1. Origin of Neutrino Mass
Hitoshi Murayama (UC Berkeley)
Neutrinos in Cosmology, in Astro, Particle and Nuclear Physics
Erice, 17th September, 2005

2. Outline Introduction Implications of Neutrino Mass Seven Questions
Why do we exist?
Models of Flavor
Conclusion
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3. Introduction

4. Window to (way) high energy scales beyond the Standard Model!
The Question
So much activity on neutrino mass already.
Why are we doing this?
Window to (way) high energy scales beyond the Standard Model!
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5. Why Beyond the Standard Model
Standard Model is sooooo successful. But none of us are satisfied with the SM. Why?
Because it leaves so many great questions unanswered
 Drive to go beyond the Standard Model
Two ways:
Go to high energies
Study rare, tiny effects 
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6. Rare Effects from High-Energies
Effects of physics beyond the SM as effective operators
Can be classified systematically (Weinberg)
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7. Unique Role of Neutrino Mass
Lowest order effect of physics at short distances
Tiny effect (mn/En)2~(eV/GeV)2=10–18!
Inteferometry (i.e., Michaelson-Morley)!
Need coherent source
Need interference (i.e., large mixing angles)
Need long baseline
Nature was kind to provide all of them!
“neutrino interferometry” (a.k.a. neutrino oscillation) a unique tool to study physics at very high scales
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8. Ubiquitous Neutrinos
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9. Sun as a neutrino source
SuperK image of the Sun
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10. We don’t get enough We need survival probabilities of 8B: ~1/3
7Be: <1/3
pp: ~2/3
Can we get three numbers correctly with two parameters?
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11. Year of Neutrino: 2002 March 2002 April 2002 with SNO Dec 2002
with KamLAND
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12. Solar Neutrino Problem Finally Solved After 35 Years!

13. Historic Era in Neutrino Physics
We learned:
Atmospheric nms are lost. P=4.2 10–26 (SK)
converted most likely to nt
Solar ne is converted to either nm or nt (SNO)
Reactor anti-ne disappear and reappear (KamLAND)
Only the LMA solution left for solar neutrinos
Neutrinos have tiny but finite mass
the first evidence for
incompleteness of Minimal Standard Model
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14. CP Violation Possible only if: Can we see CP violation?
Dm122, s12 large enough (LMA)
q13 large enough
Can we see CP violation?
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15. Typical Theorists’ View ca. 1990
Solar neutrino solution must be small angle MSW solution because it’s cute
Natural scale for Dm223 ~ 10–100 eV2 because it is cosmologically interesting
Angle q23 must be ~ Vcb =0.04
Atmospheric neutrino anomaly must go away because it needs a large angle
Wrong!
Wrong!
Wrong!
Wrong!
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16. Implications of Neutrino Mass

17. Neutrinos are Left-handed
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18. Neutrinos must be Massless
All neutrinos left-handed  massless
If they have mass, can’t go at speed of light.
Now neutrino right-handed??
 contradiction  can’t be massive
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19. Standard Model
We have seen only left-handed neutrinos and right-handed anti-neutrinos (CPT)
Neutrinos are strictly massless in the Standard Model
Finite mass of neutrinos implies that the Standard Model is incomplete!
Not just incomplete but probably a lot more profound
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20. Mass Spectrum
What do we do now?
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21. 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?
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22. Extra Dimensions 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; Grossman, Neubert)
mn ~ 1/R if one extra dim  R~10mm
An infinite tower of sterile neutrinos
Or anomaly mediated SUSY breaking
(Arkani-Hamed, Kaplan, HM, Nomura)
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23. Two ways to go (2) Majorana Neutrinos:
There are no new light particles
Why if I pass a neutrino and look back?
Must be right-handed anti-neutrinos
No fundamental distinction between neutrinos and anti-neutrinos!
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24. Seesaw Mechanism Why is neutrino mass so small?
Need right-handed neutrinos to generate neutrino mass
, but nR SM neutral
To obtain m3~(Dm2atm)1/2, mD~mt, M3~1015GeV (GUT!)
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25. Neutrino mass may be probing unification:
Grand Unification M3
electromagnetic, weak, and strong forces have very different strengths
But their strengths become the same at 1016 GeV if supersymmetry
To obtain
m3~(Dm2atm)1/2, mD~mt
 M3~1015GeV!
Neutrino mass may be probing unification:
Einstein’s dream
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26. Seven Questions

27. Three-generation Framework
Standard parameterization of MNS matrix for 3 generations
atmospheric
???
solar
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28. Three-generation
Solar, reactor, atmospheric and K2K data easily accommodated within three generations
sin22q23 near maximal Dm2atm ~ 2.510–3eV2
sin22q12 large Dm2solar ~810–5eV2
sin22q13=|Ue3|2< 0.05 from CHOOZ, Palo Verde
Because of small sin22q13, solar (reactor) & atmospheric n oscillations almost decouple
Maltoni et al, hep-ph/
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29. Six Seven Questions Dirac or Majorana? Absolute mass scale?
How small is q13?
CP Violation?
Mass hierarchy?
Verify Oscillation?
LSND? Sterile neutrino(s)? CPT violation?
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30. KamLAND oscillation
Now strong evidence that neutrinos do disappear and reappear (and again)
Oscillation!
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31. Neutrinoless Double-beta Decay
The only known practical approach to discriminate Majorana vs Dirac neutrinos
0nbb: nn  ppe–e– with no neutrinos
Matrix element  <mne>=SimniUei2
Current limit
|<mne>| ≤ about 1eV
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32. Three Types of Mass Spectrum
Degenerate
All three around >0.1eV with small splittings
Laboratory limit: m<2.3eV
May be confirmed by KATRIN, cosmology
|<mne>|=|SimniUei2|>m cos22q12>0.07m
Inverted
m3~0, m1~m2~(Dm223)1/2≈0.05eV
May be confirmed by long-baseline experiment with matter effect
|<mne>|=|SimniUei2|>(Dm223)1/2 cos22q12>0.013eV (HM, Peña-Garay)
Normal
m1~m2~0, m3~(Dm223)1/2≈0.05eV
|<mne>|=|SimniUei2| may be zero even if Majorana
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33. Cosmological Limit
CMB+LSS+Lyman a (Seljak et al, astro-ph/ ) :
Si mi<0.42 eV, m1<0.13 eV (95% CL)
Puts upper limit on the effective neutrino mass in the neutrinoless double beta decay (Pierce, HM)
|<mne>|=|SimniUei2|<Simni |Uei2|<0.13eV
Heidelberg-Moscow: |<mne>|=0.11–0.56 eV
Reanalysis with Vogel’s MEs: |<mne>|=0.4–1.3 eV
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34. Cosmology vs Laboratory
Global fit to the “World Data”
indeed, tension between the Heidelberg-Moscow claim and cosmology
Still subject to the uncertainties in nuclear matrix element (Bahcall, HM, Peña-Garay)
Better data and theory needed!
Lisi et al, hep-ph/
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35. Why do we exist? Matter Anti-matter Asymmetry

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37. Matter and Anti-Matter Early Universe
10,000,000,001
10,000,000,000
Matter
Anti-matter
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38. Matter and Anti-Matter Current Universeus 1
Matter
Anti-matter
The Great Annihilation
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39. Baryogenesis Gaussian scale-invariant fluctuation  inflation
Initial condition wiped out
What created this tiny excess matter?
Necessary conditions for baryogenesis (Sakharov):
Baryon number non-conservation
CP violation
(subtle difference between matter and anti-matter)
Non-equilibrium
 G(DB>0) > G(DB<0)
It looks like neutrinos have no role in this…
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40. Electroweak Anomaly Actually, SM converts L (n) to B (quarks).
In Early Universe (T > 200GeV), W is massless and fluctuate in W plasma
Energy levels for left-handed quarks/leptons fluctuate correspon-dingly
DL=DQ=DQ=DQ=DB=1  D(B–L)=0
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41. Leptogenesis You generate Lepton Asymmetry first. (Fukugita, Yanagida)
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”
Despite detailed information on neutrino masses, it still works! (e.g., Bari, Buchmüller, Plümacher)

42. Origin of Universe ~ R amplitude size of the universe
Maybe an even bigger role: inflation
Need a spinless field that
slowly rolls down the potential
oscillates around it minimum
decays to produce a thermal bath
The superpartner of right-handed neutrino fits the bill
When it decays, it produces the lepton asymmetry at the same time
(HM, Suzuki, Yanagida, Yokoyama)
Decay products: supersymmetry and hence dark matter
Neutrino is mother of the Universe?
amplitude
size of the universe
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43. Origin of the Universe Right-handed scalar neutrino: V=m2f2 ns=0.96
Detection possible in the near future
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44. Can we prove it experimentally?
Unfortunately, no: it is difficult to reconstruct relevant CP-violating phases from neutrino data
But: we will probably believe it if
0nbb found
CP violation found in neutrino oscillation
EW baryogenesis ruled out
Archeological evidences
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45. Models of Flavor

46. 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
Repeat Gell-Mann Okubo!
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47. Broken Flavor Symmetry
Flavor quantum numbers (SU(5)-like):
10(Q, uR, eR) (+2, +1, 0)
5*(L, dR) (+1, +1, +1)
Flavor symmetry broken by a VEV ~0.02
mu:mc:mt ~ md2:ms2:mb2 ~ me2:mm2:mt2 ~4: 2 :1
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48. Not bad! mb~ 3mt, ms ~ 3mm, md ~ 3me
mu:mc:mt ~ md2:ms2:mb2 ~ me2:mm2:mt2
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49. New Insight 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?
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50. Is There a Structure in Neutrino Masses & Mixings?
Monte Carlo random complex 33 matrices with seesaw mechanism
(Hall, HM, Weiner; Haba, HM)
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51. Anarchy Reasonable distributions from randomness
 Underlying symmetries don’t distinguish 3 neutrinos.
Flavor quantum numbers:
10(Q, uR, eR) (+2, +1, 0)
5*(L, dR) (+1, +1, +1)
Inconceivable just a few years ago
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52. q13 in Anarchy q13 cannot be too small if anarchy
How often can “large” angle fluctuate down to the CHOOZ limit?
Kolmogorov–Smirnov test: 12%
sin2 2q13>0.004 (3s)
CP violation likely observable at long baseline experiment
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(de Gouvêa, HM)

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
sin22q13 just below the bound
Ideal for superbeam, n-factory
 Pro-globalization!
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54. Different Flavor Symmetries
Altarelli-Feruglio-Masina hep-ph/
Hall, HM, Weiner
Sato, Yanagida
Vissani
Barbieri et al
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55. Critical Measurements
sin2 2q23=1.000.01?
Determines a need for a new symmetry to enforce the maximal mixing
sin2 2q13<0.01?
Determines if the flavor quantum number of electron is different from mu, tau
Normal or inverted hierarchy?
Most symmetries predict the normal hierarchy
CP Violation?
Plausibility test of leptogenesis
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56. Large q23 and quarks Large mixing between nt and nm Make it SU(5) GUT
Then a large mixing between sR and bR
Mixing among right-handed fields drop out from CKM matrix
But mixing among superpartners physical
O(1) effects on bs transition possible
(Chang, Masiero, HM)
Expect CP violation in neutrino sector especially if leptogenesis
BsJ/y f Bdf Ks
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57. 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(tmg), B(meg), me at interesting (or too-large) levels
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58. Dynamics behind flavor symmetry?
Once flavor symmetry structure identified (e.g., Gell-Man–Okubo), what is dynamics? (e.g., QCD)
Supersymmetry:
Anomalous U(1) gauge symmetry with Green-Schwarz mechanism
Large Extra Dimensions:
Fat brane with physically separated left- and right-handed particles
Technicolor:
New broken gauge symmetries at 100TeV scale
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59. Conclusions Revolutions in neutrino physics
The solar neutrino problem solved!
Small but finite neutrino mass:
Probes physics beyond the standard model
New insights into the origin of flavor
Interesting interplay between neutrinos and cosmos
Neutrino mass may be responsible for our existence
Neutrinos may even be the origin of the universe
A lot more to learn in the next few years
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