Minimal Grand Unified Theories (GUTs, e.g. SU(5)) merge the strong, weak and electromagnetic forces into one gauge group at an enormous energy scale MX. That unification introduces heavy X/Y bosons which let a quark turn into a lepton, so the proton is no longer perfectly stable — the dominant predicted channel is:
p -> e+ + π0 (then π0 -> γ + γ)
The decay amplitude scales as 1/MX2 (heavy-boson exchange), so the rate scales as 1/MX4 and the lifetime grows as MX4:
tau_p(M_X) = tau_ref * (M_X / M_ref)^4
M_ref = 2*10^16 GeV, tau_ref = 10^36 yr (SUSY-GUT benchmark)
This 2D cross-section shows the same real physics as the 3D detector: a lattice of sampled protons sits in a circular tank wall lined with photomultiplier tubes (PMTs). Each simulated decay is drawn from a genuine Poisson process whose expected rate is N / τp, where N is the real number of protons in your fiducial mass (using Super-Kamiokande's ~3.35×10^32 free+bound protons per kiloton of water). A decay sends two back-to-back decay products outward; each radiates light at the fixed Cherenkov angle in water:
cos(theta_c) = 1/(n*beta) => theta_c ~ 41.2 deg for beta ~ 1, n = 1.33
The expanding light front is drawn as it sweeps outward, and only the PMTs sitting at the correct Cherenkov angle from each decay product's direction actually flash — exactly the ring-shaped hit pattern real detectors search for. The bottom chart plots the cumulative number of observed decays against the theoretical expectation line (rate × elapsed time), so you can watch the Monte-Carlo count track N/τ as statistics build up.
- MX slider — moves the GUT scale; higher MX means a much longer lifetime and rarer flashes (MX4 scaling).
- Fiducial mass slider — more water means more protons watched, proportionally more decays/year.
- Time speed slider — how many simulated years pass per real second (a true Poisson process is run under the hood, not a fixed timer).
- Force a decay now — injects one extra visual event immediately, for inspection, without affecting the statistics above.
No proton decay has ever been confirmed; Super-Kamiokande's non-observation already rules out minimal (non-SUSY) SU(5) and constrains τp beyond ~1.6×10^34 years for this channel.