Neutrino Physics III

Hitoshi MurayamaUniversity of PisaFebruary 26, 2003

2

Outline

• Three Generations• LSND• Implications of Neutrino Mass• Why do we exist?• Models of flavor• Conclusions

Three Generations

4

MNS matrix

• Standard parameterization of Maki-Nakagawa-Sakata matrix for 3 generations

UMNS =Ue1 Ue2 Ue3Uμ1 Uμ2 Uμ3Uτ1 Uτ2 Uτ3

⎛

⎝

⎜ ⎜ ⎜

⎞

⎠

⎟ ⎟ ⎟

=1

c23 s23−s23 c23

⎛

⎝

⎜ ⎜ ⎜

⎞

⎠

⎟ ⎟ ⎟

c13 s13e−iδ

1−s13e

iδ c13

⎛

⎝

⎜ ⎜ ⎜

⎞

⎠

⎟ ⎟ ⎟

c12 s12−s12 c12

1

⎛

⎝

⎜ ⎜ ⎜

⎞

⎠

⎟ ⎟ ⎟

atmospheric ??? solar

5

Three-generation

• Solar & atmospheric oscillations easily accommodated within three generations

• sin2223 near maximal, m2atm ~ 310–3eV2

• sin2212 large, m2solar ~ 510–5eV2

• sin2213 < 0.05 from CHOOZ, Palo Verde

• Because of small sin2213, solar & atmospheric oscillations almost decouple

• Need to know sin2213,

and mass hierarchy

6

Raised More Questions

• Why do neutrinos have mass at all?

• Why so small?• We have seen mass

differences. What are the masses?

~m/15eV• Do we need a fourth

neutrino?• Are neutrinos and anti-

neutrinos the same? • How do we extend the Standard Model to incorporate massive neutrinos?

7

3-flavor mixing

• If m1 and m2 not very different, it reduces to the 2-flavor problem

€

τ μ ,t =Uτ 1* Uμ1 e−im1

2t /2 p

+Uτ 2* Uμ 2 e−im2

2t /2 p +Uτ 3* Uμ 3 e−im3

2t /2 p

≅ Uτ 1* Uμ1 +Uτ 2

* Uμ 2( )e−im1

2t /2 p +Uτ 3* Uμ 3 e−im3

2t / 2 p

= −Uτ 3* Uμ 3e−im1

2t /2 p +Uτ 3* Uμ 3 e−im3

2t /2 p

= eiφ sinθ −e−im12t / 2 p + e−im3

2t /2 p ⎛ ⎝ ⎜

⎞ ⎠ ⎟

8

When is 3-flavor important?

€

τ μ ,t2

= Uτi*UμiUτjUμj

* e−i mi

2 − m j2

( )t / 2 p

i, j∑

= −2ℜe Uτi*UμiUτjUμj

*( ) sin2 mi

2 − m j2

4 pi, j∑ t

+ ℑm Uτi*UμiUτjUμj

*( ) sin

mi2 − m j

2

2 pi, j∑ t

When all masses significantly differentAnti-neutrinos: UU*, the last term flips signPossible CP violation

9

CP Violation

• Possible only if:– m12

2, s12 large enough (LMA)

– 13 large enough

P(νe → νμ)−P(νe → νμ) =16s12c12s13c132 s23c23

sinδsin Δm122

4EL

⎛ ⎝ ⎜

⎞ ⎠ ⎟ sin Δm13

2

4EL

⎛ ⎝ ⎜

⎞ ⎠ ⎟ sin Δm23

2

4EL

⎛ ⎝ ⎜

⎞ ⎠ ⎟

10

11

LSND

12

ν μν e?

ν ep→ e+n

μ+→ e+νeν μ

p→ π +

π+→ μ+νμ

13

3.3 Signal

• Excess positron events over calculated BG

P(ν μ → ν e)=(0.264±0.067±0.045)%

14

Mini-BooNE

• LSND unconfirmed• Neutrino beam from

Fermilab booster• Settles the issue of

LSND evidence• Started data taking the

summer 2002

15

LSND Affects SN1987A neutrino burst

HM, Yanagida

• Kamiokande’s 11 events:– 1st event is forward

may well be e from deleptonization burst(p e- n e to become neutron star)

– Later events most likely e

• LSND parameters cause complete MSW conversion ofeμ if light side (e lighter)eμ if dark side (e heavier)

• Either mass spectrum disfavored

_

_ _

16

LSND Affects SN1987A neutrino burst

HM, Yanagida

17

Sterile Neutrino

• LSND, atmospheric and solar neutrino oscillation signalsm2

LSND ~ eV2

m2atm ~ 310–3eV2

m2solar < 10–3eV2

Can’t be accommodated with 3 neutrinos

Need a sterile neutrinoNew type of neutrino with no

weak interaction

• 3+1 or 2+2 spectrum?

18

Sterile Neutrino getting tight

• 3+1 spectrum: sin22LSND=4|U4e|2|U4μ|2

– |U4μ|2 can’t be big because of CDHS, SK U/D

– |U4e|2 can’t be big because of Bugey– Marginally allowed

• 2+2 spectrum: past fits preferred– Atmospheric mostly μτ

– Solar mostly es (or vice versa)

– Now pretty much ruled out(Barger et al, Giunti et al, Gonzalez-Garcia et al, Strumia, Maltoni et al)

19

WMAPMaltoni, Schwetz, Tortola, Vallehep-ph/0209368

20

CPT Violation?“A desperate remedy…”

• LSND evidence:anti-neutrinos

• Solar evidence:neutrinos

• If neutrinos and anti-neutrinos have different mass spectra, atmospheric, solar, LSND accommodated without a sterile neutrino

(HM, Yanagida)(Barenboim, Lykken, et al)

Best fit to data before KamLAND (Strumia)

21

KamLAND impact

• However, now there is an evidence for “solar” oscillation in anti-neutrinos from KamLAND

• Barenboim, Borissov, Lykken: evidence for atmospheric neutrino oscillation is dominantly for neutrinos. Anti-neutrinos suppressed by a factor of 3.

• Not a great fit (Strumia)

• New CPT violation:

22

CPT Theorem

• Based on three assumptions:– Locality– Lorentz invariance– Hermiticity of Hamiltonian

• Violation of any one of them: big impact on fundamental physics

• Neutrino mass: tiny effect from high-scale physics– Non-local Hamiltonian? (HM, Yanagida)– Brane world? (Barenboim, Borissov, Lykken, Smirnov)– Dipole Field Theory? (Bergman, Dasgupta, Ganor, Karczmarek, Rajesh)

23

Implications on Experiments

• Mini-BooNE experiment will not see oscillation in neutrino mode, but will in anti-neutrino mode

• Because KamLAND is consistent with LMA, atmospheric neutrino oscillation relies on m2

LSND ~ eV2 (not a great fit)

• Katrin may see endpoint spectrum distortion in t3He+e–+e

We’ll see!

_

24

Maybe even more surprisesin neutrinos!

25

Mass Spectrum

What do we do now?

26

Two ways to go

(1) Dirac Neutrinos:– There are new

particles, right-handed neutrinos, after all

– Why haven’t we seen them?

– Right-handed neutrino must be very very weakly coupled

– Why?

27

Extra Dimension

• All charged particles are on a 3-brane• Right-handed neutrinos SM gauge singlet

Can propagate in the “bulk”• Makes neutrino mass small

(Arkani-Hamed, Dimopoulos, Dvali, March-Russell;Dienes, Dudas, Gherghetta)

• Barbieri-Strumia: SN1987A constraint“Warped” extra dimension (Grossman, Neubert)

• Or SUSY breaking(Arkani-Hamed, Hall, HM, Smith, Weiner;

Arkani-Hamed, Kaplan, HM, Nomura)

€

d 4θ S*

M (LHu N∫ )

28

Two ways to go

(2) Majorana Neutrinos:– There are no new light

particles– What if I pass a

neutrino and look back?

– Must be right-handed anti-neutrinos

– No fundamental distinction between neutrinos and anti-neutrinos!

29

Seesaw Mechanism

• Why is neutrino mass so small?• Need right-handed neutrinos to generate

neutrino mass

νL νR( )mD

mD

⎛ ⎝ ⎜

⎞ ⎠ ⎟

νLνR

⎛ ⎝ ⎜

⎞ ⎠ ⎟ νL νR( )

mDmD M

⎛ ⎝ ⎜

⎞ ⎠ ⎟

νLνR

⎛ ⎝ ⎜

⎞ ⎠ ⎟ mν =mD

2

M<<mD

To obtain m3~(m2atm)1/2, mD~mt, M3~1015GeV (GUT!)

, but R SM neutral

30

Grand Unification

• electromagnetic, weak, and strong forces have very different strengths

• But their strengths become the same at 1016 GeV if supersymmetry

• To obtain m3~(m2

atm)1/2, mD~mt

M3~1015GeV!Neutrino mass may be probing unification:

Einstein’s dream

M3

Why do we exist?Matter Anti-matter Asymmetry

32

Big-Bang NucleosynthesisCosmic Microwave Background

η =nBnγ

= 4.7−0.8+1.0( )×10−10

5.0±0.5( )×10−10

(Thuan, Izatov)

(Burles, Nollett, Turner)

WMAP

33

Matter and Anti-MatterEarly Universe

10,000,000,001 10,000,000,000

Matter Anti-matter

34

Matter and Anti-MatterCurrent Universe

The Great Annihilation

1

us

Matter Anti-matter

35

Sakharov’s Conditionsfor Baryogenesis

• Necessary requirements for baryogenesis:– Baryon number violation– CP violation– Non-equilibrium (B>0) > (B<0)

• Possible new consequences in– Proton decay– CP violation

36

Original GUT Baryogenesis

• GUT necessarily breaks B. • A GUT-scale particle X decays out-of-equilibrium

with direct CP violation

• Now direct CP violation observed: ’!

• But keeps B–L0 “anomaly washout”• Also monopole problem

B(X → q) ≠B(X → q)

B(K0 → π+π−) ≠B(K0 → π+π−)

37

Electroweak Anomaly

• Actually, SM converts L to B.– In Early Universe (T >

200GeV), W/Z are massless and fluctuate in W/Z plasma

– Energy levels for left-handed quarks/leptons fluctuate correspon-dingly

L=Q=Q=Q=B=1 B–L)=0

38

Two Main Directions

• BL0 gets washed out at T>TEW~174GeV• Electroweak Baryogenesis (Kuzmin, Rubakov, Shaposhnikov)

– Start with B=L=0– First-order phase transition non-equilibrium– Try to create BL0

• Leptogenesis (Fukugita, Yanagida)

– Create L0 somehow from L-violation– Anomaly partially converts L to B

39

Leptogenesis

• You generate Lepton Asymmetry first.• Generate L from the direct CP violation in right-handed

neutrino decay

• L gets converted to B via EW anomaly More matter than anti-matter We have survived “The Great Annihilation”

Γ(N1→ νiH)−Γ(N1 → νiH)∝ Im(h1jh1khlk* hlj

*)

40

Does Leptogenesis Work?

• Much more details worked out(Buchmüller, Plümacher; Pilaftsis)

• ~1010 GeV R OK• Some tension with supersymmetry because

of unwanted gravitino overproduction• Ways around: coherent oscillation of right-

handed sneutrino (HM, Yanagida+Hamaguchi)

41

Does Leptogenesis Work?

• Some tension with supersymmetry:– unwanted gravitino

overproduction– gravitino decay

dissociates light nuclei– destroys the success of

Big-Bang Nucleosynthesis

– Need TRH<109 GeV(Kawasaki, Kohri, Moroi)

42

Leptogenesis Works!

• Coherent oscillation of right-handed sneutrino (Bose-Einstein condensate) (HM, Yanagida+Hamaguchi)

– Inflation ends with a large sneutrino amplitude

– Starts oscillation – dominates the Universe– Its decay produces asymmetry– Consistent with observed

oscillation pattern– isocurvature perturbation at

WMAP? (Moroi, HM)nBs

~εTdecay

M1~ nB

s⎛ ⎝ ⎜ ⎞

⎠ ⎟ obs

Tdecay

106GeVargh132

h332

43

Can we prove it experimentally?

• We studied this question at Snowmass2001 (Ellis, Gavela, Kayser, HM, Chang)

– Unfortunately, no: it is difficult to reconstruct relevant CP-violating phases from neutrino data

• But: we will probably believe it if– 0 found– CP violation found in neutrino oscillation– EW baryogenesis ruled out

Archeological evidences

Models of Flavor

45

Question of Flavor

• What distinguishes different generations?– Same gauge quantum numbers, yet different

• Hierarchy with small mixings: Need some ordered structure

• Probably a hidden flavor quantum number Need flavor symmetry

– Flavor symmetry must allow top Yukawa– Other Yukawas forbidden– Small symmetry breaking generates small Yukawas

46

Fermion Mass Relationin SU(5)

• down- and lepton-Yukawa couplings come from the same SU(5) operator 10 5* H

• Fermion mass relationmb= mτ, ms = mμ, md = me @MGUT Reality:mb≈ mτ, 3ms ≈ mμ, md ≈ 3me @MGUT

• Not bad! (small correction compared to inter-generational splitting ~20–200)

47

Broken Flavor Symmetry

• Flavor symmetry broken by a VEV ~0.02• SU(5)-like:

– 10(Q, uR, eR) (+2, +1, 0)

– 5*(L, dR) (+1, +1, +1)

– mu:mc:mt ~ md2:ms

2:mb2

~ me2:mμ

2:mτ2 ~4: 2 :1

Mu ~ε4 ε3 ε2

ε3 ε2 εε2 ε 1

⎛

⎝

⎜ ⎜ ⎜

⎞

⎠

⎟ ⎟ ⎟ ,Md~

ε3 ε3 ε3

ε2 ε2 ε2

ε ε ε

⎛

⎝

⎜ ⎜ ⎜

⎞

⎠

⎟ ⎟ ⎟ ,Ml~

ε3 ε2 εε2 ε2 εε3 ε2 ε

⎛

⎝

⎜ ⎜ ⎜

⎞

⎠

⎟ ⎟ ⎟

48

Not bad!

• mb~ mτ, ms ~ mμ, md ~ me @MGUT

• mu:mc:mt ~ md2:ms

2:mb2

~ me2:mμ

2:mτ2

49

New Data from Neutrinos

• Neutrinos are already providing significant new information about flavor symmetries

• If LMA, all mixing except Ue3 large

– Two mass splittings not very different– Atmospheric mixing maximal– Any new symmetry or structure behind it?

e μ τ( )big big smallbig big bigbig big big

⎛

⎝

⎜ ⎜ ⎜

⎞

⎠

⎟ ⎟ ⎟

νeνμντ

⎛

⎝

⎜ ⎜ ⎜

⎞

⎠

⎟ ⎟ ⎟

Δmsolar2

Δmatm2 ~0.01– 0.2

50

Is There A StructureIn Neutrino Masses & Mixings?

• Monte Carlo random complex 33 matrices with seesaw mechanism

(Hall, HM, Weiner; Haba, HM)

51

Anarchy

• No particular structure in neutrino mass matrix– All three angles large– CP violation O(1)– Ratio of two mass splittings just right for LMA

• Three out of four distributions OK– Reasonable Underlying symmetries don’t distinguish 3 neutrinos.

52

13 in Anarchy

• 13 cannot be too small if anarchy

• How often can “large” angle fluctuate down to the CHOOZ limit?

• Kolmogorov–Smirnov test: 12%

• sin2 213>0.004 (3)• If so, CP violation

observable at long baseline experiment

53

Anarchy is Peaceful

• Anarchy (Miriam-Webster): “A utopian society of individuals who enjoy complete freedom without government”

• Peaceful ideology that neutrinos work together based on their good will

• Predicts large mixings, LMA, large CP violation• sin2213 just below the bound• Ideal for VLBL experiments• Wants globalization!

54

Program:More flavor parameters

• Squarks, sleptons also come with mass matrices• Off-diagonal elements violate flavor: suppressed by flavor symmetries

• Look for flavor violation due to SUSY loops• Then look for patterns to identify symmetries

Repeat Gell-Mann–Okubo!• Need to know SUSY masses

M ˜ Q 2 ~M ˜ L

2 ~1 ε ε2

ε 1 εε2 ε 1

⎛

⎝

⎜ ⎜ ⎜

⎞

⎠

⎟ ⎟ ⎟

55

To Figure It Out…

• Models differ in flavor quantum number assignments

• Need data on sin2213, solar neutrinos, CP violation, B-physics, LFV, EWSB, proton decay

• Archaeology• We will learn insight on origin of flavor by

studying as many fossils as possible– cf. CMBR in cosmology

56

More Fossils:Lepton Flavor Violation

• Neutrino oscillation lepton family number is not conserved!– Any tests using charged leptons?– Top quark unified with leptons– Slepton masses split in up- or neutrino-basis– Causes lepton-flavor violation (Barbieri, Hall)

– predict B(τμ), B(μe), μe at interesting (or too-large) levels

57

Barbieri, Hall, Strumia

58

More Fossils:Quark Flavor Violation

• Now also large mixing between τ and μ

– (τ, bR) and (μ , sR) unified in SU(5)

– Doesn’t show up in CKM matrix

– But can show up among squarks

– CP violation in Bs mixing (BsJ )

– Addt’l CP violation in penguin bs (Bd Ks)

(Chang, Masiero, HM)

Conclusions

60

Conclusions

• Historic era in neutrino physics• Oscillation in atmospheric neutrino: an unexpected

discovery, strong evidence for neutrino mass• Decades-long problem in solar neutrinos now being

resolved• A lot more to learn in the near future• Interesting connections to cosmology, astrophysics• We’d like to know how to build the new Standard

Model!