Kenzo Ishikawa, Yutaka Tobita
The probability to detect a neutrino produced in pion decay at a finite distance exhibits unique interference properties that depend on the absolute mass of the neutrino. We describe the neutrino, lepton, and pion by a many-body wave function and find the probability is subject to a large finite-size correction. Its rate at a distance L is expressed as $\Gamma_0+\tilde{g}(\omega_{\nu} \text{L}/c) \Gamma_{1} $, where $\tilde{g}(\omega_{\nu}\text{L}/c)$ is the universal function, $\omega_{\nu}={m_{\nu}^2c^4}/ {(2E_{\nu}\hbar)}$, $c$ is the speed of light, and $\Gamma_0$ is a constant computed with the standard plane-wave S-matrix. The finite-size correction is rigorously computed using wave packets via the light-cone singularity of a system composed of the pion and charged lepton and reveals the diffraction pattern of a single quantum. We discuss the implications of this correction for the muon-neutrino and electron-neutrino reactions. With sufficient statistics, the neutrino diffraction would supply the absolute mass of the neutrino.
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http://arxiv.org/abs/1209.5585
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