3 Neutrino Oscillation and Off-axis Experiments David Barnhill UCLA May 30, 2003

2 Neutrino Oscillations Already talked about two different n oscillations:  Solar n  Atmospheric n Flavor states are superposition of mass eigenstates (Greek subscript is flavor and Roman subscript is mass state): where

2 Neutrino Results With  m 2 sol ~ 5 x eV 2 &  m 2 atm ~ 3 x eV 2 But when plotting tan 2  and not sin 2 2 , we know m 1 <m 2 <m 3

Mass Hierarchy

3 Neutrino Oscillation Reality is that there are 3 neutrino flavors (or possibly 4 or more) and 3 neutrino mass eigenstates  This means neutrinos can oscillate between all three flavors How many parameters?

3 Neutrino Mixing Matrix Using 3  ranges from solar, atmospheric and reactor data: LM A Sola r{ Atm { React or

 13 Why is  13 important?  It is easily singled out in U e3 matrix element and is directly linked to CP violating phase element How do we measure  13 ?  Use  e experiment (To leading order) If the experiment is performed at the peak of this probability: Using CHOOZ limit, maximum appearance probability is 5% 2 neutrino case:

Reality is slightly more complex The neutrinos must pass through matter, it’s not a vacuum oscillation We need to include CP violating phase effects

Off-Axis Experiments and Superbeams Two proposed experiments to be off-axis experiments using “superbeams”  NuMI  JHF-SK Basically the idea is to create  + by p+p collision, focus these  + and get  from  + ->  + + 

Why Off-Axis? Neutrino energy in pion rest frame: assumi ng: Neutrino spectrum: Set  * to 90°:

Why Off-Axis? We see that as theta increases, there is a maximum for the neutrino energy with a wide range of pion energies contributing to it. If we desire an enhancement at a particular neutrino energy, we look close to the  max as given on the previous page.

NuMI and JHF-SK