The integrals that arise can be separated into a radial part and nonradial part the describes the geometry of the system, including the density distribution. We show that all the geometric information can be encoded into the "radial density function", which depends on the radial distance, and the number densities of the two interacting regions. Jour. Math. Phy. Vol 40, No. 2, [S0022-2488(99)00102-4]. ©1999 American Institute of Physics.
bwoodahl@iupui.edu
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