Cuts, Efficiencies, and S/N

This lab asks you to figure out the best cuts to use to maximize your chances of finding a p⁺→nK⁺proton decay event, looking at the K⁺→p⁺p⁰ decay channel. The p⁰ decays immediately to two gammas, so looking for two gammas which reconstruct to the p⁰ invariant mass is an important cut. The p⁺ is barely relativistic, so makes only a small amount of light in the opposite direction - but since these are all two body decays, the approximate amount of light expected from each pion can be calculated.

You are given the values of reconstructed p⁰ momentum (in MeV/c) and observed p⁺ charge (in units of photoelectrons) for each event which passes all the analysis cuts to this point, in both the proton decay monte carlo data sample and the atmospheric neutrino monte carlo data sample (the background, in this case). Your goal is to make cuts on these two quantities to maximize your chances of finding a real proton decay if your cuts were applied to the data. That is, you want to keep as many simulated proton decay events as possible (increasing your efficiency for finding them) while discarding as many atmospheric neutrino events as possible (thereby reducing your background). The way to maximize this sensitivity is to figure out the longest proton decay lifetime limit you could set with this data, if just as many events were really observed as your background calculation predicted.

Things you need to know to calculate lifetime limits:

• There are 22.5 kilotons (or m³ if you prefer) of H₂O in the observed detector volume. The water is very very pure.

• The water was observed for 1489 days.

• There were 34,664 p⁺→nK⁺ events simulated in the proton decay monte carlo. The atmospheric neutrino monte carlo was 100 years equivalent exposure.

What cuts would you choose? What are the resulting efficiencies and expected background in the observed data set? Demonstrate that the cuts you have chosen do indeed optimize the search. What is the Poissonian 90% confidence limit proton decay lifetime you would just barely see if in the real data there were exactly the expected number of events?

Neglect the effects of neutrino oscillations for this exercise, but qualitatively explain how some of the neutrinos disappearing before interacting with the water would change your results.

Data files:

• Momentum and Charge from Proton Decay Monte Carlo: pdcy.dat

• Momentum and Charge from Atmospheric n Monte Carlo: atmnu.dat

A published paper about this if you want more background:

Y. Hayato et al. (The Super-Kamiokande Collaboration), “Search for proton decay through p⁺→nK⁺ in a large water Cherenkov detector”, Phys. Rev. Lett. 83, 1529 (1999). Also available on arxiv.org as hep-ex/9904020.