# A Why lower limits on proton decay lifetimes depend on channel

1. Dec 1, 2016

### Anchovy

If I look at the lower limits on the proton decay lifetime $\tau$ set by, say, Super-Kamiokande, I'll see different lower limits depending on what the proton could decay into, eg. $\tau_{min}(p \rightarrow K^{+} \overline{\nu}) < \tau_{min}(p \rightarrow \mu^{+} \pi^{0}) < \tau_{min}(p \rightarrow e^{+} \pi^{0})$.

What is the reason for this? Is it to do with what the theoretical prediction for each decay channel's decay rate is? Or is experimental, ie. how good the detector is at picking up each observable decay product? Or perhaps to do with different background rates? Or something else?

2. Dec 1, 2016

### Staff: Mentor

It is an experimental effect. If you observe a fixed amount of protons, and expect to see 50% of all decays to kaons but only 5% of all decays to muons, you'll probably set better limits on the kaon decay. On the other hand, if you have a lot of background for some decay channel, your limit can be much worse.

Assuming protons decay at all, those three decay channels will have different partial lifetimes (= different branching fractions = different partial decay widths).

The 50% and 5% numbers are made up, didn't check the actual numbers.

3. Dec 1, 2016

### Anchovy

OK, so what would cause such difference in a water Cerenkov? (I think in your example it'd be the other way round, I think Super K has set a higher lower-limit for the muon channel than a kaon channel). Do kaons produce worse-quality rings at the PMTs? Or would more muons be energetic enough exceed the threshold at which they can radiate Cerenkov light? Or something else?

4. Dec 1, 2016

### Staff: Mentor

Kaons are slower, their Cherenkov cones (assuming they are fast enough at all) will be wider and not as bright. They decay to other particles which can make the event look messy.

Muons lead to a nicer Cherenkov cone, but they could suffer from more background from neutrino-induced events. Same for electrons.

The publications should give the detection efficiencies and the background levels.

5. Dec 1, 2016

OK, thanks.