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Validity of Special Relativity at Small Distances and the Velocity Dependence of the Charged-Pion Lifetime

  • Lundberg, L-E.
  • Redei, L.B.
Publication Date
May 25, 1968
DOI: 10.1103/PhysRev.169.1012
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The velocity dependence of the lifetime of the pion is investigated under the assumption that the Hamiltonian contains a spatial form factor which in the lab frame (the frame at rest with respect to the neighboring macroscopic bodies) vanishes for distances larger than some length α. In this model, there is a violation of the principles of special relativity at small distances. In particular, space-time is anisotropic at distances smaller than α. The lifetime of the pion is calculated to second order in α, and it is shown that there will be about 1% deviation from the usual formula τ(v)=(1−v2c2)−12τ(0), (which holds if special relativity is valid at arbitrarily small distances) if, e.g., the pion energy Eπ=104 MeV and α∼5×10−16 cm. The measurement of the velocity dependence of the pion lifetime at high energies could thus serve as a possible check on the validity of special relativity at small distances. The deviation is of the same order of magnitude as that previously obtained for the muon decay.

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