neutrino phenomenology

1

Neutrino Neutrino

PhenomenologPhenomenolog

yy Boris KayserScottish Summer

SchoolAugust 10, 2006 +

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What We What We Have LearnedHave Learned

3

(Mass)2

12

3

or

123

}m2so

l

m2atm

}m2so

l

m2atm

m2sol = 8.0 x 10

–5 eV2, m2

atm = 2.7 x 10–3 eV2

~ ~

Normal

Inverted

Are there more mass eigenstates, as LSND suggests?

The (Mass)2 Spectrum

4

This has the consequence that —

|i> = Ui |> .

Flavor- fraction of i = |Ui|2 .

When a i interacts and produces a charged lepton, the probability that this charged lepton will be of flavor is |Ui|2 .

Leptonic Mixing

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e [|Uei|2]

[|Ui|2] [|Ui|2]

Normal Inverted

m2atm

(Mass)2

m2sol}

m2atm

m2

sol}

or

sin213

sin213

The spectrum, showing its approximate flavor content, is

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m2atm

e [|Uei|2]

[|Ui|2]

[|Ui|2]

(Mass)2

m2sol}

Bounded by reactor exps. with L ~ 1 km

From max. atm. mixing,

€

3 ≅ν μ +ν τ

2

From (Up) oscillate but (Down) don’t{{

{

In LMA–MSW, Psol(ee) = e fraction of 2

From max. atm. mixing, includes (–)/√2

From distortion of e(solar) and e(reactor) spectra

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The 3 X 3 Unitary Mixing Matrix

€

LSM = −g

2l Lα γ λ ν LαWλ

− + ν Lα γ λ l LαWλ+

( )α =e,μ ,τ

∑

= −g

2l Lα γ λ Uαiν LiWλ

− + ν Liγλ Uαi

*l LαWλ+

( )α =e,μ ,τi = 1,2,3

∑

Caution: We are assuming the mixing matrix U to be

3 x 3 and unitary.

€

(CP) l Lα γ λ Uαiν LiWλ−

( )(CP)−1 = ν Liγλ Uαil LαWλ

+

Phases in U will lead to CP violation, unless they are removable by redefining the

leptons.

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Ui describes — i l

W+

–

Ui l W+Hi –

When i ei i , Ui ei Ui

When l ei l , Ui e–

i Ui

– –

Thus, one may multiply any column, or any row, of U by a complex phase

factor without changing the physics.

Some phases may be removed from U in this way.

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Exception: If the neutrino mass eigenstates are their own antiparticles, then —Charge conjugate i = ic =

Ci

T

One is no longer free to phase-redefine

i without consequences.

U can contain additional CP-violating phases.

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How Many Mixing Angles and CP Phases Does U Contain?

Real parameters before constraints: 18

Unitarity constraints —

Each row is a vector of length unity: – 3

Each two rows are orthogonal vectors: – 6

Rephase the three l : – 3

Rephase two i , if i i: – 2

Total physically-significant parameters: 4

Additional (Majorana) CP phases if i = i : 2

€

Uαi*Uβi

i∑ = δαβ

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How Many Of The Parameters Are Mixing Angles?

The mixing angles are the parameters

in U when it is real.

U is then a three-dimensional rotation matrix.

Everyone knows such a matrix is described in terms of 3 angles.

Thus, U contains 3 mixing angles. Summary

Mixing angles

CP phases if i i

CP phases if i = i

3 31

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The Mixing Matrix

€

U =

1 0 0

0 c23 s23

0 −s23 c23

⎡

⎣

⎢ ⎢ ⎢

⎤

⎦

⎥ ⎥ ⎥×

c13 0 s13e−iδ

0 1 0

−s13eiδ 0 c13

⎡

⎣

⎢ ⎢ ⎢

⎤

⎦

⎥ ⎥ ⎥×

c12 s12 0

−s12 c12 0

0 0 1

⎡

⎣

⎢ ⎢ ⎢

⎤

⎦

⎥ ⎥ ⎥

×

eiα1 /2 0 0

0 eiα 2 /2 0

0 0 1

⎡

⎣

⎢ ⎢ ⎢

⎤

⎦

⎥ ⎥ ⎥

12 ≈ sol ≈ 34°, 23 ≈ atm ≈ 37-53°, 13 < 10°

would lead to P() ≠ P(). CP

But note the crucial role of s13 sin 13.

cij cos ijsij sin ij

Atmospheric

Cross-Mixing

Solar

Majorana CP phases~

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The Majorana CP Phases

The phase i is associated with neutrino mass eigenstate i:

Ui = U0i exp(ii/2) for all flavors

.

Amp() = Ui* exp(– imi2L/2E)

Ui

is insensitive to the Majorana phases i.

Only the phase can cause CP violation in neutrino

oscillation.

i

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QuickTime™ and aTIFF (Uncompressed) decompressor

are needed to see this picture.The Open The Open QuestionsQuestions

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•What is the absolute scale

of neutrino mass?

•Are neutrinos their own antiparticles?

•Are there “sterile” neutrinos?

We must be alert to surprises!

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•What is the pattern of mixing among

the different types of neutrinos?

What is 13? Is 23 maximal?

•Do neutrinos violate the symmetry CP? Is P( )

P( ) ?

•Is the spectrum like or ?

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• What can neutrinos and the universe tell us about one

another?

• Is CP violation by neutrinos the key to understanding the matter – antimatter asymmetry of the

universe?

•What physics is behind neutrino mass?

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QuickTime™ and aTIFF (Uncompressed) decompressor

are needed to see this picture.

The The Importance of Importance of

the the Questions, Questions,

and How They and How They May Be May Be

AnsweredAnswered

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How far above zero is the whole pattern?

3

0

(Mass)2

m2atm

m2sol

??

12

Flavor Change

Tritium Decay, Double DecayCosmology

}}

What Is the Absolute Scale of Neutrino Mass?

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A Cosmic Connection

Cosmological Data + Cosmological Assumptions

mi < (0.17 – 1.0) eV .

Mass(i)

If there are only 3 neutrinos,

0.04 eV < Mass[Heaviest i] < (0.07 – 0.4) eV

m2atm

Cosmology

~

Oscillation Data m2atm <

Mass[Heaviest i]

Seljak, Slosar, McDonald Pastor

( )

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Are Neutrinos Are Neutrinos Majorana Majorana Particles?Particles?

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How Can the How Can the Standard Model be Standard Model be

Modified to Include Modified to Include Neutrino Masses?Neutrino Masses?

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Majorana Neutrinos or Dirac Neutrinos?

The S(tandard) M(odel)

and

couplings conserve the Lepton Number L defined by—

L() = L(l–) = – L() = – L (l+) = 1.So do the Dirac charged-lepton mass terms

mllLlR

–

–

Wl–

Z

l +(—) l

+(—)

Xml

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• Original SM: m = 0.

• Why not add a Dirac mass term,

mDLR

Then everything conserves L, so for each mass eigenstate i,

i ≠ i (Dirac neutrinos)

[L(i) = – L(i)]

• The SM contains no R field, only L.

To add the Dirac mass term, we had to add R to the SM.

XmD

(—)

(—)

—

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Unlike L, R carries no Electroweak Isospin.

Thus, no SM principle prevents the occurrence of the Majorana mass term

mRRc R

But this does not conserve L, so now

i = i (Majorana neutrinos)

[No conserved L to distinguish i from i]

We note that i = i means —i(h) = i(h)

helicity

XmR

—

—

—

—

—

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The objects R and Rc in mRRc R are not the mass eigenstates, but just the neutrinos in terms of which the model is constructed.

mRRc R induces R Rc

mixing.

As a result of K0 K0 mixing, the neutral K mass eigenstates are —

KS,L (K0 K0)/2 .

As a result of R Rc

mixing, the neutrino mass eigenstate is —

i = R + Rc = “ + ” .

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Many Theorists Expect Majorana Masses

The Standard Model (SM) is defined by the fields it contains, its

symmetries (notably Electroweak Isospin Invariance), and its

renormalizability.

Leaving neutrino masses aside, anything allowed by the SM symmetries

occurs in nature.

If this is also true for neutrino masses, then neutrinos have Majorana

masses.

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• The presence of Majorana masses

• i = i (Majorana neutrinos)

• L not conserved— are all equivalent

Any one implies the other two.

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Electromagnetic Properties

of Majorana Neutrinos Majorana neutrinos are very neutral.No charge distribution:

CPT[ ] = ≠++

+–

––

But for a Majorana neutrino,

[ ]CPT i

[ ]i

=

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No magnetic or electric dipole moment:

[ ] [ ]e+ e– =

–

But for a Majorana neutrino,

i i=

Therefore, [i

]=[i

] =

0

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Transition dipole moments are possible, leading to —

e

e1

2

One can look for the dipole moments this way.

To be visible, they would have to vastly exceed Standard Model

predictions.

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How Can We Demonstrate That i = i?We assume neutrino interactions are

correctly described by the SM. Then the interactions conserve L ( l– ; l+).

An Idea that Does Not Work[and illustrates why most ideas do not

work]

Produce a i via—

+i +

SpinPion Rest Frame

(Lab) > ( Rest Frame)

+ i

+Lab. Frame

Give the neutrino a Boost:

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The SM weak interaction causes—

i

+

Recoil

Target at rest

—

i i

— i

,

will make + too.

i = i means that i(h) = i(h).helicity

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Minor Technical Difficulties

(Lab) > ( Rest Frame)

E(Lab) E( Rest Frame) m m

E(Lab) > 105 TeV if m ~ 0.05 eV

Fraction of all – decay i that get helicity flipped

( )2 ~ 10-18 if m~ 0.05 eV

Since L-violation comes only from Majorana neutrino masses, any attempt to observe it will be at the mercy of the neutrino masses.

(BK & Stodolsky)

i

>

~ i

i

m

E( Rest Frame)

i

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The Idea That Can Work —

Neutrinoless Double Beta Decay [0]

Observation would imply L and i = i .

By avoiding competition, this process can cope with the small neutrino masses.

ii

W– W–

e– e–

Nuclear Process

Nucl Nucl’

i

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0e– e–

u d d u

()R L

W W

Whatever diagrams cause 0, its observation would imply the

existence of a Majorana mass term:Schechter and Valle

()R L : A Majorana mass term

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ii

W– W–

e– e–

Nuclear Process

Nucl Nucl’

In

the i is emitted [RH + O{mi/E}LH].

Thus, Amp [i contribution] mi

Amp[0] miUei2 m

Uei

Uei

i

SM vertex

i

Mixing matrix

Mass (i)

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The proportionality of 0 to mass is no surprise.

0 violates L. But the SM interactions conserve L.

The L – violation in 0 comes from underlying Majorana mass terms.

3939

Backup Backup SlidesSlides

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How Large is m?

How sensitive need an experiment be?

Suppose there are only 3 neutrino mass eigenstates. (More might help.)

Then the spectrum looks like —

sol < 21

3atm

3

sol < 12

atmo

r

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m miUei2

€

U =

1 0 0

0 c23 s23

0 −s23 c23

⎡

⎣

⎢ ⎢ ⎢

⎤

⎦

⎥ ⎥ ⎥×

c13 0 s13e−iδ

0 1 0

−s13eiδ 0 c13

⎡

⎣

⎢ ⎢ ⎢

⎤

⎦

⎥ ⎥ ⎥×

c12 s12 0

−s12 c12 0

0 0 1

⎡

⎣

⎢ ⎢ ⎢

⎤

⎦

⎥ ⎥ ⎥

×

eiα1 /2 0 0

0 eiα 2 /2 0

0 0 1

⎡

⎣

⎢ ⎢ ⎢

⎤

⎦

⎥ ⎥ ⎥

The e (top) row of U reads —

€

(Ue1,Ue2,Ue3) = (c12c13eiα1 /2, s12c13eiα 2 /2, s13e−iδ )

12 ≈ ≈ 34°, but s132 < 0.032

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If the spectrum looks like—

then–

m ≅ m0[1 - sin22 sin2(–––––)]½ .Solar mixing angle

m0 cos 2 m m0

At 90% CL,m0 > 46 meV (MINOS); cos 2 > 0.28

(SNO),so

m > 13 meV .

2–12

Majorana CP phases

{

sol <atm

m0

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If the spectrum looks like

then —

0 < m < Present Bound [(0.3–1.0) eV] .

(Petcov et al.)

Analyses of m vs. Neutrino Parameters

Barger, Bilenky, Farzan, Giunti, Glashow, Grimus, BK, Kim, Klapdor-Kleingrothaus, Langacker, Marfatia, Monteno, Murayama, Pascoli, Päs, Peña-Garay, Peres, Petcov, Rodejohann, Smirnov, Vissani, Whisnant, Wolfenstein,

Review of Decay: Elliott & Vogel

sol <

atm

Evidence for 0 with m = (0.05 – 0.84) eV?

Klapdor-Kleingrothaus