Relativistic theory of unstable particles. 2
Aug, 19596 pages
Published in:
- Phys.Rev. 115 (1959) 1079-1084
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Abstract: (APS)
This paper is a direct continuation of an earlier paper (I) where an attempt was made to set up a field-theoretic foundation for the theory of mean mass and lifetime of an unstable particle. It was argued in I that the decay-time plot of a beam of unstable particles is a concept peculiar to a single-particle theory; that from a field-theoretic point of view, mass (the variable conjugate to proper time) rather than time has the primary significance. Here we show that the spectral function ρ(m2) appearing in the (field-theoretic) one-particle propagator has a direct significance as the probability of finding in production an unstable particle of mass m. This allows us to define a "one-particle" state for the unstable particle as a superposition of its outgoing decay states suitably weighted in mass space [with a factor which is the square-root of ρ(m2)]. The proper-time propagation of this state gives the decay amplitude, and its modulus is ideally the experimentally observed decay-time plot.
The time plot is explicitly evaluated for π decay. Insofar as the distribution of mass values for the π meson starts with the μ mass (assumed stable), the time plot is not merely the conventional decay exponential e−ττ0. There are additional terms which become important about a hundred lifetimes after the particle is created.
Finally we compare the time plots for particle and antiparticle decays on the basis of CTP invariance.- particle: relativistic
- propagator
- spectral representation
- pi: decay
- decay: pi
- invariance: CPT
- lifetime
- mass
- antiparticle
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