Neutrino diffraction induced by many body interaction

Abstract

The neutrino produced in the pion decay reveals a new diffraction phenomenon due to many-body interactions in an intermediate time region when wave functions of the parent and daughters overlap. Because of diffraction, the probability to detect the neutrino involves a large finite-size correction that depends on the neutrino mass, $m_{\nu }$ and energy, $E_{\nu }$, the speed of light, $c$, and the distance $L$ between the positions of the initial pion and final neutrino, $m_{\nu }^2{c}^{4}L/(2E_{\nu }\hslash )$. The correction vanishes for the charged leptons and is finite for the neutrino at a macroscopic distance, $L$, of near-detector regions in ground experiments. A new method for determining the absolute neutrino mass is proposed.

Comments: 11 pages, 2 figure. effect of pion's life-time added, new figures added, presentation improved