A new method for measuring the absolute neutrino mass

Abstract

The probability of the event that a neutrino produced in pion decay is detected in the intermediate $T$ shorter than the life-time ${\tau }_{\pi }$, $T\le {\tau }_{\pi }$, is sensitive to the absolute mass of the neutrino. With a newly formulated S-matrix $S[T]$ that satisfies the boundary conditions of the experiments at a finite $T$, the rate of the event is computed as ${\Gamma }_0+\tilde{g}({\omega }_{\nu },T;{\tau }_{\pi }){\tilde{\Gamma }}_1$, where $\tilde{g}({\omega }_{\nu },T;{\tau }_{\pi })$ depends weakly on ${\tau }_{\pi }$ and ${\omega }_{\nu }=m_{\nu }^2{c}^4/(2E_{\nu }\hslash )$, $c$ is the speed of light. ${\Gamma }_0$ is the standard one and the correction, $\tilde{g}({\omega }_{\nu },T;{\tau }_{\pi }){\tilde{\Gamma }}_1$, reflects relativistic invariance and is rigorously computed via the light-cone singularity of the system and reveals the diffraction pattern of a single quantum. The formula explains unsolved anomalies of neutrino experiments and indicates the heavy neutrino mass, $0.098\pm 0.022$ or $0.083\pm 0.026$ {eV}/ $c^2$ for normal or inverted mass hierarchies, respectively.

36 pages, 12 figures; title changed

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