1. Search for Lepton-number Violating Processes
Pheno 2006
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2. Neutrinos are massive
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3. There are only three “active” light neutrinos
We also know
There are only three “active” light neutrinos
N = § 0.008, from Z pole at LEP-1.
Direct lab bound: m < 2.2 eV
from Tritium beta decay
 mi < 0.17 – 1 eV
from WMAP, SDSS (Ly spectra), SNIa.
The absence of neutrinoless double beta decay
bound on Majorana mass <m> ee < 1 eV
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4. Hierarchy – inverted or normal?
Absolute mass scale ?
Hierarchy – inverted or normal?
 m2a
 m2s m1 m2 m3
Normal
Inverted
Dirac or Majorana?
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7. Charged current and Neutral current
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8. L = 2 process  Majorana nature of neutrino
The transition rates are proportional to:
for light neutrino [1]
for intermediate mass neutrino [2]
for heavy neutrino [3] f1
f2’
f1’ f2
generic diagram
[1] AA, V Barger, T Han, Phys. Rev. D 71,
(2005) [arXiv:hep-ph/ ]
[2] AA, T Han, S Pascoli to appear
[3] T Han, B Zhang [arXiv:hep-ph/ ]
AA, T Han, S pascoli, B Zhang to appear
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9. Light (active) Majorana neutrinof1
f2’
f1’ f2
We have six effective neutrino masses
: 0 , rare meson decay :  decay
: - e+ conversion, rare meson decay :  decay
: rare meson decay : none
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10. Determination of effective neutrino masses
Parameter
Input
|ma2|
1.9£10-3 eV £10-3 eV2
|ms2|
90% CL m2s vs tan2s plot a
90% CL m2a vs sin22a plot s
90%CL m2s vs tan2s plot x
90% CL CHOOZ exclusion plot 
0 to 2 2 3 
0.42 eV at 95% CL
3 masses: m1, m2 and m3
 = m1 + m2 + m3 and
 m2a and  m2s
3 mixing angles: a, s and x
3 phases: , 2 and 3
AA, V Barger, T Han, Phys. Rev. D 71, (2005) [arXiv:hep-ph/ ]
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12. Neutrinoless Double Beta Decay (0)
Isotope
Half-life (yrs)
hmiee (eV)
Year
48Ca
> 1.4 £ 1022
<7.2 – 44.7
2004
76Ge
> 1.9 £ 1025
<0.35
2001
> 1.6 £ 1025
<0.33 – 1.35
2002
= 1.2 £ 1025
= 0.44
82Se
> 2.7 £ 1022
<5
1992
100Mo
> 5.5 £ 1022
<2.1
116Cd
> 1.7 £ 1023
<1.7
2003
128Te
> 7.7 £ 1024
<1.1 – 1.5
1993
130Te
> 5.5 £ 1023
<0.37 – 1.9
136Xe
> 4.4 £ 1023
<1.8 – 5.2
1998
150Nd
> 1.2 £ 1021
< 3.0
1997
(A,Z)
Nuclear Physics
(A,Z+2)
S.R. Elliott and J. Engel, J. Physics G30 (2004) R183, [arXiv:hep-ph/ ]
= 0.14 (0.06) eV
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13. Lepton Number Violating Tau Decays
Decay Mode
Bexp
- ! e+ - -
1.9 £ 10-6
12 TeV
- ! e+ - K-
2.1 £ 10-6
46 TeV
- ! e+ K- K-
3.8 £ 10-6
730 TeV
- ! + - -
3.4 £ 10-6
20 TeV
- ! + - K-
7.0 £ 10-6
100 TeV
- ! + K- K-
6.0 £ 10-6
1000 TeV
CLEO Collaboration, D.Bliss et al., Phys. Rev. D 57 (1998) 5903, [arXiv:hep-ex/ ]
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14. Rare Meson Decays Decay Mode Bexp TeV D+ ! K- e+ e+ 1.2 £ 10-4 1900
1.3 £ 10-5
670
D+ ! K- e+ +
1.3 £ 10-4
1500
Ds+ ! K- e+ e+
6.3 £ 10-4
990
Ds+ ! K- + +
150
Ds+ ! K- e+ +
6.8 £ 10-4
740
B+ ! K- e+ e+
1.0 £ 10-6
1300
B+ ! K- + +
1.8 £ 10-6
1800
B+ ! K- e+ +
2.0 £ 10-6
Decay Mode
Bexp
TeV
D+ ! - e+ e+
9.6 £ 10-5
320
D+ ! - + +
4.8 £ 10-6 76
D+ ! - e+ +
5.0 £ 10-5
170
Ds+ ! - e+ e+
6.9 £ 10-4
200
Ds+ ! - + +
2.9 £ 10-5 42
Ds+ ! - e+ +
7.3 £ 10-4
150
B+ ! - e+ e+
1.6 £ 10-6
420
B+ ! - + +
1.4 £ 10-6
400
B+ ! - e+ +
1.3 £ 10-6
270
K+ ! - e+ e+
6.4 £ 10-10
0.11
K+ ! - + +
3.0 £ 10-9
0.48
K+ ! - e+ +
5.0 £ 10-10
0.09
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15. Muon – Positron Conversion
(A,Z)
Nuclear Physics
(A,Z-2)
· 17(82) MeV
K. Zuber, [arXiv:hep-ph/ ]
SINDRUM II Collaboration, J. Kaulard et al., Phys. Lett. B 422 (1998) 334
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16. Summary 0 - - e+ conversion - ! e+ - - - ! + - -
Cosmo Bounds
Exp Bounds
Experiment
0.14 (0.06) eV
0.33 eV
0
17 MeV*
- - e+ conversion
12 TeV
- ! e+ - -
480 GeV
K+ ! - + +
19 TeV
- ! + - -
none
B- ! M- t+ t+
* 90 GeV from K+  - e+ +
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17. Intermediate mass Majorana neutrino *f1
f2’
f1’ f2
resonant enhancement, transition rates
tau decay, rare meson decay
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* AA, T Han and S Pascoli, to appear

18. Width of Intermediate mass Majorana neutrino
2 body decays :
CC decays 
NC decays 
3 body decays:
CC decays 
NC decays 
CC + NC decays  combination of CC + NC mixings
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19. 36 decay modes to look for lepton number violation !!!!
Parameters for MC sampling
mass of neutrino m4
resonant mass region
three mixings ~ 0 to 1
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25. Current bounds on sterile neutrino: peak searches accelerator searches
heavy atmospheric neutrinos
cosmology, BBN, WMAP
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26. It is of fundamental importance to verify Majorana nature of neutrinos
We look for genuine  L = 2 processes
For the three active ’s 0 is the best hope
For a sterile neutrino N (or 4)
Rare  and meson decays are sensitive to
140 MeV < m4 < 5 GeV, 10-9 < |V l4|2 < 10-2
Depending on the unknown mixing and mass 4 can show up in any channel
Other processes to look for
B+  e+ + M-, B+  + + M-, B+  + + M-
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27. Thank You !!!!!
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