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 $\tau_{\pi}$, $T \leq \tau_{\pi}$, 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 $\omega_{\nu}={m_{\nu}^2c^4}/{(2E_{\nu}\hbar)}$, $c$ 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.