= Water Cherenkov neutrino reconstruction
{title2=$t_i\simeq t_0+\frac n c|\mathbf r_i-\mathbf r_0|$}
<Water Cherenkov neutrino reconstruction> infers a vertex, time and <charged particle> direction from <photomultiplier> pulses. The 1987 analysis recorded charge and timing, calibrated with decaying <muons> and source-produced <gamma rays>, and rejected outer-detector activity and events following <muons>.<Observation of a Neutrino Burst from the Supernova SN1987A by K. Hirata and others>[pp. 1490–1491; Fig. 1 and event-selection criteria]{ref}
\Image[/kamiokande-water-cherenkov-readout.png]
{title=Water Cherenkov readout: light paths, timing and direction}
{description=Functional schematic of <Kamiokande>; dimensions and light paths are illustrative. The ideal timing calculation is an original point-flash example.}
In an ideal point-flash approximation, a light source at $\mathbf r_0$ and time $t_0$ gives the displayed travel-time relation at sensor $\mathbf r_i$ in a medium of <refractive index> $n$. Subtracting two times eliminates $t_0$. With a chosen constant $n=1.33$ and path lengths $3\,\mathrm m$ and $6\,\mathrm m$, the arrival-time difference is $n(3\,\mathrm m)/c\simeq13.31\,\mathrm{ns}$. These are synthetic inputs, not detector measurements. Several sensors constrain the vertex; an extended moving track requires the light-emission position and time along that track as well.
For a <charged particle> moving at $v=\beta c$, the <Cherenkov cone angle> satisfies $\cos\theta_C=1/(n\beta)$ when $n\beta>1$. With $\beta\simeq1$ and the illustrative $n=1.33$, $\theta_C\simeq41.25^\circ$. The geometrical cone carries track-direction information; <Electron> deflections and the spread of emission positions broaden the observed pattern. The <neutrino> itself does not draw the light cone.
A <Cherenkov radiation> threshold and an analysis threshold are different constraints. For a fixed $n$, an <Electron> must exceed $T_C=m_ec^2[(1-n^{-2})^{-1/2}-1]$. With $m_ec^2=0.511\,\mathrm{MeV}$ and the chosen $n=1.33$, this gives about $0.264\,\mathrm{MeV}$. Recording and selecting a useful event requires much more light: the 1987 detector's trigger accepted $8.5\,\mathrm{MeV}$ <Electrons> with 50% efficiency.<Observation of a Neutrino Burst from the Supernova SN1987A by K. Hirata and others>[p. 1491: trigger acceptance]{ref}
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