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### and

Dark Energy from Mass Varying Neutrinos

Neutrino Oscillation Experiments

Neutrino Factory 2004, based on

Rob Fardon, A.E.N., Neal Weiner; astro-ph/0309800

David B. Kaplan, A.E.N., Neal Weiner; hep-ph/0401099

Kathryn Zurek, hep-ph/0405141

Kiyoshi Shiraishi, unpublished

1998, First Convincing evidence for Physics Beyond the Standard Model from

- SuperK, evidence for atmospheric neutrino oscillations
- But, the“Breakthrough of the Year”is the supernovae evidence for the acceleration of the universe
- Einstein was wrong about having blundered? (Cosmological Constant?)
- “Why Now” and finetuning are evidence for the Anthropic Principle?

Strong Evidence for two kinds:

23% Dark Matter -> some garden variety pressureless clumpy fluid

73% “Dark Energy” -> exotic negative pressure smoothsubstance

usually attributed to the energy of the vacuum⎯energy density which does not dilute with expansion and is therefore equivalent to Einstein’s cosmological constant. I will assume this is zero.

sometimes assumed to be some weird dynamical “quintessence” substance with equation of state parameter w near -1 which nevertheless does not clump (not your typical nonrelativistic stuff)

Our Universe is mostly mysterious dark stuff

“Smooth, Dark, Tension” Sean Carroll

- Negative Pressure=Tension
- Smooth Tension= Oxymoron?
- “Normal” Stuff under tension prefers to Clump
- Weird particle physics counterexamples:
1vacuum energy

la slowly rolling scalar field (m~H-1~ 10-33eV)

dfrustrated network of strings/domain walls

4relativistic, freely streaming particles

After Six Years of Surprises, Do we Almost Completely Understand Neutrinos Now?

q13

Flavor

Composition

of n Mass

Eigenstates

q13

Absolute mass scale? CP? Majorana or Dirac? LSND outlier?

Why recent Concordance in the neutrino oscillation Industry? Understand Neutrinos Now?

- Neutrinos are Special! Expect exotic physics to be discovered there! Window on the Dark Sector!
- Can mix with ‘dark’ fermions (aka sterile neutrinos)
- Can thus experience ‘dark forces’ much more strongly than other particles
- Oscillations are sensitive to tiny GUT suppressed operators (standard seesaw)
- Environment dependence of oscillations is sensitive to new millimeter range forces which are subgravitational strength for other particles

Beyond the Understand Neutrinos Now?n Standard Model

- Subject still in experimental youth
- Neutrino oscillations offer incredible
sensitivity to new forces, high scales,

ultraweak interactions, new states

- Conventional Wisdom about neutrinos,
neutrino expts. has always been wrong!

Coincidences? Understand Neutrinos Now?

- Density of “Dark Energy” ~ (2 10-3 )4 eV 4
- Solar Neutrino Mass2 splitting ~ (4 10-3 )2eV 2
- Atmospheric Neutrino Mass2 splitting ~ (3 10-2 ) 2eV 2
- Convincing evidence for Dark Energy found in 1998
- Convincing evidence for Neutrino Oscillations found in 1998
- Low Scale SUSY gravitino mass ~ 10-3 eV

More Coincidences- Understand Neutrinos Now?

Why so complicated?

Can dark energy be related to something we know? Understand Neutrinos Now?

- Dark Matter? We know scaling behavior of dark
matter from large scale structure. Dark energy

currently scales very differently.

Scaling behavior of dark energy must have recently

changed (Why Now?)

- Neutrinos? Could neutrino energy density
scale like dark energy?

- Requires neutrino ‘mass’ to increase with scale factor

Isn’t varying neutrino mass crazy?

No !

Varying ‘Mass’ is Everywhere! Understand Neutrinos Now?

- Index of refraction
- KS regeneration
- Quasi particles in condensed matter
- MSW effect
- All Standard Model fermion mass terms depend on value of Higgs scalar which can vary (slightly)
- All known masses depend on environment

The issue is not ‘whether’, but

‘how much’ neutrino mass should vary !

A simple Ma Understand Neutrinos Now?ssVaryingNeutrino Model

Assume “Dark Sector” (= unknown particles with no standard Model charges) contains

1A scalar field A

1A fermion field n

1A Yukawa coupling A n n

1 A scalar potential V ( A )

Assume “Our sector” contains

1Active Neutrinos n

- 1Higgs Field H
- Allow tiny (y =O (10-12) )coupling yH n n

0

æNeutrino mass matrix ( )

y H

y H

A

.

Neutrino Masses vary as Understand Neutrinos Now?A-1

n

n

Neutrino mass matrix ( )

n

0

y H

y H

A

n

For large <A> light neutrino mass is (y H) 2/ A

Assume V ( A )slowly increasing function of A.

V is then slowly decreasing function of the light neutrino mass

V(A (mn) ) ~ mn(1+w)/ w

- Neutrino mass increases adiabatically as neutrino density dilutes
- Combined neutrino + scalar potential energy decreases slowly

What is the Scale? dilutes

- We have 2 pieces of evidence suggesting
a milli-eV scale for new physics.

- This is also the inverse cosmic neutrino
spacing.

- A milli-eV scale for the A potential (and
mass) leads to Dark Energy

- Contrast with ‘cosmon’ type quintessence
model, which requires a mass scale of

10-33 eV.

Smoothness of MaVaN Dark Energy dilutes

- When n’s go nonrelativistic, they gravitationally clump at large scales
- MaVaN’s go nonrelativistic very late (z= a few)
- MaVaN’s get lighter and more relativistic inside clumps => ‘anti-clumping mechanism’
- Dark energy much smoother than neutrinos V ~ (nn) (1+w)

Sterile Neutrinos? dilutes

- Sterile neutrino mass increasing function of
neutrino density

- Mixing with sterile neutrino decreasing function of neutrino density
- Simple to reconcile sterile neutrino with BBN F mass always much heavier than temperature
- May similarly evade Supernovae bounds

Can we test MaVaN Dark Energy? dilutes

- Cosmological tests of neutrino mass from large scale structure: MaVaN mass was much lighter at high redshift.
- Model independent relation: mn= (1+w) V/nn
(V= dark energy density)

- No terrestrial sources of high scalar neutrino density (neutrino density weighted by (m/E)), relative to cosmological, other than nuclear fireball.
- Main interesting astrophysical source of high scalar neutrino density is supernova.

Generic tests difficult, not impossible.

A dilutesshould have coupling to matter

Loop suppressed and/or

Planck/String scale suppressed

Possible very interesting terms:

Other effects of environment?

Recent unofficial, preliminary analysis of SuperK atmospheric neutrinos by Kiyoshi Shiraishi assuming no oscillations in air fits all data well

Very weak (consistent with LSND?) upper bound on mass squared difference in rock from contained, partially contained events, K2K

reanalysis of upward through going and upward stopping muons underway, probably yields best upper bound on Dm2 in rock

Do Neutrinos ever oscillate in air?

The Outlier: atmospheric neutrinos by Kiyoshi Shiraishi assuming

LSND

Conventional Wisdom: need > 3 neutrinos to get 3 independent masses squared, and oscillations involving extra dark states constrained by Bugey, CDHS, Cosmology, and Supernova, so LSND must be wrong

Constraints from

oscillations in High

Density Material

only

Constraints on Standard

Neutrinos

To Do: Theorists atmospheric neutrinos by Kiyoshi Shiraishi assuming

- Model building exploration
- MaVaN consequences for Supernova
- How much room for non standard environment dependence in Solar/atmospheric/terrestial neutrino oscillations?
- Consequences for flavor dependence/energy spectrum of astrophysical neutrino sources
- Early Universe cosmology of acceleron
- More general constraints on sterile neutrinos from supernovae, cosmology

To Do: Experimentalists atmospheric neutrinos by Kiyoshi Shiraishi assuming

- Document and consider environment of neutrino path in neutrino oscillation experiments
- Consider q13 measurements in reactor experiments with pathlength in air and in rock
- Consider environment of neutrinos in direct mass search and 0nbb measurements
- Short baseline experiments to search for heavier sterile neutrinos with small mixing angles; consider varying density of material in neutrino path

Effects of environment in neutrino oscillations? atmospheric neutrinos by Kiyoshi Shiraishi assuming

0nbb decay depends on density of source?

Tritium endpoint searches for absolute n mass depends on density of source?

Cosmologically “impossible” sterile neutrinos?

Cosmologically “inconsistent” neutrino masses?

A MiniBooNE signal for nmdisappearanceor ne appearance

Smoking Guns for MaVaNs

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