Kenzo Ishikawa, Yutaka Tobita
The many-body wave function of a pion and its decay products shows that the probability of detecting a neutrino possesses a unique finite size correction. The detection rate at a finite distance $\text{L}$ is expressed as $\Gamma_0+\tilde g(\omega_{\nu} \text{L}/c) \Gamma_{1} $, where $\omega_{\nu}={m_{\nu}^2c^4}/{2E_{\nu}\hbar}$ and $c$ is the light velocity. $\Gamma_0$ is a constant that is computed with the standard S-matrix of plane waves and the second term is a finite size correction that is computed with wave packets. The value of $\tilde g(x)$ decreases rapidly with $x$ and vanishes in charged leptons, but is finite in neutrinos at a macroscopic L. The finite size correction reveals a diffraction pattern of a single neutrino and can be computed rigorously with the light-cone singularity of a system consisting of a pion and a muon. We predict that the neutrino diffraction would be observed at near-detector regions of ground experiments and that it could be used for the experimental determination of the neutrino mass.
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http://arxiv.org/abs/1106.4968
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