1. Neutrino masses Determination of absolute mass scale with beta decays:
single beta decays: energy spectra
search for neutrinoless double beta decays
The latter is extremely important in order to understand the Universe and sources of particle masses

2. Neutrino (mass)2 spectrum} or
Normal
Inverted
From neutrinos... DK&ER lecture11

3. Various and complementary ways to measure neutrino mass
Cosmology
Oscillation
Beta decay
wzory z PDG2008
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4. Three roads to neutrino masses

5. Direct measurements of neutrino masses
νe: tritium β decay
νμ: π decay
ντ: τ decay
Information from the end of the energy spectrum.
„Mass” of flavor α – combination of mass states.
Very high precision of measurements needed.
Up to now only limits.
From neutrinos... DK&ER lecture11

6. β-decay and neutrino mass
Model independent neutrino mass from ß-decay kinematics
experimental observable is mν2
ß-source requirements :
high ß-decay rate (short t1/2)
low ß-endpoint energy E0
superallowed ß-transition
few inelastic scatters of ß‘s
ß-detection requirements :
- high resolution (ΔE< few eV)
- large solid angle
- low background
E0 = 18.6 keV
T1/2 = 12.3 y

7. History of tritium measurements
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8. Electrostatic filter with magnetic adiabatic collimation
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9. Status of previous tritium measurements
Mainz & Troitsk have reached their intrinsic limit of sensitivity
Troitsk Mainz
windowless gaseous T2 source quench condensed solid T2 source
analysis 1994 to 1999, analysis 1998/99, 2001/02
both experiments now used for systematic investigations
From neutrinos... DK&ER lecture11

10. Designing a next-generation experiment
experimental observable in ß-decay is mν2
aim : improve mν by one order of magnitude (2 eV  0.2 eV )
requires : improve mν by two orders of magnitude (4 eV2  0.04 eV2 )
problem : count rate close to ß-end point drops very fast (~δE3)
improve statistics :
stronger tritium source (factor 80) (& large analysing plane, Ø=10m)
- longer measuring period (~100 days  ~1000 days)
improve energy resolution :
large electrostatic spectrometer with ΔE=0.93 eV (factor 4 improvement)
reduce systematic errors :
- better control of systematics, energy losses (reduce to less than 1/10) 2
L=23 m
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11. From neutrinos... DK&ER lecture11
Katrin
From neutrinos... DK&ER lecture11
KATRIN will reach a final sensitivity of 200 meV at 90\% C.L. on the absolute neutrino mass scale.

12. From neutrinos... DK&ER lecture11
KATRIN experiment
Karlsruhe Tritium Neutrino
Experiment
at Forschungszentrum Karlsruhe
unique facility for closed T2 cycle:
Tritium Laboratory Karlsruhe
TLK
~ 75 m linear setup with 40 s.c. solenoids
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13. From neutrinos... DK&ER lecture11
Transport of KATRIN
Complicated transport of the spectrometer in Dec. 2006
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14. From neutrinos... DK&ER lecture11
KATRIN sensitivity
sensitivity optimisation: LoI (2001)  reference design (2004)
improved statistics: source luminosity, scanning
reduced systematics: ß-energy losses in source
improved sensitivity
sensitivity (90% CL)
m(ν) < 0.2 eV
discovery potential
m(ν) = 0.35 eV (5σ)
From neutrinos... DK&ER lecture11

15. Search for neutrinoless double beta decays
Why so important?
What it would tell us (if seen)?
Reminder:
Leptons are (mostly) left handed
Anti-leptons are (mostly) right handed
Contribution of states with
„wrong helicity” is proportional to:
 for m=0 particle – no such
contribution
From neutrinos... DK&ER lecture11

16. Dirac neutrino vs Majorana neutrino
Majorana particles
Special case: particle is it’s own
anti-particle
Dirac particles
Lorentz
Boost,
E, B C P T C P T
only neutral particles
are candidates for beeing
Majorana particle
Example of such is π0
Spinor is fermion representation
(in Dirac equation)
For particles with m=0 reduces to
2 non-zero states

17. From neutrinos... DK&ER lecture11
Double beta decays
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18. Double Beta Decay Candidates
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19. Phenomenology of 0νββ and 2νββ
pairing interaction between nucleons (even-even nuclei more bound than the odd-odd nuclei)
e.g. 136Xe and 136Ce are stable against β decay, but unstable against ββ decay (β-β- for 136Xe and β+β+ for 136Ce)
odd-odd
Even-even – parzysto-parzyste
Odd-odd = nieparzysto-nieparzyste
even-even
m(A,Z) > m(A,Z+2)

20. Phenomenology of 0νββ and 2νββ
Phase space
(very well known)
Nuclear matrix element (NME)
(challenging to calculate)

21. Pontecorvo – Maki – Nakagawa - Sakata (PMNS) matrix
Neutrino mixing and oscillations
Pontecorvo – Maki – Nakagawa - Sakata (PMNS) matrix
eigenstates
weak
eigenstates
mass
3 mixing angles + 1 phase
Majorana
Phases
only 0νββ
Solar
Atmospheric
Reactor
Atmospheric

22. Candidate Nuclei for Double Beta Decay
Q (MeV) Abundance(%)
48Ca→48Ti
4.271
0.187
76Ge→76Se
2.040
7.8
82Se→82Kr
2.995
9.2
96Zr→96Mo
3.350
2.8
100Mo→100Ru
3.034
9.6
110Pd→110Cd
2.013
11.8
116Cd→116Sn
2.802
7.5
124Sn→124Te
2.228
5.64
130Te→130Xe
2.533
34.5
136Xe→136Ba
2.479
8.9
150Nd→150Sm
3.367
5.6
From neutrinos... DK&ER lecture11

23. Electron spectrum from double β decays
Missing energy
Energy resolution
High rates capabilities
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24. From neutrinos... DK&ER lecture11
ββ history
ββ(2ν) rate first calculated by Maria Goeppert-Mayer
Majorana proposes his theory of two-component neutrino
1987 – Direct laboratory evidence for 2νββ:
S. Elliot et al., Phys. Rev. Lett. 59, 2020, 1987
Direct evidence for two-neutrino double-beta decay in 82Se
Why it took so long? Background
t1/2(U, Th) ~ 1010 years
while signal: t1/2(2νββ) ~ 1020 years
But next we want to look for a process with:
t1/2(0νββ) ~ years
From neutrinos... DK&ER lecture11

25. From neutrinos... DK&ER lecture11
ββ history
2004 – controversial claim of observation of 0νββ:
From neutrinos... DK&ER lecture11

26. From neutrinos... DK&ER lecture11

27. Experiments with active targets
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28. From neutrinos... DK&ER lecture11
76Ge spectrum
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29. From neutrinos... DK&ER lecture11
76Ge spectrum with a possible 0νββ peak
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30. 76Ge spectrum with a possible 0νββ peak
Exposure
(total):
71.7 kg.y
Clearly this needs to be verified...

31. New experiment with Ge: GERDA
To check the questionable result – new experiment with Ge is prepared GERDA (with contribution from Jagiellonian Uniw.), the background reduction will be better …
Uzywaja detektorow germanowych Klapdora

32. Tracking and calorimeter
Experimental techniques
Calorimeter
Source=detector
Resolution, efficiency
Background, isotope choice
Tracking and calorimeter
Source ≠ detector
TPC (Xe)
Efficiency, Mass
Main features:
High energy resolution
Modest background rejection
Main features:
High background rejection
Modest energy resolution
0νββ
0νββ
F. Piquemal (CENBG) LP07

33. Separation of 0νββ from 2νββ
0nbb spectrum
(5% FWHM)
(normalized to 10-6)
2νββ spectrum
(normalized to 1)
E1 + E2 (normalized to Qββ)
Energy resolution is essential
0νββ spectrum
(5% FWHM)
(normalized to 10-2)
F. T. Avignone, G. S. King and Yu. G. Zdesenko,
``Next generation double-beta decay experiments:
Metrics for their evaluation,’’ New J. Phys. 7, 6 (2005).
from S. Elliott and P. Vogel

34. Fréjus Underground Laboratory :
NEMO-3 detector
Fréjus Underground Laboratory :
4800 m.w.e.
3 m
4 m
B (25 G)
20 sectors
Source: 10 kg of ββ isotopic foils
area = 20 m2, thickness ~ 60 mg/cm2
Tracking detector:
drift wire chamber operating (9 layers)
in Geiger mode (6180 cells)
Gas: He + 4% ethyl alcohol + 1% Ar + 0.1% H2O
Calorimeter:
1940 plastic scintillators
coupled to low radioactivity PMTs
Magnetic field: 25 Gauss
Gamma shield: pure iron (d = 18cm)
Neutron shield: 30 cm water (ext. wall)
40 cm wood (top and bottom)
(since March 2004: water + boron)
Particle ID: e-, e+, γ and α

35. Fréjus Underground Laboratory : 4800 m.w.e.
NEMO-3 detector
Fréjus Underground Laboratory : 4800 m.w.e.
Source: 10 kg of isotopic foils
area = 20 m2, thickness ~ 60 mg/cm2
Tracking detector:
drift wire chamber operating (9 layers)
in Geiger mode (6180 cells)
Gas: He + 4% ethyl alcohol + 1% Ar + 0.1% H2O
Calorimeter:
1940 plastic scintillators
coupled to low radioactivity PMTs
Magnetic field: 25 Gauss
Gamma shield: pure iron (d = 18cm)
Neutron shield: 30 cm water (ext. wall)
40 cm wood (top and bottom)
(since March 2004:
water + boron)

36. ββ decay isotopes NEMO-3
ββ2ν measurement
116Cd g
Qbb = keV
96Zr g
Qbb = 3350 keV
150Nd g
Qbb = keV
48Ca g
Qbb = 4272 keV
130Te g
Qbb = 2529 keV
External bkg
measurement
100Mo kg
Qbb = 3034 keV
82Se kg
Qbb = 2995 keV
natTe g
Cu g
ββ0ν search
(All enriched isotopes produced in Russia)

37. Cathod rings Wire chamber Calibration tube bb isotope foils PMTs
scintillators
bb isotope foils

38. ββ events in NEMO-3 experiment
Typical ββ2ν event observed from 100Mo
Top view
Side view
From neutrinos... DK&ER lecture11

39. During installation AUGUST 2001

40. Laboratoire Souterrain de Modane
4700 m.w.e
COMMISSARIAT À L’ÉNERGIE ATOMIQUE
DIRECTION DES SCIENCES DE LA MATIÈRE
Built for taup experiment (proton decay) in

41. From neutrinos... DK&ER lecture11
100Mo ββ2ν results
(Data Feb – Dec. 2004)
Sum Energy Spectrum
Angular Distribution
events
6914 g
389 days
S/B = 40
events
6914 g
389 days
S/B = 40
NEMO-3
NEMO-3
100Mo
100Mo
Data
Data
ββ2ν
Monte Carlo
ββ2ν
Monte Carlo
Background
subtracted
Background
subtracted
E1 + E2 (keV)
Cos(ϑ)
7.37 kg.y
T1/2 = 7.11 ± 0.02 (stat) ± 0.54 (syst) x 1018 y
From neutrinos... DK&ER lecture11

42. Other results from NEMO-3: 2νββ
454 g,
534 days
109 events
S/B = 0.25
130Te
NEMO-3
NEMO-3
932 g,
389 days
2750 events
S/B = 4
82Se
E1 + E2 (MeV)
9.6 ± 0.3 (stat) ± 1.0 (sys) 1019 y
2.8 ± 0.1 (stat) ± 0.3 (sys) 1019 y
7.6 ± 1.5 (stat) ± 0.8 (sys) 1020 y
133 events
S/B 6.76
48Ca
96Zr
150Nd
948 days 7g
925 days
S/B 1.01
9.41g
E1 + E2 (MeV)
(stat) ± 0.63 (sys) 1018 y
2.3 ± 0.2 (stat) ± 0.3 (sys) 1019 y
(stat)± 0.4 (sys) y

43. Results for 2β0ν searches
Upper limits
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
From neutrinos... DK&ER lecture11

44. From Elliot and Vogel, hep-ph/0202264
Neutrinoless ββ-decay limits
From Elliot and Vogel, hep-ph/
From neutrinos... DK&ER lecture11

45. Neutrino mass and mass ordering
Quasi
Degenerate
Inverted
Normal
Mass ordering – kolejnosc mass, uporzadkowanie ? ?
m(“νe”) < 2.2 eV
Σmν < eV
m(“νμ”) < 190 keV
m(“ντ”) < 18.2 MeV
Mainz-Troitsk 3H decay
Cosmological models

46. What is the scale of neutrino masses?
Strumia and F. Vissani, ``Neutrino masses and mixings.’’
arXiv:hep-ph/
F. Feruglio, C. Hagedorn, Y. Lin and L. Merlo,
``Theory of the Neutrino Mass,’’ arXiv: [hep-ph].
Na ciemnoczerwono (ciemnozielono) zaznaczony obszar niepewnosci zwiazany z nieznanymi fazami Majorany.
Jasnoczerwono (jasnozielono) niepewnosc parametrow oscylacji
mββ may be very tiny in case of cancellations due to phases

47. Projections – ββ0ν HM Claim NEMO 3
CUORICINO, EXO-200
GERDA(PII)
SuperNEMO
CUORE,EXO
>2020,
1t experiments ( ≥ 2)
Cosmologically disfavoured region (WMAP)
>>2020,
>10t experiment 47

48. From neutrinos... DK&ER lecture11
Summary
Direct neutrino mass measurements – sensitivity good enough only for νe - may be successful in case of inverted hierarchy
Search for 0νββ – extremely important because:
It may answer the following basic questions:
Is the total lepton number conserved? Essential for understanding the matter-antimatter asymmetry in Universe
What is nature of neutrinos: Dirac or Majorana
( 0νββ possible only for Majorana neutrinos)
- essential for understanding the source of particle masses
From neutrinos... DK&ER lecture11