Super-Kamiokande's fiducial volume of of water contains protons

PHYSICS · Subjective · Fermi University Physics · Particle Physics & Quantum Fields · Beyond the Standard Model · Beyond the Standard Model

Symmetry and Flavour, Ch Grand unification: running couplings, SU(5), proton decay and the hierarchy problem

Problem

Super-Kamiokande's fiducial volume of

22.5\,\mathrm{kt}

of water contains

7.5\times10^{33}

protons. Hyper-Kamiokande's fiducial mass is about eight times larger. Suppose the true proton lifetime for

p \to e^+\pi^0

sits exactly at the Super-Kamiokande limit,

\tau = 2.4\times10^{34}\,\mathrm{yr}

, and Hyper-Kamiokande's detection efficiency for this mode is

\varepsilon = 0.40

. Calculate the number of candidate decays expected in a

10

-year run.