A new method for measuring the absolute neutrino mass

The probability of the event that a neutrino produced in pion decay is detected in the intermediate $T$ shorter than the life-time $τ_π$, $T \leq τ_π$, 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 $Γ_0+\tilde{g}(ω_ν, {T};τ_π) \tilde Γ_{1}$, where $\tilde{g}(ω_ν,{T};τ_π)$ depends weakly on $τ_π$ and $ω_ν={m_ν^2c^4}/{(2E_ν\hbar)}$, $c$ is the speed of light. $Γ_0$ is the standard one and the correction, $\tilde{g}(ω_ν, {T};τ_π) \tilde Γ_{1}$, 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.

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