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キーワード:
High Energy Physics - Phenomenology, hep-ph, Astrophysics, Solar and Stellar Astrophysics, astro-ph.SR,High Energy Physics - Experiment, hep-ex
要旨:
Neutrino oscillations are only observable when the neutrino production,
propagation and detection coherence conditions are satisfied. In this paper we
consider in detail neutrino production coherence, taking \pi\to \mu \nu \ decay
as an example. We compare the oscillation probabilities obtained in two
different ways: (1) coherent summation of the amplitudes of neutrino production
at different points along the trajectory of the parent pion; (2) averaging of
the standard oscillation probability over the neutrino production coordinate in
the source. We demonstrate that the results of these two different approaches
exactly coincide, provided that the parent pion is considered as pointlike and
the detection process is perfectly localized. In this case the standard
averaging of the oscillation probability over the finite spatial extensions of
the neutrino source (and detector) properly takes possible decoherence effects
into account. We analyze the reason for this equivalence of the two approaches
and demonstrate that for pion wave packets of finite width \sigma_{x\pi} the
equivalence is broken. The leading order correction to the oscillation
probability due to \sigma_{x\pi}\ne 0 is shown to be \sim
[v_g/(v_g-v_\pi)]\sigma_{x\pi}/l_{osc}, where v_g and v_\pi \ are the group
velocities of the neutrino and pion wave packets, and l_{osc} is the neutrino
oscillation length.
