Probing into Decay Products at Finite Distance in Muon Decay

This paper elucidates the anomalous decay of the muon ascribed to extended waves. Due to a large overlap of the parent and daughters, the transition amplitude and probability for the neutrinos are modified from the standard formula. A rigorous probability from the von Neumann's fundamental principle of the quantum mechanics at a large time interval $T$ is, $P=T\Gamma + P^{(d)}$, where $\Gamma$ is derived from the Fermi's golden rule, and $P^{(d)}$ is a correction term. A new term $P^{(d)}$ has origins in the overlapping waves, and influences the determinations of physical parameters. By including $P^{(d)}$, short-baseline neutrino experiments with LSND, KARMEN, and MiniBooNE become consistent each other and with the solar, long-baseline, and reactor experiments within the three neutrinos. Byproduct is that the absolute neutrino mass of the neutrinos can be measured.