1. On the Importance of Neutrino Mass
A. Para, Fermilab
Is it really important? Why? Who cares?
What is a Neutrino ?
What is Mass ?
Keys to the Puzzle ?
More questions than answers..

2. 11 Greatest Unanswered Questions of Physics
What is dark matter ?
What is dark energy ?
How were the elements from iron to uranium made?
Do neutrinos have mass ? …
Are protons unstable ?
What is gravity ?
Are there additional dimensions ?
How did the Universe begin ?
Discover February 2002

3. Particle Physics at the End of the XX Century:Theory of Matter and Forces
Periodic table of elementary particles

4. Expanding our Ignorance: Composition of the Universe
65+-10% Dark(vacuum) energy
30+-7% Dark matter
% Ordinary matter
0.5% Stars
0.5% Neutrinos
0.02% C,N,O,…,Fe,…
Unknown, not understood
Known, poorly understood
“Us”
N(n) >~109N(protons, neutrons, electrons)

5. Theory of Matter and Forces: the Right-handed Stuff?
Right-handed SU(2) singlets
No neutrinos!
Do not participate in weak interactions, we know of their existence because of their strong/electromagnetic interactions
Left-handed SU(2) doublets
Quark <-> lepton symmetry (anomaly free)

6. Quarks and charged leptons
Neutrinos are special
Neutrinos
Members of SU(2) doublets (left-handed), no singlets
Electric charge = 0
obey Dirac equation? Majorana equation?
Do have anitparticles? Are self-conjugate?
Magnetic moments?
Sterile neutrinos?
Quarks and charged leptons
members of SU(2) doublets (left-handed) and singlets (right handed)
Electric charges 1/3, 2/3, 1
4-component Dirac spinors
Have antiparticles distinct from particles
Are these facts/questions related?

7. Enigma of Masses of Elementary Particles
Masses of all charged fermions within a given generation are the same within a factor of 10
Masses of neutrinos are a factor ~109 smaller
Why ??? What makes masses so different?
Notice: if mn~me we would not be here to ask such questions !

8. The meaning of Mass: A Worldline of a Massive Particle in its Rest Frame
Q(t) is a spinor of a massless particle with momentum t
R.H.
L.H.

9. A Massive Particle in its Rest Frame
What are R,L ? R L
Interaction with vacuum changes left-handed particle into right-handed one
Electron case
L = left handed electron
R = right handed electron (not positron! Because of charge conservation)
Neutrino case
L = left handed neutrino
R = right handed antineutrino??
right handed neutrino??

10. CPT transformation of a spinorfL C f P f
CPT Invariance implies:
fL fR T fR

11. From Schrodinger to Dirac
Non-relativistic
Schrodinger
Klein-Gordon
Non-positive probabibility
Dirac
Square root of K-G

12. g matrices, Weyl representation

13. The ‘other’ square root
Majorana
Which equation describes neutrino? Dirac? Majorana?
This question arises only for neutral fermions

14. Dirac neutrino vs Majorana neutrino
Lorentz
Boost,
E, B C P T C P T

15. A General Lagrangian (Neutral Fermions)
Left, right handed fields

16. The physical states are eigenstates of the mass matrix
See-saw mechanism
The physical states are eigenstates of the mass matrix
Let all fermions have the same Dirac mass MD (~ mq or ml), ML=0 if MR>>MD than mn<<ml
Is neutrino a Majorana particle?
Is a very heavy Majorana mass an explanation for the smallness of the observed mass eigenstate? Are we witnessing a first sign of the physics at very high energies?

17. Neutrino Masses: a Key to the Mass Generation Mechanism?
Possible examples:
m1 : m2 : m3 = mu2 : mc2 : mt2
mn ~ mq2/Mx
See-saw mechanism for Majorana neutrinos
New interactions at the scale Mx
m1 : m2 : m3 = mu : mc : mt
mn ~ mq
Top members of weak doublets couple to the same Higgs field
m1 : m2 : m3 = me : mm : mt
mn ~ ml
‘Leptonic’ Higgs generates mass of leptons

18. Direct measurements of neutrino mass
Techniques
time of flight (SN1987a)
particle decay kinematics
beta decay spectrum shape (ne)
muon momentum in pion decay (nm)
invariant mass studies of multiparticle semileptonic decays (nt)
Advantages
sensitive to absolute mass scale
purely kinematical observables
no assumptions about n properties

19. Neutrino Masses: Experimental Progress
J. Wilkerson
points without error bars represent upper limits
note: different scale for different neutrinos types

20. Tritium beta decay spectrum
n p+e-+ne

21. Two leading experiments: Troitsk and Mainz

22. Breakthrough technique: MAC-E-Filter
Magnetic Adiabatic Collimation followed by Electrostatic Filter
Integrating high pass filter: high intensity
Large acceptance ~ 2p
High resolution,
DE~2-6 eV at E=20 keV
Developed specifically for tritium beta decay experiments

23. New Twist: Neutrino Mixing (SuperK 1997)
Weak eigenstates are mixtures of mass eigenstates
Large mixing angle q12 ~ 35o
Large mixing angle q23 ~ 45o
Mixing angle q13 ~ small

24. What is an electron neutrino?p
Electron (muon,tau) neutrino is not a mass eigenstate
Electron (muon, tau) neutrino is a coherent mixture of mass eigenstates e n ne
What do neutrino mass experiments measure?

25. b-decay spectrum and neutrino mixing
The beta spectrum shape depends on:
the neutrino masses
the number of neutrino mass eigenstates
the leptonic mixing matrix elements
An “effective mass” : mb 2 = S |Uei |2 mni 2

26. Neutrino Oscillations: Tool for Measuring Mass Differences
If neutrinos have mass, then it is likely that flavor and mass eigenstates are different  Neutrino Oscillations
Example: two families of neutrinos
Amplitude
Oscillation frequency

27. Neutrino Interferometry, or How do Neutrinos Oscillate?
Components of the initial state have different time evolution => Y(t)  Y(0)
Amplitude
Amplitude
3-slit interference Experiment: mass difference  difference in optical path length

28. Oscillation Probability
where

29. Neutrino Oscillations Primer
if all masses are equal i.e Neutrino oscillations are sensitive to mass differences only.
oscillates as a function of L/E
for Appearance experiment.
: disappearance experiment
:total number of neutrinos is conserved
If Uai is complex then hence T (or CP) violation

30. Neutrino Oscillations
Disappearance experiment:
Start with neutrinos of type x (say nm), detect the flux at a distance L, Fnm(L)< Fnm(0)
Appearance experiment:
Start with neutrinos of type x (say nm), detect the neutrinos of type y (say nt), at a distance L
Does really happen?

31. How does the Sun ‘work’? (H. Bethe)
Solar model
Tiny fraction

32. Detecting Solar Neutrinos
SuperKamiokande:
Electron neutrino scatters elastically of an atomic electron
Scattered electrons follow the direction of the incoming neutrino
R. Davis, Homestake:
680 ton of CCl4
~ 15 atoms of 37Ar produced per month !!!

33. Solar Neutrino Results (~1999)
Only about 50% of the predicted flux is detected
Solar neutrino ‘problem’

34. n Reactions in heavy water (SNO)
ne + d ® p + p + e Ethres= 1.4 MeV
Charged Current Reaction:
• 6-9 events per day
• ne flux and energy spectrum
• Some directional sensitivity (1 - 1/3cosqe)
 ne: (15) x 106 cm-2 s-1
nSSM: x 106 cm-2 s-1
Elastic Scattering Reaction:
• events per day
• Directional sensitivity (very forward peaked) CC ne e- W n p
nx + e- ® nx + e Ethres = 0 MeV ES
nmt: 3.69(113) x 106 cm-2 s-1
ntotal: 5.44(99) x 106 cm-2 s-1 ne ne ne n e- n W Z W e- e- e- ne e- e-

35. KamLAND: the ultimate proof of solar neutrino oscillations

36. Disappearing electron antineutrinos
Reactor neutrinos (== electron antineutrinos!!) disappear at distances ~ 100 km
consistent with solar neutrino experiment
Dm2 ~ 1-14 x 10-5 eV2
Solar neutrino problem no longer a problem
Neutrinos oscillate

37. Atmospheric Neutrinos
SuperK n
Earth

38. Results from Super-K Experiment
nm flux reduced by about 50% for long flight path
if it is a result of the neutrino oscillations, then :
the dominant mode is nm to nt
mixing angle is very large
Dm2 :

39. Long Baseline Neutrino Oscillation Exp’s
Reproduce atmospheric effect using accelerator produced n-beam
K2K (KEK to SuperK) L = 250 km Now
MINOS (Fermilab to Minnesota)
L = 730 km 2003
CNGS (Cern to Gran Sasso, Italy) L = 750 km 2005?

40. Oscillation Experiment
The MINOS Beamline
Two Detector Neutrino
Oscillation Experiment
(Start 2005)
Far Detector (5.4 ktons) :
- 8m diameter by 1” steel plates
- 4cm wide solid scintillator strips
- Steel magnetized at 1.5 T
Det. 2
Det. 1

41. Do Neutrinos Oscillate? Decay? Travel in Extra Dimensions
Expected event spectrum
Observed (perhaps?) event spectrum
Observed energy distribution of nm CC interactions provide a measure of the nm survival probability as a function of En

42. Three outstanding questions ~ 2003
Neutrino mass pattern: This ? Or that?
Electron component of n3 (sin22q13)
Complex phase of s  CP violation in a neutrino sector  (?) baryon number of the universe

43. The key: nm  ne oscillation experiment
A. Cervera et al., Nuclear Physics B 579 (2000) 17 – 55, expansion to second order in

44. Neutrino Propagation in Matter
Matter effects reduce mass of ne and increase mass of ne
Matter effects increase Dm223 for normal hierarchy and reduce Dm223 for inverted hierarchy

45. Anatomy of Bi-probability ellipses
Minakata and Nunokawa, hep-ph/
~cosd
Observables are: P
Interpretation in terms of sin22q13, d and sign of Dm223 depends on the value of these parameters and on the conditions of the experiment: L and E d
~sind
sin22q13

46. NuMI Beam + Off-axis Detector(s)
Search for nm to ne transition
Measure mixing angle sin22q13
Search for CP violation in a neutrino sector

47. How about the nature of neutrino?
Dirac or Majorana particle?
Does it have a distinct antiparticle?
Is it its own antiparticle?

48. Masses of Nuclei: even A Case
Lowest energy state reachable only through two simultaneous weak beta decays  very low rate, very long lifetimes (exceeding age of the Universe)

49. Neutrinoless Double b decay: Key to the Nature of the Neutrino
Two beta decays
If (neutrino=antineutrino)
{they can ‘annihilate’
each other}
Process allowed only for a Majorana neutrino

50. Electron Spectrum From Double b Decay: from Theory to Practice
Energy resolution
High rates capabilities

51. Double Beta Decay Experiments: Results
Isotope
Experiment
48Ca
HEP Beijing
>1.1x1022*
23-50
76Ge
Heidelberg-Moscow
>5.7x1025
2-8
IGEX
>0.8x1025
82Se
Irvine
>2.7x1022
4-14
NEMO 2
>9.5x1021
96Zr
>1.3x1021
100Mo
LBL
>2.2x1022*
3-111
UCI
>2.6x1021
Osaka
5.5x1022 2
NEMO2
>5x1021
130Te
Milano
>1.4x1023
2-5
136Xe
Caltech/PSI/Neuchatel
>4.4x1023
150Nd
>1.2x1021
5-6
Germanium
diode cal.
Te02 cryo calorim.
Xe TPC

52. What do 0nbb Experiments Measure?
Where:
a phase space factor
a nuclear matrix element (QRPA, NSM,..)
If CP is conserved
Majorana phases

53. The quest for 20-50 meV sensitivity
CUORE – 210 kg of 130Te, Grand Sasso
EXO - (liguid or gaseous) 136Xe WIPP? Homestake?
GENIUS - 1t of enriched 76Ge in liquid N2 shield
MAJORANA – 500 kg of enriched segmented 76Ge detectors
MOON – thin foils of (enriched?) 100 Mo Homestake? Japan?
Large mass of the source material, enriched if possible
Innovative background suppression
Intermediate steps

54. Large scale clusters
Large scale structures originate from fluctuations of the primordial mass/energy distribution
Significant contribution of the mass/energy in a form of fast moving neutrinos would tend to wash out fluctuations

55. Weighing Neutrinos with Galaxy Surveys
Large scale cluster formation
Fraction of energy in neutrinos
Sloan Sky Survey of Bright Red Galaxies
W. Hu, D.J. Eisenstein, M. Tegmark, PRL80, p5255, 1998

56. The pattern and absolute scale of n masses
Key issues in particle physics
hierarchical or degenerate neutrino mass spectrum
understanding the scale of new physics beyond SM
potential insight into origin of fermion masses
Nature of the neutrino
Cosmology and astrophysics connection
early universe, relic neutrinos (HDM), structure formation, anisotropies of CMBR
supernovae, r-process, origin of elements
potential influence on UHE cosmic rays

57. (Instead of) Conclusions
We are living in interesting times.
It is fun to study neutrinos

58. Stellar Evolution

59. Supernova Explosion

60. Supernova 1987A
February 1984
March 8,1987
Seven years later..

61. Supernova as a Neutrino Laboratory (Examples)
Neutrino mass:
If neutrinos have mass m then neutrinos with different energies will travel with different speed. Difference of arrival time of neutrinos with energy E1 and E2:
Neutrino lifetime:
Neutrinos come from a distance L. Their lifetime must be such, that:
SN1987A: mn<15 eV
SN1987A:
tn>5x1012 s

62. Neutrinos from Supernova 1987A
Energy spectrum of neutrinos
total energy radiated (1.4 solar masses)
size of the resulting neutron star (15 km)

63. Dec 1930: A Desperate Remedy
“I have done something very bad today by proposing a particle that cannot be detected; it is something no theorist should ever do.”
W. Pauli

64. Weak Interactions
Current-current interaction :Fermi Paper rejected by ‘Nature’ because “it contained speculations too remote from reality to be of interest to the reader”
Modern version:
is a projection operator onto left-handed states for fermions and right-handed states for antifermions
Only left handed ferminos and right handed anti-fermions participate in weak interactions: Parity violation

65. Reines and Cowan: an Audacious Proposal (1946)
Nuclear reactor will do the same
1956, Savannah River:”We are happy to inform you (Pauli) that we have definitely detected neutrinos…”
1995 Nobel Prize for Reines

66. How Many Neutrinos?

67. Energy Spectrum of Solar Neutrinos
Two body reaction: line
Three body decay: phase space, like muon decay spectrum

68. Neutrino survival probability
Small Mixing
P(ne → ne)
Large Mixing
Night
Distortion of the observed energy spectrum differentiates between different oscillations scenarios
Day
LOW
Just-so
En (MeV)