= SN 1987A neutrino burst
{c}
The original <Kamiokande> paper reported a low-energy event cluster on 23 February 1987 above surrounding background. <Inverse beta decay>, $\bar\nu_e+p\longrightarrow e^++n$, provides an <electron antineutrino> channel through <Positron> light. <Neutrino>-<Electron> <elastic scattering> is more directional. The burst supported <core-collapse supernova> <neutrino> emission, with limited statistics and channel ambiguity.<Observation of a Neutrino Burst from the Supernova SN1987A by K. Hirata and others>[pp. 1490–1493; Fig. 2, Table I and discussion]{ref}
An original counting illustration shows why timing matters. Suppose an independently measured background is a <Poisson process> of rate $b$. In a prespecified window $\Delta t$, the probability of at least two background events is
$$
P(N\ge2)=1-e^{-b\Delta t}(1+b\Delta t).
$$
For the synthetic choice $b\Delta t=0.1$, this is about $0.004679$, obtained by subtracting the zero- and one-event probabilities of the <Poisson distribution>. The <Homestake experiment>'s delayed extraction cannot supply such capture-time clustering. This calculation is not a significance estimate for <SN 1987A>: searching many possible windows, varying acceptance and correlated backgrounds change the inference.
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