A water Cherenkov detector watches kilotonnes of water ( ) for years

PHYSICS · Multi-part · Fermi University Physics · Particle Physics & Quantum Fields · Particles, interactions and experiment · Particles, interactions and experiment

Particle Physics, Ch Quantum numbers, conservation laws and allowed reactions

Problem

A water Cherenkov detector watches 2020 kilotonnes of water (2.0×1010 g2.0\times10^{10}\,\mathrm{g}) for 5.05.0 years, searching for the decay p→e+π0p\to e^+\pi^0 with a detection efficiency ε=0.35\varepsilon=0.35, and records no candidate. Water has molar mass 18.0 g mol−118.0\,\mathrm{g\,mol^{-1}}, each molecule holds ten protons, and NA=6.022×1023 mol−1N_A=6.022\times10^{23}\,\mathrm{mol^{-1}}. ((a)) Find the number of protons watched, NN, and the exposure NtNt in proton-years. ((b)) Using the rough argument that seeing no events rules out any partial lifetime below εNt\varepsilon Nt, find the bound this search sets on the partial lifetime for p→e+π0p\to e^+\pi^0, and compare it with the age of the universe, 1.4×10101.4\times10^{10} years. ((c)) Explain why a proper limit from the same data, stated at 90 per cent confidence, would come out lower than your rough bound, and name the two conservation laws the null result tests.

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