3 Neutrino Oscillation and Off-axis ExperimentsDavid Barnhill

UCLAMay 30, 2003

2 Neutrino Oscillations

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

where

2 Neutrino Results

With m2sol ~ 5 x 10-5 eV2 & m2

atm ~ 3 x 10-3 eV2

But when plotting tan2 and not sin22, we know m1<m2<m3

Mass Hierarchy

3 Neutrino Oscillation

Reality is that there are 3 neutrino flavors (or possibly 4 or more) and 3 neutrino mass eigenstatesThis means neutrinos can oscillate between all three flavors

How many parameters?

3 Neutrino Mixing Matrix

Using 3 ranges from solar, atmospheric and reactor data:

LMA

Solar{Atm{ React

or

13

Why is 13 important? It is easily singled out in Ue3 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 oscillationWe need to include CP violating phase effects

Off-Axis Experiments and Superbeams

Two proposed experiments to be off-axis experiments using “superbeams”NuMI JHF-SKBasically the idea is to create + by p+p collision, focus these + and get from +->+ +

Why Off-Axis?

Neutrino energy in pion rest frame:

assuming:

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