1. The Neutrino World: Present and Future Boris Kayser
Rencontres du Vietnam
August 9, 2004

2. Breakthrough
Neutrinos have nonzero masses!
Leptons mix!

3. There is some spectrum of 3 or more neutrino mass eigenstates i:
Neutrino masses
There is some spectrum of 3 or more neutrino mass eigenstates i: 4 3
(Mass)2 2 1
Mass (i)  mi

4. U is the Leptonic Mixing Matrix. U is unitary.+
l(le  e, l , l  ) W
Ui * i _
l
Ui i W
Detector
U is the Leptonic Mixing Matrix. U is unitary.

5. |> =  Ui |i> . l(le  e, l , l  ) iW
Ui * i
The neutrino state |> produced together with lis
|> =  Ui |i> . * i
Neutrino of flavor 
Neutrino of definite mass mi
Inversely, |i> =  Ui |> . 
Flavor- fraction of i = |<|i>|2 = |Ui|2 .

6. only the  component contributes.In
l
Ui i W
Detector
only the  component contributes.
An e is made by a e.
A  “ .
A  “ .

7. The evidence for neutrino mass and mixing is the discovery of neutrino flavor change:
 

8. Neutrino Flavor Change (Oscillation) in Vacuum
Imagine an experiment in which neutrinos travel a distance L, and have an energy E

9. - - = ∑ l l  Amp • • () () l l i Amp • • Ui* i+
l
(e.g. )
l
(e.g. ) 
Amp • • W
() () W
Source
Target - +
l
l i
= ∑
Amp • • W
Ui*
exp (-imi2L/2E)
Ui W i
Source
Target

10. ∑ Thus Amp( ) = Ui exp (-imi2L/2E) Ui*
Amp( ) = Ui exp (-imi2L/2E) Ui i
Often, only 2 neutrinos need to be considered.
Then —
Mixing Angle
Then, for  = , —
m22 - m12
Prob( ) = sin22 sin2[1.27 m2(eV2) L(km)/E(GeV)]
Neutrino flavor change implies neutrino mass & mixing.

11. Neutrino Flavor Change in Matter
Coherent forward scattering from ambient matter can have a big effect.
#e/vol
#n/vol

12. Neutrino mass is established.
The Standard Model interactions between neutrinos and matter do not change neutrino flavor.
Thus, flavor change requires neutrino mass and mixing even when it occurs inside matter.
The probability of atmospheric  flavor change is observed to depend on L/E.
Apart from a proportionality constant, L/E is just the time elapsed in the  rest frame during its journey.
Neutrino mass is established.

13. ( ) Evidence For Flavor Change Neutrinos Evidence of Flavor Change
Solar
Reactor (L ~ 180 km)
Atmospheric
Accelerator (L = 250 km)
Stopped + Decay LSND L  30 m
Evidence of Flavor Change
Compelling
Strong
Unconfirmed ( )

14. Solar Neutrinos e e +  + 
Nuclear reactions in the core of the sun produce e. Only e.
Sudbury Neutrino Observatory (SNO) measures, for the high-energy part of the solar neutrino flux:
sol d  e p p  e
sol d   n p  e +  + 
From the two reactions,
e
e +  + 
——————— = ± (stat) ±0.024 (syst)
Clearly, +  ≠ Neutrinos do change flavor.

15. The now-established mechanism for solar e   /  is not oscillation in vacuum but the —
Large Mixing Angle —
Mikheyev Smirnov Wolfenstein
— Effect.
This effect occurs as the neutrinos stream outward through solar material. It requires both interactions with matter and neutrino mass and mixing.

16. Reactor (Anti)Neutrinos
The neutrino properties m2sol and sol implied by LMA-MSW 
KamLAND, ~ 180 km from reactor e sources, should see substantial disappearance of e flux.
KamLAND actually does see —
= ± 0.044(stat) ± 0.045(syst)
Reactor e do disappear.
Flavor change, with m2sol and sol in the LMA-MSW range, fits both the solar and reactor data.
e
e No disappearance

17. From
hep-ex/
Solar m2 and mixing angle from KamLAND analysis of KamLAND and solar neutrino data

18. Atmospheric Neutrinos
Detector 
Cosmic ray
Isotropy of the > 2 GeV cosmic rays + Gauss’ Law + No  disappearance
 ––––––– = 1 .
But Super-Kamiokande finds for E > 1.3 GeV
–––––––––––– = ± ~
 (Up)
 (Down)
 (Up)
 (Down)

19. Half of the upward-going, long-distance-traveling are disappearing.
Voluminous atmospheric neutrino data are well described by —
 
with —
1.9  < m2atm < 3.0  10-3 eV2
and —
sin2 2atm > 0.90
Super-K
90%CL ( )

20. z
(Super-K)

21. Accelerator - generated  also disappear (K2K)
KEK
Super – K 
250 km
Near
Detector
Expect
Observe 108
Common values of m2sol and sol describe both atmospheric and K2K data.

22. L(iquid) S(cintillator) N(eutrino) D(etector)
Unconfirmed   e signal e+
30m
  e
Detector
e
Confirmation of the LSND oscillation would imply the existence of a fourth neutrino species: the sterile neutrino.
Unlike e, , or , a sterile neutrino does not interact even weakly.

23. What Have We Learned ?

24. We do not know how many neutrino mass eigenstates there are.
There are at least 3.
If LSND is confirmed, there are more than 3.
4? 6? ?
If LSND is not confirmed, nature may contain only 3 neutrinos.
Then, from the existing data, the neutrino spectrum looks like —

25. sin2 13 Bounded by reactor exps. with L ~ 1 km
From max. atm. mixing,
From (Up) oscillate but (Down) don’t {
In LMA–MSW, Psol(ee) = e fraction of 2
From max. atm. mixing, 1+2 includes (–)/√2
From distortion of e(solar) and e (reactor) spectra 3
m2atm
(Mass)2 2 }
m2sol 1
e [|Uei|2]
[|Ui|2]
[|Ui|2]

26. The Mixing Matrix
The flavor content picture shows the |Ui|2, but not the signs or phases of the Ui.
Atmospheric
Cross-Mixing
Solar
cij  cos ij sij  sin ij
Majorana CP phases
12 ≈ sol ≈ 32°, 23 ≈ atm ≈ 35-55°, 13 < 15°
 would lead to P( ) ≠ P( ). CP
But note the crucial role of s13  sin 13. ~

27. What Would We Like To Find Out?

28. — The Future — Some of the Open Questions
How many neutrino species are there? Are there sterile neutrinos?
MiniBooNE will confirm or refute LSND.
What are the masses of the mass eigenstates i?
(Mass)2
m2atm
m2sol ?? 1 2
Flavor Change
Tritium Decay, Double  Decay Cosmology } 3
Is the spectral pattern or ?
 behavior in earth matter can distinguish.
How far above zero is the whole pattern??
( — )

29. Generically, SO(10) grand unified models predict .
is un-quark-like, and would probably involve a lepton symmetry with no quark analogue.

30. 0.04 eV < Mass[Heaviest i] < 0.23 eV
A Cosmic Connection
Cosmological Data + Cosmological Assumptions 
 mi < 0.71 eV .
95% CL Mass(i) Spergel et al.
If there are only 3 neutrinos,
0.04 eV < Mass[Heaviest i] < 0.23 eV
m2atm Cosmology ( ) ~

31. Does —
i = i (Majorana neutrinos) or
i ≠ i (Dirac neutrinos) ?
e+ ≠ e– since Charge(e+) = – Charge(e–).
But neutrinos may not carry any conserved charge-like quantum number.
A conserved Lepton Number L defined by— L() = L(l–) = –L() = –L(l+) = 1 may not exist.
If it does not, then nothing distinguishes i from i . We then have Majorana neutrinos.
Then we can have —

32. e+ e– i i W– W+
It is more practical to seek —
Neutrinoless Double Beta Decay [0] e– e– i i W– W–
Nucl
Nuclear Process
Nucl’
Observation would imply i = i , making the neutrinos very different from the charged leptons and quarks.

33. Do neutrino interactions violate CP?
Do the leptonic interactions, like the quark interactions, violate the fundamental symmetry of CP?
Is leptonic CP responsible for the
Matter antimatter
asymmetry of the universe?

34.  Is neutrino CP the reason we exist?
The universe contains Matter, but essentially no antimatter.
Good thing for us:
Poof!
Matter
Antimatter
This preponderance of Matter over antimatter could not have developed unless the two behave differently.
The observed difference between Quark and antiquark behavior, as described by the Standard Model, is inadequate.
Could the interactions of Matter and antimatter with neutrinos provide the crucial difference?

35. { } See-Saw Mechanism N There is a natural way in which they could.
The most popular theory of why neutrinos are so light is the —
See-Saw Mechanism {
Familiar light neutrino 
Very heavy neutrino } N
The heavy neutrinos N would have been made in the hot Big Bang.

36. The heavy neutrinos N, like the light ones , are Majorana particles
The heavy neutrinos N, like the light ones , are Majorana particles. Thus, an N can decay into e- or e+.
But if, in violation of CP, Matter and antimatter couple differently to these heavy neutrinos N, then we can have —
Probability [ N  e- + … ] ≠ Probability [ N  e+ + … ]
Matter antimatter
in the early universe.
This phenomenon (leptogenesis) would have led to a universe containing unequal amounts of leptonic Matter and antimatter.
SM sphaleron processes would then have converted some of the leptonic asymmetry into a baryon asymmetry.

37. We cannot repeat the early universe.
But we can lend credibility to the hypothesis of leptogenesis by showing that Matter and antimatter couple differently to the light neutrinos .
A neutrino flavor change involving Matter: e-  
Source
Detector
A neutrino flavor change involving antimatter: e+  
Source
Detector
If these two flavor changes have different probabilities, then quite likely so do —
N  e- + … and N  e+ + …

38. If N decays led to the present preponderance of Matter over antimatter, then we are all descendants of heavy neutrinos.

39. Conclusion
Wonderful experiments, involving the beautiful physics of flavor change, have led to the discovery of neutrino mass.
This discovery has raised very interesting questions that we must now try to answer.

40. Back Up Slides

41. From Ed
Kearns
From L/E
Atmospheric m2 and mixing angle from SuperKamiokande L/E analysis and full data set

42. } } Is the spectrum or m2sol m2atm m2atm m2sol (Mass)2 3 2 1 2
e [|Uei|2]
[|Ui|2]
 [|Ui|2]

43. { { Sign depends on character of spectrum
(—)
sin2 2M = sin2 213 / [sin2 213 + (cos 213 (+) x)2]
At superbeam energies,
sin2 2M = sin2 213 [ S ] .
Sign[m2( ) - m2( )]
At oscillation maximum,
P( e) >1 ;
P( e) <1 ;
30% ; E = 2 GeV (NOA) % ; E = 0.7 GeV (T2K)
(—) ~
E 6 GeV
(—) { {
The effect is

44. Why Many Theorists Think L Is Not Conserved
The Standard Model (SM) is defined by the fields it contains, its symmetries (notably Electroweak Isospin Invariance), and its renormalizability.
Anything allowed by the symmetries occurs.
The SM contains no R field, only L, and no  mass.
But now we know the neutrino has mass.
If we try to conserve L, we accommodate this mass by adding a Dirac, L - conserving, mass term: mDLR.
To do that, we had to add R to the SM.

45. Unlike L , R carries no Electroweak Isospin.
Thus, no SM symmetry prevents the occurrence of the Majorana mass term mMRc R.
This mass term causes   . It does not conserve L.
If L is not conserved, and neutrinos are their own antiparticles, then we can have

46. the i is emitted [RH + O{mi/E}LH]. Thus, Amp [i contribution]  mi In
SM vertex e– e– i i
Uei
Uei W– W–
Nucl
Nuclear Process
Nucl’
the i is emitted [RH + O{mi/E}LH].
Thus, Amp [i contribution]  mi
Amp[0]   miUei2 m i

47. 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.

48. In Pursuit of 13 How may 13 be measured?
Both CP violation and our ability to tell whether the spectrum is normal or inverted depend on 13.
How may 13 be measured?

49. } sin213 = Ue32 is the small e piece of 3.
m2atm
(Mass)2 2 }
m2sol 1
sin213 = Ue32 is the small e piece of 3.
3 is at one end of m2atm.
We need an experiment with L/E sensitive to m2atm, and involving e.

50. Possibilities Reactor e disappearance while traveling L ~ 1.5 km.
L/E ~ 500 km/GeV.
Accelerator   e while traveling L > Several hundred km. L/E ~ 400 km/GeV.