Physics – High Energy Physics – High Energy Physics - Phenomenology
Scientific paper
1995-11-02
Annals Phys. 249 (1996) 298-361
Physics
High Energy Physics
High Energy Physics - Phenomenology
81 pages, 15 Postscript figures, uses a non-standard style file "table.sty" which is appended at the end of the latex file
Scientific paper
10.1006/aphy.1996.0072
The electron neutrino mass has been measured in several tritium beta decay experiments. These experiments are sensitive to a small neutrino mass because the energy release of the decay is small. But the very smallness of the energy release implies that the Coulomb interactions of the slowly moving emitted beta electron are relatively large. Using field theoretic techniques, we derive a systematic and controlled expansion which accounts for the Coulomb effects, including the mutual interaction of the beta ray electron and the electron in the final $^3{\rm He}^+$ ion. In our formulation, an effective potential which describes the long range Coulomb force experienced by the beta ray is introduced to ensure that our expansion is free of infrared divergences. Both the exclusive differential decay rate to a specific final $^3{\rm He}^+$ state and the inclusive differential decay rate are calculated to order $\eta^2$, where $\eta$ is the usual Coulomb parameter. We analyze the order $\eta^2$ correction to the beta ray spectrum and estimate how it may affect the neutrino mass squared parameter and the endpoint energy when this corrected spectrum is used to compare with the experiments. We find that the effect is small.
Brown Lowell
Zhai Chengxing
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