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reνolution

Three Neutrino OscillationLecture Two

Lindley WinslowMassachusetts Institute of Technology

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The neutrino is neutral.

The neutrino only interacts weakly.

The neutrino has a small non-zero mass.

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From Yesterday’s Lecture

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νe

n→ p + e- + νe

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νe

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Atmospheric Neutrinos from above cosθ=1

from below cosθ= -1

Things are about to get interesting....

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!e!

!2"

!µ"

!1!

#"

#"

Two neutrino mixing determined by one mixing angle and and one mass difference squared.

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Three neutrino mixing will be defined by three mixing angles and two independent mass differences.

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Factor the Matrix

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Atmospheric/Accelerator

Schwetz et al. arXiv:1103.0734

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Solar/KamLAND

Schwetz et al. arXiv:1103.0734

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?

What do we know about this third mixing angle?

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E=3MeVsin22θ13 ~ 0.2Δm312=2.5×10-5eV2

The Full Reactor Antineutrino Survival Probability

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E=3MeVsin22θ13 ~ 0.2Δm312=2.5×10-5eV2

To be Sensitivity to θ13 you need to be closer....

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Do not look at the blue line....

The best fit comes from Chooz, sin22θ13 < 0.16, and putting together everything sin22θ13 ~ 0.06.

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Our Current Knowledge

Schwetz et al. arXiv:1103.0734

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u c! t!d s! b!

CC

We have seen this before...

u c! t!d s! b

is actually

This is the famous CKM Matrix that describes the

quark mixing.

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(! )!This is Quark Mixing

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(! )! (! )!This is Quark Mixing This is Neutrino Mixing

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?

What is that thing hanging around with the θ13?

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or

What is CP Violation?

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From H. Murayama

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One rule we hold dear.... CPT Conservation

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CPT conservation is all mixed together with the Lorentz invariance, locality and causality of your theory, so we do not like to mess with it.

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Disappearance Experiments.... CPT and CP are the same condition.

So you can never detect plain CP violation in a disappearance experiment.

or

We need an appearance experiment.

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Appearance Probability in Vacuum:

There are mass splitting terms

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Appearance Probability in Vacuum:

There are mixing angle terms.

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Appearance Probability in Vacuum:

And there are terms for the CP violating phase which is really what we want to go after.....

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Posc(!"# !$)!

P osc(! "#

!$)!

CP

%&

CP parameter!

0

'&

Visualizing the effect of the CP phase.....

First Approach:A Beam

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An Example Neutrino Beamline

Choose a Pion....

Look here for νe.

Look here for νe.

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You want the biggest effect possible.....

Maximize This!

atmospheric Δm2 is ~0.001 eV2

standard beam energy is 1GeV

Your beam needs to go 1,000km!

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Fermilab to South Dakota, Go West Little Neutrinos!

Long Baseline Neutrino ExperimentLBNE

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Getting a beam to South Dakota...

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Remember that MSW effect for neutrinos going through matter.

Posc(!"# !$)!

P osc(! "#

!$)!

CP

CP + matter,

%&

CP parameter!

0

'&

Matter will effect only neutrinos so this is a type of CP violation but not the effect we want to measure!

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Kayser and Parke 2009

And we have been kind of ignoring something.....

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Kayser and Parke 2009

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Posc(!"# !$)!

P osc(! "#

!$)!

CP

CP + matter, %&m2 <0

CP + matter, &m2 >0

'%

So in order to interpret data you will need to model the matter between FermiLab and South Dakota.

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A Detector...

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Take Super-K and multiply X 2

Then Build N Detectors.

For now N=2.

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Liquid Argon is super cool....

Proposals for multi-kton LAr detectors are in the running,but I will focus on the water Cerenkov Detector.

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Looking for Charge Current Interactions....

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νe e-

And our desired reaction....

From Yesterday: A Wimpy 8 MeV Solar Neutrino in Super-K

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A 603MeV muon in Super-K.

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A 492MeV electron in Super-K.

It’s a bit fuzzier.

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Anti-neutrinos are harder to detect and make.

And your beam is a bit “dirty”.....

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This is what we know....

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Now let’s pretend.....

Your sensitivity contours kind of look like a jelly bean.

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Ten years of running LBNE,If the hierarchy is normal and there are no upgrades to the FermiLab beam.

A lot of different jelly beans to choose from....

Second Approach:Multiple Cyclotrons

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DAE!ALUS

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The basic idea is the same....

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But Now....

They are super conducting.

They are stackable.

And possibly hug-able....

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What we want is a decay at rest beam (DAR)....

P DumpPions! neutrinos No νe!

These are harder to make and the μ- capture.

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free !protons!

20km! 8km! 1.5km!

osc max (!/2)!at 40 MeV!

off max (!/4) !at 40 MeV!

A multiple-baseline,!single-detector!experiment!

Constrains!flux!

And here is the idea....

Re-use your gigantic detector!

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And with the multiple baselines.....

You can use the interference between the terms to pull out the magnitude of the CP effect.

p

!̄ep

Gd

n

e+

Anti-Neutrino Detection - Inverse Beta Decay

Event #1 Ee = Eν - 0.8MeV

Event #2 Eγ~8MeV

30μs

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And you saw this trick before......

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Two backgrounds, “invisible” muons from atmospheric neutrinos.....

and the diffuse supernova background.

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Near

Middle Far

With 10 years of running ....

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Daedalus Phase 1 + 2

We can measure CP Violation!

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Daedalus Phase 1 + 2 LBNE 5 yrs nu + 5 yrs nubar

By Construction our performance is similar to LBNE,

but the systematic uncertainties are completely different!

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Working together is always better.....

With Different interactions, Different beams, Different energies, We beat down the systematic uncertainties and We win!

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(! )!(! )! vs.

vs.

They have decided to have tiny masses.

They have decided to have large mixing.

Why not an inverse hierarchy and large CP violation?

The race is on for θ13...

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A little more about the cyclotrons.....

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Not Enough Too Much

Just Right

Choosing your proton energy, a “goldilocks” problem...

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Kayser and Parke 2009

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