# Why are reactor experiments measuring theta13, not theta12?

1. May 18, 2010

### Aturen

The question I have came from a talk I saw about the MINOS experiment. They say they can measure theta13 from their beam of mostly muon neutrinos by measuring electron neutrino appearance. Why would this not involve theta12?
Is what is happening that the dominant chain is muon neutrinos going to tau neutrinos before oscillating to electron neutrinos (if so, how does one calculate those rates?), or that the length at which the detector is (735 km) is further than the oscillation length for muon neutrinos directly changing to electron neutrinos (if so, what is the energy to use in calculating the length, L = (4E)/(delta m^2)?).

I have found a few places that have stated that the probability that a muon neutrino oscillates to an electron neutrino is:
$$P(\nu_\mu \to \nu_e) = \sin^2 (2 \theta_{13}) \sin^2 (\theta_{23}) \sin^2 (\Delta m^2_{atm} L/4E)$$

But I don't know how to derive this. I tried using the PMNS 3x3 matrix, but it doesn't simplify well. The probability for neutrino oscillation, assuming two species, is close to this expression, but involves only two sines.