Double beta decay and neutrino physics

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Double beta decay and neutrino physics

• Osaka University
• M. Nomachi

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Outline

• Weak interaction and neutrino property
• Exercise Helicity
• Exercise parity violation
• Neutrino mass
• Exercise Seesaw mechanism
• Neutrino oscillation
• Exercise Neutrino oscillation
• Oscillation experiments
• Neutrino mass measurement
• Beta decay
• Exercise Beta ray energy spectrum
• Double beat decay

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Beta decay
In the modern view
Weak interaction
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Neutrino
Lepton Spin ½ No charge Three generations Mass ??
http//particleadventure.org/particleadventure/ind
ex.html
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Helicity
spin
Helicity 1
Helicity -1
spin
Helicity 1
spin
Helicity is not Lorentz invariant
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Free Dirac equation
are 4x4 matrix
Special relativity
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Pseudo Scalar operator
Chirality operator
Diagonal representation
In usual representation, ßis diagonal
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The solution of the Dirac equation is
Helicity operator and its eigen states
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Is zero for mass-less particle
Chirality
1 Right handed -1 Left handed
Helicity eigenstate chirality eigenstate for
mass-less particle
Wrong helicity
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Weak interaction
Weak current
Projection operator of negative (left handed)
chirality
In Weak interaction Electron and neutrino are
always left handed While Positron and
anti-neutrino are always right handed
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Parity violation
In Weak interaction Electron and neutrino are
always left handed While Positron and
anti-neutrino are always right handed
electron
electron
anti-neutrino
anti-neutrino
spin
spin
We can know which is our world!
mirror
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Beta decay of 60Co
Z
Z
electron
Z
Electron should be left handed Electron must have
Electron and anti-neutron spin
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Angular distribution
Z
Z
Rotation of spin 1/2
For angular momentum conservation, spin must be
down. Angular distribution will be
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Dirac particle and Majorana particle

• Dirac particle
• Particle and anti-particle can be distinguished
• Majorana particle
• Particle and anti-particle can not be
  distinguished

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Mass
Dirac mass
Majorana mass
Charge conjugate
Charged particle cannot have Majorana mass.
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Neutrino mass
Neutrino may have both Dirac mass and Majorana
mass.
Dirac mass breaks chiral symmetry.
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Mass eigenvalue
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Seesaw mechanism
Dirac mass will be the same order as the others.
(0.110 GeV) Right handed Majorana mass will be
at GUT scale 1015 GeV
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Mixing and oscillation
Time evolution
Mixing
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Mixing and oscillation
Assuming
Probability to be at t is
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For non relativistic limit
For small mass particle
?m2
Mixing angle
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0.2 GeV fm or 0.2x10-6 eV m
The value you have to remember
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Atmospheric Neutrinos
Super Kamiokande DATA
µ neutrino disappearance
Figures from Prof. Y. Suzuki at TAUP 2005
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Solar neutrino
Electron neutrino disappearance
Nuclear fusion reaction in the sun is WEAK
interaction.
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MNS matrix
By Minakata
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Mass hierarchy
Mass hierarchy is not derived from the
oscillation measurements.
Normal hierarchy
Inverted hierarchy
?m2 (atmospheric)
?m2 (solar)
m0
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Beta ray spectrum
The transition rate is
the density of final states
the matrix element
Assuming plane wave
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Phase space volume
The number of state in momentum p in the volume V
The transition rate will be
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gives
The transition rate will be
Assuming neutrino mass is zero,
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Because of the coulomb potential, the electron
wave function is not plane wave. It causes the
modification of the result
Fermi-function
consequently
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Neutrino mass in beta decay
The end point of beta-ray depends on neutrino
mass.
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Beta decay experiments
3H beta decay, end point energy
KATRIN experiment
http//www-ik.fzk.de/katrin/
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Figure from http//www-ik.fzk.de/katrin/overview/
index.html
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FINAL RESULTS FROM PHASE II OF THE MAINZ NEUTRINO
MASS SEARCH IN TRITIUM BETA DECAY.Ch. Kraus et
al.. Dec 2004. 22pp. Published in
Eur.Phys.J.C40447-468,2005 e-Print Archive
hep-ex/0412056
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Double beta decay
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Double beta decay
1) 2 neutrino double beta decay.
2) 0 neutrino double beta decay Neutrino has
mass Neutrino is Majorana particle
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Lepton number non-conservation
Lepton number 2 electron 2 2 anti
neutrino -2 Lepton number is conserved. (Baryon
number is conserved.)
Lepton number 2 electron 2 Lepton number is
NOT conserved. (Baryon number is conserved)
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Mass measurement
electron
electron
W
W
Mass term
Probability of helicity flip (wrong helicity) is
proportional to m.
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Beta decay observable
It should be larger than that of double beta
decay measurements.
Double beta decay observable
It depends on the phase. Could be zero.
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?e
50meV
?e
5meV
Next generation experiments are aiming to explore
50meV region
From NOON2004 summary by A. Yu. Smirnov
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Mass hierarchy
0.1 eV 10 meV
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Double beta decay
100Mo
S.Elliott, Annu.Rev.Nucl.Part.Sci. 52, 115(2002)
Background Natural radio activities Cosmogenic
background 2 neutrino double beta decay
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NEMO3
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bb events selection in NEMO-3
Typical bb2n event observed from 100Mo
Transverse view
Run Number 2040 Event Number 9732 Date
2003-03-20
Longitudinal view
100Mo foil
100Mo foil
Geiger plasma longitudinal propagation
Scintillator PMT
Hideaki OHSUMI for the NEMO-3 Collaboration
APN04 Osaka
12-14 July 2004
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100Mo 2?2? preliminary results
(Data 14 Feb. 2003 22 Mar. 2004)
Sum Energy Spectrum
Angular Distribution
145 245 events 6914 g 241.5 days S/B 45.8
145 245 events 6914 g 241.5 days S/B 45.8
NEMO-3
NEMO-3
100Mo
100Mo
2?2? Monte Carlo
Background subtracted
2?2? Monte Carlo
Background subtracted
Cos(?)
E1 E2 (keV)
T1/2 7.72 0.02 (stat) 0.54 (syst) ? 1018 y
4.57 kg.y
Hideaki OHSUMI for the NEMO-3 Collaboration
APN04 Paris 12-14
July 2004
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bb0n Analysis with 100Mo
100Mo
2.6ltE1E2lt3.2
2.8ltE1E2lt3.2
1.4 ? 0.2
32.3 ? 1.9
100Mo 2b2n M-C
5.6 ? 1.7
23.5 ? 6.7
Radon M-C
7.0 ? 1.7
55.8 ? 7.0
TOTAL Monte-Carlo
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DATA
V-A T1/2(bb0n) gt 3 1023 y VA
T1/2 gt 1.8 1023 y with ?E1-
E2?gt 800 keV Majoron T1/2 gt 1.4 1022 y
with Esingle gt 700 keV
Hideaki OHSUMI for the NEMO-3 Collaboration
APN04
Osaka 12-14 July 2004
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MOON Osaka U. , U. of Washington etc.
100Mo Plastic scintillator
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CANDLES Osaka U.
48Ca CaF scintillator
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Majorana Detector

• GOAL Sensitive to effective Majorana n mass near
  50 meV
• 0n bb decay of 76Ge potentially measured at 2039
  keV
• Based on well known 76Ge detector technology
  plus
• Pulse-shape analysis
• Detector segmentation
• Requires
• Deep underground location
• 500 kg enriched 86 76Ge
• many crystals, segmentation
• Pulse shape discrimination
• Time/Spatial Correlation
• Special low-background materials

• Reference Configuration

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Homework

• Probability to have wrong helicity
• Beta ray angular distribution
• Seesaw mechanism
• Neutrino oscillation
• Beta ray energy spectrum