Quantum Diffraction of Neutrino

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 $Γ_0+g(ω_ν \textL/c) Γ_1 $, where $g(ω_ν\textL/c)$ is the universal function, $ω_ν=m_ν^2c^4/ (2E_ν\hbar)$, $c$ is the speed of light, and $Γ_0$ 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.