Proton Decay: GUT Cherenkov Detector

GUT Parameters

Unification scale M_X 1.0 × 10^16 GeV

Detector fiducial mass 22.5 kt

Simulated time speed 1 yr/s

Show Cherenkov cones

Live Readouts

Predicted proton lifetime τ_p

Predicted decay rate, this detector

Simulated elapsed time

0 yr

Decays observed

How it works

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 M_X. 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/M_X² (heavy-boson exchange), so the rate scales as 1/M_X⁴ and the lifetime grows as M_X⁴:

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)

Real detectors are giant tanks of ultra-pure water lined with photomultiplier tubes (PMTs). The proton mass (0.938 GeV) converts into two ultra-relativistic decay products flying back-to-back. Each charged product outruns light's local phase speed in water (n = 1.33) and radiates a cone of Cherenkov light at the fixed angle:

cos(theta_c) = 1/(n*beta)  =>  theta_c ~ 41.2 deg  for beta ~ 1

That cone sweeps outward and paints a ring of PMT hits on the tank wall — exactly the signature real experiments (Super-Kamiokande, Hyper-Kamiokande) search for. This sim uses the real water proton-density of Super-K (~3.35×10^32 free+bound protons per kt) to convert your fiducial-mass slider into an actual expected decay rate, then compresses time so you can watch a Poisson process of decays unfold instead of waiting 10^34 years.

M_X slider — moves the GUT scale; higher M_X means a much longer lifetime and rarer flashes (M_X⁴ 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 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 τ_p beyond ~1.6×10^34 years for this channel.

Cherenkov light front PMT hit PMT (idle)

Decay detected

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