1

Neutrinos: Neutrinos: Results and Results and

FutureFutureBoris KayserBoris KayserDESYDESY

March 4, 2008March 4, 2008

2

Evidence For Flavor ChangeNeutrinos

Solar Reactor

(L ~ 180 km)

AtmosphericAccelerator

(L = 250 and 735 km)

Stopped Decay LSND

L 30 m

Evidence of Flavor Change

CompellingCompelling

CompellingCompelling

Unconfirmed by MiniBooNE

( )

3

Neutrinos have nonzero masses

Leptons mix.

The neutrino flavor-change observations imply that —

and that —

4

What We What We Have LearnedHave Learned

5

(Mass)2

12

3

or

123

}m2so

l

m2atm

}m2so

l

m2atm

m2sol = 7.6 x 10

–5 eV2, m2

atm = 2.4 x 10–3 eV2

~ ~

Normal

Inverted

The (Mass)2 Spectrum

6

Are There MoreMore Than 3 Mass Eigenstates?

Rapid oscillation reported by LSND —

1eV2

in contrast to

> m2sol = 7.6 x

10–5 eV2

m2atm = 2.4 x

10–3 eV2

At least 4 mass eigenstates.

When only two neutrinos count,

€

P ν α → ν β( ) = sin 2 2θ sin2 1.27Δm2 eV 2( )

L km( )

E GeV( )

⎡

⎣ ⎢

⎤

⎦ ⎥

€

→ e

7

MiniBooNE Search for e

•No excess above background for energies E > 475 MeV.

•Unexplained excess for E < 475 MeV.

•Two-neutrino oscillation cannot fit LSND and MiniBooNE.

•More complicated fits are possible.

R.Tayloe at LP07

8

MiniBooNE in the NuMI Beam

The MiniBooNE detector is illuminated by both

the MiniBooNE beam, and the NuMI beam pointed at MINOS.Distance to MiniBooNE —

L (from NuMI source) 1.4 L (from MiniBooNE source)

Neutrino oscillation depends on L and E only through L/E.

Therefore, if an anomaly seen at some E in the MiniBooNE-beam data is due

to oscillation, it should appear at 1.4 E in the

NuMI-beam data.

9

Outgoing electron angular Outgoing electron angular distributiondistribution

ee CCQE sample: CCQE sample: Reconstructed energy Reconstructed energy EE of of

incoming incoming

All

All e

PRELIMINARY

PRELIMINARY

(Z. Djurcic, Dec. 11, 2007)

10

To be continued …

Meanwhile, we will assume there are

only 3 neutrino mass eigenstates.

11

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

PMNS Leptonic Mixing Matrix

Mass eigenstate

Flavor eigenstate

e, , or

12

e [|Uei|2]

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

Normal Inverted

m2atm

(Mass)2

m2sol}

m2atm

m2sol}

or

sin213

sin213

The spectrum, showing its approximate flavor content, is

13

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~

14

“Atmospheric” m2 and mixing angle

from MINOS, Super-K, and K2K.

From talk by

N. Saoulid

ou

15

“Solar” m2 and mixing angle from KamLAND and solar

experiments.

Presented by

KamLAND, a reactor

e experiment

.

m sol

2eV2

€

tan2 θsol

16

KamLAND Evidence for Oscillation

L0 = 180 km is a flux-weighted average travel distance.

P(e e) actually oscillates!

17

7Be Solar Neutrinos

Until recently, only the 8B solar neutrinos,

with E 7 MeV, had been studied in detail.

The Large Mixing Angle MSW (matter) effect boosts the

fraction of the 8B solar e that get transformed into neutrinos of

other flavors to roughly 70%.

At the energy E = 0.862 MeV of the 7Be solar neutrinos, the matter effect is expected to be very

small. Only about 45% of the 7Be solar e are expected to change into neutrinos of other flavors.

18

Borexino —

Detects the 7Be solar neutrinos via e e elastic scattering.

Event rate (Counts/day/100 tons)

Observed: 47 7(stat) 12(syst)

Expected (No Osc): 75 4

Expected (With 45% Osc): 49 4

Expected (With 70% Osc): ~ 31

19

QuickTime™ and aTIFF (Uncompressed) decompressor

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

20

•What is the absolute scale

of neutrino mass?

•Are neutrinos their own antiparticles?

•Are there “sterile” neutrinos?

We must be alert to surprises!

21

•What is the pattern of mixing among

the different types of neutrinos?

What is 13?

•Do neutrino – matter interactions violate CP?

Is P( ) P( ) ?

•Is the spectrum like or ?

22

• What can neutrinos and the universe tell us about one

another?

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

of the universe?

•What physics is behind neutrino mass?

23

QuickTime™ and aTIFF (Uncompressed) decompressor

are needed to see this picture.

The The Importance of Importance of

Some Some Questions, Questions,

and How They and How They May Be May Be

AnsweredAnswered

24

That is, for each mass eigenstate i does —

• i = i (Majorana neutrinos)

or• i ≠ i (Dirac neutrinos) ?

Does = ?

Equivalently, do neutrinos have Majorana masses? If they do, then the mass eigenstates are Majorana

neutrinos.

25

Majorana Masses

mLL Lc

Out of, say, a left-handed neutrino field, L, and its charge-conjugate, Lc, we can build a Majorana mass term —

XmL

L()R

Quark and charged-lepton Majorana masses are forbidden by electric charge conservation.

Neutrino Majorana masses would make the neutrinos very distinctive.

26

The objects L and Lc in mLL Lc are not the mass eigenstates, but just the neutrinos in terms of which the model is constructed.

mLL Lc induces L Lc

mixing.

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

KS,L (K0 K0)/2 . KS,L = KS,L .

As a result of L Lc

mixing, the neutrino mass eigenstate is —

i = L + Lc = “ + ”. i = i .

27

To Determine To Determine If Neutrinos If Neutrinos Have Majorana Have Majorana

MassesMasses

28

The Promising Approach —

Neutrinoless Double Beta Decay [0]

We are looking for a small Majorana neutrino mass. Thus, we will need a lot of parent nuclei (say, one ton of them).

e–

e–

Nucl Nucl’

29

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

0 i = i

The Central Role of 13

Both CP violation and our ability to tell whether the spectrum is normal or inverted depend on 13.

Determining 13 is an important step.

If sin2213 > 10–(2-3), we can study both

of these issues with intense but conventional accelerator

and beams, produced via + + + and – – + .

31

How 13 May Be Measured

Reactor neutrino experiments are the cleanest way.

Accelerator neutrino experiments can also probe 13 . Now it is entwined

with other parameters.

In addition, accelerator experiments can probe

whether the mass spectrum is normal or inverted,

and look for CP violation.

All of this is done by studying e and e

while the beams travel hundreds of kilometers.

32

Generically, grand unified models (GUTS) favor —

GUTS relate the Leptons to the Quarks.

is un-quark-like, and would probably involve a lepton symmetry with no quark analogue.

The Mass Spectrum: or ?

33

How To Determine If The Spectrum Is Normal Or

InvertedExploit the fact that, in matter,

W

e

e

e( )

e( )

affects and oscillation (differently), and leads to —

P( e)P( e)

> 1 ;< 1 ;

Note fake CP

Note dependence on the mass ordering

34

Q : Does matter still affect and differently when = ?

A : Yes!

“”

e+ W+

e– W–

“”

Spin

Spin

The weak interactions violate parity. Neutrino – matter interactions depend

on the neutrino polarization.

35

Is leptonic CP, through Leptogenesis, the origin of the Baryon Asymmetry of the universe?

The observed CP in the weak interactions of quarks cannot explain the Baryon Asymmetry of the universe.

Do Neutrino Interactions Violate CP?

(Fukugita, Yanagida)

Wilfried Buchmueller

Leading contributor

( )

36

See-Saw Mechanism

NVery heavy neutrino

Familiar light neutrino}

{

The very heavy neutrinos N would have been made in the hot Big Bang.

Leptogenesis In BriefThe most popular theory of why neutrinos are so light is the —

(Yanagida; Gell-Mann, Ramond, Slansky; Minkowski)

37

If neutrino oscillation violates CP, then quite likely so does N decay. In the See-Saw, these two CP violations have a common origin.

Then, in the early universe, we would have had different rates for the CP-mirror-image decays –

N l + … and N l + …

This would have led to unequal numbers of leptons and antileptons (Leptogenesis).

Then, Standard-Model Sphaleron processes would have turned 1/3 of this leptonic asymmetry into a Baryon Asymmetry.

The heavy neutrinos N, like the light ones , are Majorana particles. Thus, an N can decay into l or l+.

+

38

Look for P( ) P( )

How To Search for CP In Neutrino Oscillation

39

Q : Can CP violation still lead to P( e) P( e) when = ?

Detector

e+

“ e ”

–

Detector

e–+ e

+

–

Compare

with

A : Certainly!

Ui*

Ui Uei*

Uei

€

i∑

€

i∑

i

i

€

exp −imi2 L 2E( )

€

exp −imi2 L 2E( )

40

Separating CP From the Matter Effect

But genuine CP and the matter effect depend quite differently from each other on L and E.

One can disentangle them by making oscillation measurements

at different L and/or E.

Genuine CP and the matter effect

both lead to a difference between

and oscillation.

41

Accelerator Oscillation Probabilities

( )

€

P ν μ →ν e[ ] ≅ sin 2 2θ 13 T1 − α sin 2θ 13 T2 + α sin 2θ 13 T3 + α 2 T4€

≡m212 Δm31

2

€

≡m31

2 L

4E

€

x ≡2 2GF Ne E

Δm312

€

T4 = cos2 θ23 sin2 2θ12sin2 xΔ( )

x2€

T1 = sin2 θ23

sin2 1− x( )Δ[ ]

1− x( )2

€

T2 = sinδ sin 2θ12 sin 2θ23 sin Δsin xΔ( )

x

sin 1− x( )Δ[ ]

1− x( )

€

T3 = cosδ sin 2θ12 sin 2θ23 cosΔsin xΔ( )

x

sin 1− x( )Δ[ ]

1− x( )

With , , and —

,

,

,

;

€

P ν μ → ν e[ ]

€

P ν μ → ν e[ ]= with – and x – x.

(Cervera et al., Freund, Akhmedov et al.)

Atmospheric

CP-odd interference

CP-even interference

Solar

42

The matter-effect parameter x has E/12 GeV.

€

x

At L/E of the 1st “atmospheric” oscillation peak, and E 1 GeV, the effect of matter on the neutrino atmospheric oscillation term (sin2213 T1) is —

€

1 1− x( )2 ≅ 1± E 6GeV( )

Strategies

At fixed L/E, genuine CP effects do not change with E, but the matter effect grows, enhancing (suppressing) the oscillation if the hierarchy is Normal (Inverted).

Normal

Inverted

43

If E E/3 at fixed L, we go from the

1st atmospheric oscillation peak to the 2nd one.

When E E/3 at fixed L, CP is tripled, but

the matter effect is reduced by a factor of 3.

44

Neutrino Vision Neutrino Vision at Fermilabat Fermilab

45

Develop a Develop a

phased approach withphased approach with

ever increasing beam ever increasing beam

intensitiesintensities

and ever increasing and ever increasing

detector capabilitiesdetector capabilitiesProbe Mixing, Mass Ordering, Probe Mixing, Mass Ordering,

CP ViolationCP ViolationY-K Y-K KimKim

46

NuMI (NOvA)8 GeV ILC-like Linac

Project X = 8 GeV ILC-like LinacProject X = 8 GeV ILC-like Linac+ Recycler+ Recycler

+ Main Injector+ Main Injector

Main Injector: 2.3 MW (120 GeV) for neutrinosRecycler: 200 kW (8 GeV) for kaons, muons, …

The Intensity Frontier With The Intensity Frontier With Project XProject X

National Project with International Collaboration

DUSEL

Y-K Kim

47

Project X: Properties

~2.3 MW at 120 GeV for Neutrino ScienceInitially NOvA, Possibly DUSEL later

200 kW at 8 GeV for Precision Physics

8 GeV H- Linac with ILC Beam Parameters (9mA x 1msec x 5Hz)

v = c (ILC Linac)v < c

(Young-Kee Kim)

48

(Y-K Kim)

49

Booster

AccumulatorDebuncher

RecyclerMain Injector

Tevatron

MiniBooNESciBooNE

MINOS(200 kW, 120 GeV)

Present:MINOS: • best measurement of m2

23

• provide an early glimpse on 13

MiniBooNE, SciBooNE:• probe neutrino parameters• measure neutrino x-sections

Y-K Kim

50

Booster

RecyclerMain Injector

Phase 1:MINOSMINERvANOvA(700 kW, 120 GeV)

NOvA: • provide the first glimpse of the mass hierarchy for large 13 - the only near term probe of hierarchy in the world

• excellent sensitivity to 13

MINERvA:• measure neutrino x-sections (above 1 GeV) to high precision

Y-K Kim

51

The NOA Experiment

Gary Feldman

810 km

52

NOA

•A study of e and e

• 15 kton liquid scintillator detector

• Off the axis of Fermilab’s NuMI neutrino beamline

•L = 810 km; E 2 GeV (L/E near 1st

osc. peak)

•Main goal: Try to determine whether the spectrum is Normal or Inverted

53

Booster

RecyclerMain Injector

Phase 1.5:

neutrinosFrom Booster

NOvALAr 5 kton at Soudan(700 kW, 120 GeV)

LAr 5 kton:• if small scale R&D / experiments are successful.

NOvA + LAr 5 kton: • enhancing the NOvA sensitivity• enabling a new detector technology

Y-K Kim

54

RecyclerMain Injector

Project X Linac

Phase 2:NOvALAr 5 kton at Soudan(2.3 MW, 120 GeV)

NOvA w/ Project Xor NOvA + LAr 5 kton w/ Project X:

• enhancing sensitivity even further

Project XBeam Power (kW)

Y-K Kim

55

RecyclerMain Injector

Project X Linac

Phase 3

DUSEL (WC or/and LAr)(>2 MW, 50 – 120 GeV)

( Detector = Proton Decay Detector)

Project X beam to DUSEL:

• enhancing the sensitivity markedly

Project XBeam Power (kW)

Y-K Kim

56

The 3The 3 Reach of the Reach of the Successive PhasesSuccessive Phases

sin2213 Mass Ordering

CP Violation

N. Saoulidou

€

10−1

€

10−2

€

10−3

€

10−4

€

10−1

€

10−2

€

10−3

€

10−4

57

Project X Linac Upgrade

4 GeV Factory

2 MW Target

DUSEL

Toward “Proton Intensity Upgrade”Evolutionary Path to a Neutrino Factory

Neutrino Beam to DUSEL

Y-K Kim

58

We have learned a lot about the neutrinos in the last

decade.

What we have learned raises some very interesting

questions.

We look forward to answering them.

SummarySummary

59

Backup Slides

6040

61

U.S. Long Baseline Neutrino Study

Explored two approaches:

1.Add detector mass, beyond NOA, in Fermilab’s NuMI beamline

2.Build at Fermilab a new, wide-band beam aimed at a very large ( and p-decay) detector more than 1000 km away, possibly in a Deep Underground Science and Engineering Laboratory (DUSEL) The 2nd approach has greater

physics reach, particularly for determining whether the spectrum is Normal or Inverted, and greater

cost.

(Brookhaven & Fermilab)

62

ILC Decision Timelines

Possible ILC Decision Timelines

LHC discoveries

International

Agreements

ILC

2010 ILC DecisionSite

selec

ted

US collidersShutdownGreat Opportunityfor ILC

EPP2010 & P5 Assumption

ILC

2010 ILC Decision

ILC RDR with Cost Estimate in Feb. 2007

(Young-Kee Kim)

63

Steering Group Report(Points relevant to

neutrinos)If ILC remains near the proposed timeline, the Fermilab neutrino program will focus on NOA and several small experiments.

If ILC start is delayed a couple of years, Fermilab should undertake SNuMI, an upgrade of the NuMI beamline.

If ILC postponement would accommodate an interim major project, the laboratory should undertake Project X, an ILC-related high-intensity proton source.

64

(Y2K)

65

(Y2K)

66

(Y2K)

67

(Young-Kee Kim)

68

Planning Backup Slides

69

NOA Timeline

Construction: 2008 – 2012 (US$36.5M requested in President’s budget for 2008)

Data taking : 2012 – 2021, evenly

split between and

70

Sensitivity reach of different long baseline experiments

(U.S. Long Baseline Neutrino Study)

71

Neutrino Scientific Assessment Group (NuSAG)

(A subpanel of HEPAP and NSAC)

Recommends preparation for a U.S. long baseline neutrino program, including R&D on both of the approaches explored by the U.S. Long Baseline Neutrino Study.

Detector R&D should include both water Cerenkov and liquid argon detectors.

Points out that, because of the different matter effects in Japan and the U.S., a cooperative program with T2K could help determine the mass ordering.

72

Project X would make possible a high-intensity, flexible-energy, neutrino

beam aimed at a distant (L > 1000 km) large

detector.

It would also be a high-intensity source of muons and quarks for experiments in precision physics.

73

If the ILC is constructed outside of the U.S., Fermilab should pursue additional neutrino science with SNuMI at a minimum, and Project X if possible.In all scenarios —

R&D on Project X should start now

R&D on future accelerator options, concentrating on a Neutrino Factory and a Muon Collider, should be increased

74

Backup Slides

75

Why Many Theorists Think Majorana Mass Terms Are

LikelyThe Standard Model (SM) is defined by the fields it contains, its symmetries (notably Weak Isospin Invariance), and its renormalizability.

Anything allowed by the symmetries occurs in nature.

The SM contains no mass, and no R field, only L.

Now that we know the neutrino has mass, we must somehow extend the SM to accommodate it. In doing this, we can either add R, or not add it.

76

If we do not add R, then the only neutrino mass term we can construct is , a Majorana mass term.

If we do add R, then we can construct the Dirac mass term mDLR. If this term is all there is, the neutrino gets its mass the same way that a quark or charged lepton does. No Majorana neutrino masses.

However —

Unlike L , R carries no Weak Isospin.

Thus, once R has been added, no SM symmetry prevents the occurrence of the Majorana mass term mRRc R.

mLLc L

77

If anything allowed by the extended SM occurs in nature, then neutrinos

have Majorana masses.

Hence, the neutrino mass eigenstates are their own antiparticles.

78

ii

W– W–

e– e–

Nuclear Process

Nucl Nucl’

Uei

Uei

SM vertex

i

Mixing matrix

We anticipate that 0 is dominated by

a diagram with Standard Model vertices:

Then —

Amp[0] miUei2 m

Mass (i)

79

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

rNormal

hierarchy Inverted hierarchy

80

m

Smallest

95% CLTakes 1 ton

Takes 100 tons

m For Each Hierarchy

81

How Large Is 13?We know only that sin213 < 0.032

(at 2). The theoretical prediction of 13 is not sharp:

Albright & Chen( )

Present

bound

82

sin213 = Ue32 is the small e piece of 3.

3 is at one end of m2atm.

We need an experiment with L/E sensitive to m2

atm (L/E ~ 500 km/GeV) , and involving e.

m2atm

(Mass)2

m2sol}

sin213

How 13 May Be Measured

83

P(e Disappearance) =

= sin2213 sin2[1.27m2

atm(eV2)L(km)/E(GeV)]

Reactor Experiments

Looking for disappearance of reactor e while they travel L ~

1.5 km with energy E ~ 3 MeV is the cleanest way to

determine 13 .

(Possible experiment in Japan?)

84

Does Leptogenesis Require Neutrino Mass?

Could leptogenesis occur even if

the light neutrinos were massless??

(André de Gouvêa, B.K., and Paul Langacker)

85

Leptogenesis is an outgrowth of the see-saw picture.

In a straightforward (i.e., Type I) see-saw picture,

€

L new = −Mi2

NiRcNiR

i=1

3∑ − yαi ναL ϕ 0 − l αLϕ − ⎡

⎣ ⎢ ⎤ ⎦ ⎥NiR

α , i=1

3∑ + h.c.

SM Higgs doublet

Yukawa couplings

The Yukawa couplings yi play two roles:

They cause the heavy neutrinos to decayThey give masses to the light neutrinos

The light neutrino masses can have implications for Leptogenesis.

Real, positive

Diagonal basis

86

€

L new = −Mi2

NiRcNiR

i=1

2∑ − yi ν L ϕ 0 − l Lϕ − ⎡

⎣ ⎢ ⎤ ⎦ ⎥NiR

i=1

2∑ + h.c.

SM Higgs doublet

Yukawa couplings

Leptogenesis In a Minimal Model

A minimal model:

Two heavy RH neutrinos, N1R and N2R

One light LH lepton doublet, (L, lL) In the basis where the Majorana mass term is diagonal, with real positive eigenvalues,

87

Long ago —

N1 l– + +

+

+

88

The decay rates were —

(N1 l– + +) = ay1 + by1*y2

22and

(N1 l+ + –) = ay1* + by1y2*22

These rates produced a matter – antimatter asymmetry if —

(N1 l– + +) – (N1 l+ + –)

m(ab*)

m(y1*2y22) 0.

(LeptogeneLeptogenesissis)

89

Today —

0vac v 0

The light neutrino now has a nonzero mass unless —

Det(M) = 0 .

Mass matrix

The product P of all the heavy and light neutrino eigenmasses satisfies —

P2 = Det(MM*) = |Det(M)|2 .

90

The only natural solution to this constraint is —

y1 = y2 = 0.

Then N1 and N2 do not decay, and there is no Leptogenesis.

Det(M) = 0

€

y12

M1+

y22

M2= 0

Masses of N1, N2

91

The loophole —

€

y12

M1+

y22

M2= 0

can be satisfied by a cancellation between the terms.

This requires a conspiracy between the Yukawa sector and the Majorana sector of the theory.

But suppose this conspiracy happens:

Then y12 and y2

2 must be relatively real, so that —

m(y1*2y22) = 0

Thus, there is still no Leptogenesis!

92

In the minimal model that can give

Leptogenesis, the light neutrino

must have a nonzero mass

or Leptogenesis cannot occur.

Perhaps neutrino mass is

essential to our existence.

93

When There Are Three Light Doublets and Three Heavy

Neutrinos

€

L new = −Mi2

NiRcNiR

i=1

3∑ − yαi ναL ϕ 0 − l αLϕ − ⎡

⎣ ⎢ ⎤ ⎦ ⎥NiR

α , i=1

3∑ + h.c.

The condition that all 3 light neutrinos be massless is —

The only natural solution to these 6 constraints is —The Yukawa coupling

matrix y = 0.Then the Ni do not decay, and there is

no Leptogenesis.

.

€

yαi1

M i

yβii=1

3∑ ≅ 0 ; α , β =1, 3

94

The loophole —

can be satisfied by a cancellation between the terms.

This requires a conspiracy between the Yukawa sector and the Majorana sector of the theory.

In addition, the Yukawa coupling matrix y must be singular.

While mathematically possible, these circumstances are quite unnatural.

€

yαi1

Miyβi

i=1

3∑ = 0 ; α , β =1, 3

95

However, suppose they occur:

For hierarchical heavy neutrino masses (M2, 3 >> M1) —

(N1 l– + +) – (N1 l+ + –)

(Dutta & Mohapatra)

Then there is still no Leptogenesis.€

∝ℑm yα 1* yβ1

* yαi1

M i

yβii=1

3∑ ⎛

⎝ ⎜

⎞

⎠ ⎟

α ,β =1

3∑

⎡

⎣ ⎢

⎤

⎦ ⎥yi yiy1 y1

* *

96

If the three light neutrinos are all

massless, Leptogenesis is possible, but quite

unlikely.

97

Double beta decay backup

slides

98

This leads many theorists to expect

Majorana masses, hence L and i = i.

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.

99

Do We Expect That i = i?

How can the S(tandard) M(odel) be

extended to include neutrino masses?

How does the SM become the SM?

100

The S(tandard) M(odel)

and

couplings conserve the Lepton Number L.

So do the Dirac charged-lepton mass terms

mllRlL

–

Wl–

Z

l +(—) l

+(—)

Xml

R(L) Right(Left) Handed

101

• Original SM: m = 0.

• Why not add a Dirac mass term,

mDRL

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. (Only Left-Handed fermions couple to the W boson.)

XmD

(—)

(—)—

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

102

Unlike L, R carries no Electroweak Isospin.

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

mRRc R

Charge-conjugate fields:

c = (Particle Antiparticle)

The Majorana mass does not conserve L, so

now

i = i (Majorana neutrinos)

[No conserved L to distinguish i from i]

XmR

—

Charge conjugate

103

This leads many theorists to expect

Majorana masses, hence L and i = i.

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.

104

• The presence of Majorana masses

• i = i (Majorana neutrinos)

• L not conserved— are all equivalent

Any one implies the other two.

(Recent work: Hirsch, Kovalenko, Schmidt)

105

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

Thus, Amp [i contribution] mi

Amp[0] miUei2 m

i

ii

W– W–

e– e–

Nuclear Process

Nucl Nucl’

In

Uei

Uei

SM vertex

i

Mixing matrix

Mass (i)

106

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 neutrino mass terms.

The 0 amplitude would be proportional to neutrinomass even if there were no helicity mismatch.

107

Possible Information From Neutrino Magnetic

MomentsBoth Majorana and Dirac neutrinos can have transition magnetic dipole moments :

i j

For Dirac neutrinos, < 10–

15 Bohr

For Majorana neutrinos, < Present bound Present

bound =

7 x 10–11 Bohr ; Wong et al. (Reactor)

3 x10–12 Bohr ; Raffelt (Stellar E loss)

108

An observed below the present bound

but well above 10–15 Bohr would imply that neutrinos are Majorana

particles.

However, a dipole moment that large requires

L-violating new physics below 100 TeV.

Bell, Cirigliano, Davidson, Gorbahn, Gorchtein,

Ramsey-Musolf, Santamaria, Vogel, Wise, Wang

( )Neutrinoless double beta decay at the planned level of sensitivity only requires this new physics at 1015 GeV, near the Grand Unification scale.