1. Neutrino Masses, Leptogenesis and Beyond
The Incredible Foresight of
ETTORE MAJORANA
Haim Harari
Erice, September 1, 2006

2. neutrino from an anti-neutrino? n may be its own antiparticle !
The Foresight
Can you tell a
neutrino from an anti-neutrino?
MAJORANA
n may be its own antiparticle !

3. Is n Massless or Very Light ? “Direct” experiments m (ne) < few eV
Theory
No good reason for massless n.
Simple argument for very light n.
n is the only “chargeless” particle.
All quarks and leptons  “Dirac Mass”
n  also “Majorana Mass”

4. Is n Massless or Very Light ?m L
M1 ~ O(L)
M2 ~ O(m2/L)
“See-Saw” L m n
Majorana
Mass
Gell-Mann, Ramond, Slansky, Yanagida

5. Mikheyev-Smirnov-Wolfenstein
Solar Neutrinos
The sun emits 1038 n per second.
1029 go to direction earth.
Per 100 ton detector hits per month
Homestake
n + Cl37  e + A37
400 ton C2Cl4
Mikheyev-Smirnov-Wolfenstein

7. Kamiokande Super - Kamiokande
n + n e + p
50,000 ton/clean water

10. GALLEX
n + Ga e + Ge71
30 ton

14. GALLEX n + Ga71 e + Ge71 SNO 30 ton
1000 ton D2O (+2 ton Salt) 10,000 phototubes
ne + d e + p + p (charged Current)
nx + d nx + p + n (Neutral Current)
nx + e nx + e (Elastic Scattering)
Count total n – flux and ne - flux

20. m(nm) ~ 8 meV q12 Large Solar Model is Right! Neutrinos Oscillate
Neutrinos have Mass
m(nm) ~ 8 meV
q12 Large

21. Kamland – Japan R R R R KAM L ~ 180 km E ~ O (MeV)
Probe: ∆m2<<eV2

24. Cosmic Radiation p p m e ne nm nm atmosphere earth m (nt) ~ 50 meV
Energetic protons arrive p
Pions created in atmosphere
In p-decay: N(nm)
N(ne)
atmosphere p
= 2 m e
= 1.2 !!!
KAMIOKANDE:
N(nm)
N(ne)
m (nt) ~ 50 meV ne nm nm
earth

25. The Universe m(nt) ~ 50 meV m(nm) ~ 8 meV m(ne) ~ smaller
70% Dark Energy
25% Dark Matter
4% H, He
0.5% Heavy Nuclei
0.5% Neutrinos
m(nt) ~ 50 meV
m(nm) ~ 8 meV
m(ne) ~ smaller
Large angles!
Also K2K, MINOS, others

26. ( ) ( ) ( ) ( ) ( ) ( ) u d c s t b “The Standard Model” ne e nm m nt
Generation
1st
2nd
3rd Q u c t
2/3 d s b
Quarks
-1/3
ne?
nm?
nt? e m t
Leptons -1 -6 -5 -4 -2 -3 -1 -0 1 2 3 4 5 6 7 8 9 10 11 12
meV eV
MeV
keV
GeV
TeV ( ) ( ) ( ) u d c s t b
“The Standard Model” ( ne e ) ( nm m ) ( nt t )

27. ( ) ( ) ( ) ( ) ( ) ( ) u d c s t b “The Standard Model” ne e nm m nt
Generation
1st
2nd
3rd Q u c t
2/3 d s b
Quarks
-1/3 nm nt
ne? e m t
Leptons -1 -6 -5 -4 -2 -3 -1 -0 1 2 3 4 5 6 7 8 9 10 11 12
meV eV
MeV
keV
GeV
TeV ( ) ( ) ( ) u d c s t b
“The Standard Model” ( ne e ) ( nm m ) ( nt t )

28. WHEN AND HOW DID IT HAPPEN?
Why are we here?
B-Violation (also L-Violation)
CP-Violation
Non-equilibrium (also no “wash-out”)
Sakharov-1967
B-Violation (and L-Violation)
p-decay
GUT scale or higher
Not seen (but SN87A!)
n-oscillations and mass
CP-Violation
KM phase for quarks (requires 3 generations)
CP-violation in leptons (requires 2 generations)
WHEN AND HOW DID IT HAPPEN?

29. At Big Bang: B=0 , L=0 (also B-L=0)
Why are we here?
At Big Bang: B=0 , L= (also B-L=0)
We need to create a nonzero B (also B-L?)
“Leptogenesis” (other theories: GUT, electroweak) :
If we could create a nonzero L
and then trade B for L,
we could create a positive B.
IT IS NOT ENOUGH TO TRADE B for L
WE MUST ALSO CREATE B-L

30. (qiqjqk) (qiqjqk) (qiqjqk) (ℓiℓjℓk)
B and L violation in the standard model (but no B-L)
(qiqjqk) (qiqjqk) (qiqjqk) (ℓiℓjℓk)
“instanton” terms:
i,j,k = generations
“SPHALERON”: Connecting degenerate ground states
L and B can change (together)
each by 3 UNITS (for Ng = 3)
B – L is conserved (and must be nonzero)
B + L is violated e.g. D(B + L) = 6 is allowed
THE STANDARD MODEL CREATES (together) B AND L

31. Neutrino oscillations  m(n) ≠ 0, very small
The universe is made of
QUARKS and LEPTONS
Note:
↔ n
is possible u d n e- d u e+ n
Neutrino oscillations  m(n) ≠ 0, very small 
m(n) ~ m2 M
Seesaw mechanism:
0 m
m M
L=0 AT BIG BANG
BUT DL ≠ 0 PROCESSES ARE ABUNDANT !
<nn> ≠ 0, n-n mixing, heavy neutrino with mass M
Hence: n is a Majorana neutrino

32. NEUTRINO COGITO ERGO SUM LEPTOGENESIS At Big Bang: B = L = 0.
Majorana: DL≠0 and D(B-L)≠0 are allowed.
Hence, the universe has L≠0 and B-L≠ 0 .
LEADING TO B≠0 !!!
(Elaborate quantitative estimates).
e.g. Buchmueller-Peccei-Yanagida
The particle, which is its own antiparticle,
is responsible for having
more particles than antiparticles in the universe
NEUTRINO
COGITO
ERGO SUM

33. Perhaps it all happens at the subparticle level !? Warning
And in 2056 – for Majorana’s 150th birthday .
Perhaps it all happens
at the subparticle level !?
Warning
No evidence for
subquarks and subleptons.
No reasonable dynamical theory

34. The Quark - Lepton Connection
Why q and ℓ have simple charge ratios?
(0, -1)
( +2/3, -1/3 )
Why p and e+ have same charge?
Why SQi = 0 for q’s and ℓ’s in one generation?
[ SQi = (-1) + (0) + 3(+2/3) +3(-1/3) = 0 ]
Why three colors and three generations?
PREONS?
TOY MODELS?

35. Rishons HH+Seiberg Anomaly cancellation: NH = NC = NG = 3 n SU(3)HQ
SU(3) H C N
3(B-L) T V T V
+ 1/3 3 1 -1 T V 3
- 1/3 -1 1
“Matter” e+ u d n
TTT
TTV
TVV
VVV
(+1)
(+2/3)
(+1/3)
(0) 1 3
color
“Antimatter”
VVV
VVT
VTT
TTT n d u e-
(0)
(- 1/3)
(- 2/3)
(-1) 1 3
color
SU(3)H
Singlets
e+ TTT
p TTT(TT)(VV)(VV)
e- TTT
p TTT(TT)(VV)(VV)
Anomaly cancellation: NH = NC = NG = 3
Buchmann+Schmid

36. <VVVVVV>≠0 ERGO SUM
HH+Seiberg
Rishons Q
SU(3) H C N
3(B-L) T V T V
+ 1/3 3 1 -1 T V 3
- 1/3 -1 1
“Matter” e+ u d n
TTT
TTV
TVV
VVV
(+1)
(+2/3)
(+1/3)
(0) 1 3
color
“Antimatter”
VVV
VVT
VTT
TTT n d u e-
(0)
(- 1/3)
(- 2/3)
(-1) 1 3
color
SU(3)H
Singlets
TO BREAK B-L WE NEED TO BREAK N
Simplest J=0, Q=0, SU(3)H – singlet, SU(3)C – singlet
IS <VVVVVV> : BREAKS L, HENCE CREATES B V
<VVVVVV>≠0 ERGO SUM

37. n in Nucleosynthesis  - Less Double -Decay n - Decays
Measuring Masses and Angles
Clues for Theory “Beyond the Standard Model”
Neutrino Astronomy
UHE Cosmic Neutrinos
Dark Matter
Z nn
n in Nucleosynthesis
 - Less Double -Decay
n - Decays
n - Magnetic Moments
Heavy n
Sterile n

38. Neutrino Masses, Leptogenesis and Beyond
ETTORE MAJORANA
WAS NO FOOL
WAS BRILLIANT !!!