Transcript Double beta decay and neutrino physics

Double beta decay and neutrino
physics
Osaka University
M. Nomachi
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
Beta decay
n  p  e 
p
n

e
u
In the modern view
d
Weak interaction

W
e
Neutrino
Lepton
Spin ½
No charge
Three generations
Mass ??
http://particleadventure.org/particleadventure/index.html
Helicity
spin
spin
Helicity = +1
Helicity = -1
Helicity = +1
spin
Helicity is not Lorentz invariant
Free Dirac equation
 

i
   p  m  
t
1, 2,3, 
Special relativity
are 4x4 matrix
Pseudo Scalar operator
  i   
5
0
1
2
3
Chirality operator
Diagonal representation
 1ˆ 0ˆ    ˆ
,   
 5  
 0ˆ
ˆ  1ˆ 
0



 0ˆ 1ˆ    0ˆ
0ˆ 

,   
,


 1ˆ 0ˆ 
 ˆ
 ˆ 



 ˆ 
0ˆ 
In usual representation, βis diagonal
 
u   

The solution of the Dirac equation is
 
E    p   m
 
E    p   m
Helicity operator and its eigen states
 
 
p
p
   ,
  
p
p
 

 





u  N  E  p , u  N  E  p 
 
 


 m

 m

 E  p  
 E  p  
, u  

u  
 E  p    E  p 




E p
Is zero for mass-less particle
Chirality
 2 E  
 0 
, u  

u  

 2 E  
 0 
5
+1: Right handed
-1: Left handed
Helicity eigenstate = chirality eigenstate for mass-less particle
 E  p  
 E  p  
, u  

u  

 E  p 
 E  p 




Wrong helicity
E p 
E 2  p2
m

m
2E
E p
Weak interaction
Weak current

ue (1   5 )u
Projection operator of negative (left handed) chirality
1  5
PL 
2
In Weak interaction
Electron and neutrino are always left handed
While
Positron and anti-neutrino are always right handed
Parity violation
In Weak interaction
Electron and neutrino are always left handed
While
Positron and anti-neutrino are always right handed
electron
spin
anti-neutrino
anti-neutrino
electron
spin
We can know which is our world!
mirror
Beta decay of 60Co
Z
Z
electron
Z

60
Co  5
60
Ni  4
Electron should be left handed
Electron must have
1
z
2
s  
Electron and anti-neutron spin
Angular distribution
Z
Z
0
 
1
Rotation of spin 1/2


 cos 2
d ( )  


sin
2

1
2
sin 2 

 
cos 2 

 sin 2 


 
 cos 2 
For angular momentum conservation, spin must be down.
Angular distribution will be
W ( )  cos
2 
2
 12 1  cos 
Dirac particle and Majorana particle
• Dirac particle
– Particle and anti-particle can be distinguished
• Majorana particle
– Particle and anti-particle can not be
distinguished
Mass
L  m   h.c.
Dirac mass
L  m R L  m L R  h.c.
Majorana mass
L  m R   R  h.c.
C
 R 
C
Charge conjugate
Charged particle cannot have Majorana mass.
Neutrino mass
LDIRAC  mD R L  h.c.
mR C
LMAJORANA    R  R  h.c.
2
Neutrino may have both Dirac mass and Majorana mass.
Lmass  ( L
C
 mL
, R )
 mD
Dirac mass breaks chiral symmetry.
mD  L 
 C   h.c.
mR  R 
Mass eigenvalue
 0

 mD
mD 

mR 
mD 
 
2
   (  mR )  mD  0
det
 mD mR   
mR  mR  4 mD

2
2
2
2
2
mR  mR  4 mD
 4 mD
mD

,
 mR ,
2
2
2
mR
2(mR  mR  4mD )
2
2
Seesaw mechanism
2
mD
mR
mR
mD
Dirac mass will be the same order as the others. (0.1~10 GeV)
mR
Right handed Majorana mass will be at GUT scale 1015 GeV
Mixing and oscillation
Time evolution

i  (t )  E  (t )
t
 (t )   (0) e
i
Et

Mixing
 a   cos
   
 b    sin 
sin   1 
 
cos  2 
Mixing and oscillation
Assuming
 (0)   a  cos 1  sin   2
 (t )  cos  1 e
Probability to be
 a  (t )
2
a
i
E1t

 sin   2 e
 cos2   e
E2t

at t is
 (cos  1  sin   2 )(cos  1 e
Et
i 1

i
 sin 2   e
E2t 2
i

Et
i 1

 sin   2 e
E t
i 2

2
)
 a  (t )
2
Et
E t
Et
E t
i 1
i 2 
i 1
i 2 
 2
  cos   e   sin 2   e   cos2   e   sin 2   e  



E E
E E
i 2 1 t
i 2 1t 

 cos4   cos2   sin 2   e   e    sin 4 


E E
E E
i 2 1 t
i 2 1t 

e  e  
2
2
2
2
2 
 (cos   sin  )  2 cos   sin  1 

2




2
2 
2 E2  E1 
 1  2 cos   sin  1  sin
t



2
2 E2  E1
 1  sin 2  cos
t

E
For non relativistic limit
For small mass particle
p2  m2
p2
E  m
2m
m2
E  p
2p
E2  E1
 a  (t )  1  sin 2  cos
t

2
2
2
2 m2  m1
Mixing angle  1  sin 2  cos
ct
2 p c
2
2
2
2
2 m2  m1
 1  sin 2  cos
L
2 p  c
2
2
⊿m2
 a  (t )
2
2

m
 1  sin 2 2  cos2
L
2 p  c
m 2

L
2 p  c
2
c 
0.2 GeV fm or 0.2x10-6 eV m
The value you have to remember


 
9
6
3

10

10

0
.
2

10
m 2  p  c 
L
12106

Atmospheric Neutrinos
Super Kamiokande DATA
μ neutrino disappearance
Figures from Prof. Y. Suzuki at TAUP 2005
Solar neutrino
Electron neutrino disappearance
Nuclear fusion reaction
in the sun is WEAK
interaction.
MNS matrix
By Minakata
Mass hierarchy
Mass hierarchy is not derived from the oscillation measurements.
Invertedhierarchy
Normal
hierarchy
Δm2 (atmospheric)
Δm2 (solar)
m=0
Beta ray spectrum
The transition rate is
2
2
R
H fi n f

the density of final states
the matrix element

H fi  GW   H N  Ni   d r
*
Nf
Assuming plane wave
*
e
*

3
1 ikr
l 
e
V
  
GW
i ( ke  k  ) r 3 
*
H fi 
 Nf H N  Ni e
d r

V
2
2GW2
dR 
M fi n ( E )ne ( Ee )  (Q  Ee  E )dEe  dE
2
V
Phase space volume
The number of state in momentum p in the volume V
nx 
px  k x 
L
    3

2  3
d p  8  d n 
d n
V
 L
3
3
3
The transition rate will be
2
2GW2
V2
3
3
dR 
M fi
(Q  Ee  E )d pe  d p
2
6
V
(2)
2
2GW2 (4)2
2
2
dR 
M fi pe p (Q  Ee  E )dpe  dp
6
 (2)
E  P c m c
2
2 2
2 4
gives
2EdE  2 pc2dp
The transition rate will be
2
2G (4 )
Ee dEe E dE
2
2
dR 
M fi pe p  (Q  Ee  E )

6
2
 (2)
pe c
p c 2
2
W
2
2
GW2
dR  3 7 4 M fi Ee pe E p (Q  Ee  E )dEe dE
2  c
Assuming neutrino mass is zero,
2
2
W
fi
e
3 7 6
G
dR 
M
2  c
E pec(Q  Ee ) 2 dEe
Because of the coulomb potential, the electron wave function is not plane
wave. It causes the modification of the result
2
GW2
2
dR  3 7 6 M fi F ( Z  1, Ee ) Ee pec(Q  Ee ) dEe
2  c
Fermi-function
2
F ( Z , Ee ) 
1  e 2
Ze2 1 Z


40c  
1
E
F ( Z , Ee )  2Z  2Z

pc
consequently
2
G Z
2
dR 
M fi Ee (Q  Ee ) 2 dEe
 c
2
W
2 7 6
Neutrino mass in beta decay
The end point of beta-ray
depends on neutrino mass.
 m 

E p  (Q  Ee  E )dE  (Q  Ee )  1  
 Q  Ee 
2
2
Beta decay experiments
3H
beta decay, end point energy
KATRIN experiment
http://www-ik.fzk.de/~katrin/
Figure from http://www-ik.fzk.de/~katrin/overview/index.html
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.C40:447-468,2005
e-Print Archive: hep-ex/0412056
Double beta decay
Double beta decay
1) 2 neutrino double beta decay.
d(n)
d(n)
W
W
e
ν
e
ν
u(p)
u(p)
T1/2 (2): ~ 1.15 x 1019year
2) 0 neutrino double beta decay
Neutrino has mass
Neutrino is Majorana particle
0
T12  m
d(n)
W
ν
ν
2
d(n)
W
u(p)
e
e
u(p)
T1/2 (0): > 1023year
Lepton number non-conservation
d(n)
d(n)
W
W
e
ν
e
ν
u(p)
u(p)
T1/2 (2): ~ 1.15 x 1019year
d(n)
W
ν
ν
d(n)
W
Lepton number
2 electron
+2
2 anti neutrino
-2
= Lepton number is conserved.
(Baryon number is conserved.)
u(p)
e
Lepton number
2 electron
+2
= Lepton number is NOT conserved.
e
u(p)
(Baryon number is conserved)
T1/2 (0): > 1023year
Mass measurement
electron
electron
i
W
U ei
i
Mass term
W
U ei
Probability of helicity flip (wrong helicity) is proportional to m.
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.
νe
νe
50meV
5meV
Next generation experiments
are aiming to explore 50meV
region
From NOON2004 summary by A. Yu. Smirnov
Mass hierarchy
0.1 eV
10 meV
Double beta decay
100Mo
0(m  0.05eV )
2 
T122  0.8 1019 y
T102  1.2 1026 y
S.Elliott, Annu.Rev.Nucl.Part.Sci.
52, 115(2002)
Background
Natural radio activities
Cosmogenic background
2 neutrino double beta decay
NEMO3
 events selection in NEMO-3
Typical 2 event observed from 100Mo
Transverse view
100Mo
Run Number: 2040
Event Number: 9732
Date: 2003-03-20
Vertex
emission
foil
Longitudinal
view
100Mo
foil
Geiger plasma
longitudinal
propagation
Vertex
emission
Drift distance
Deposited energy:
E1+E2= 2088 keV
Internal hypothesis:
(t)mes –(t)theo = 0.22 ns
Common vertex: Scintillator
PMT
(vertex) = 2.1+ mm
(vertex)// = 5.7 mm
Criteria1to
select
Trigger:
PMT
> 150
keVevents:
• 2 tracks with charge < 0 3 Geiger hits (2 neighbour layers + 1)
• Internal hypothesis (external event rejection)
• 2 PMT, each > Trigger
200 keVrate = 7 Hz
• No other isolated PMT ( rejection)
• PMT-Track association
 events: 1 event• every
1.5 minutes
No delayed
track (214Bi rejection)
• Common vertex
Hideaki OHSUMI for the NEMO-3 Collaboration
APN04 Osaka 12-14 July 2004
100Mo
22 preliminary results
(Data 14 Feb. 2003 – 22 Mar. 2004)
Sum Energy Spectrum
NEMO-3
100Mo
145 245 events
6914 g
241.5 days
S/B = 45.8
Angular Distribution
145 245 events
6914 g
241.5 days
S/B = 45.8
NEMO-3
100Mo
•
•
Data
22
Monte Carlo
Background
subtracted
Data
22
Monte Carlo
Background
subtracted
Cos()
E1 + E2 (keV)
4.57 kg.y
Hideaki OHSUMI for the NEMO-3 Collaboration
T1/2 = 7.72 ± 0.02 (stat) ± 0.54 (syst)  1018 y
APN04 Paris 12-14 July 2004
0 Analysis with 100Mo
6914 g
265 days
100Mo
265 days
Cu + natTe + 130Te
Data
Data
2
Monte-Carlo
Radon
Monte-Carlo
Radon
Monte-Carlo
0 arbitrary
unit
E1+E2 (MeV)
E1+E2 (MeV)
Cu + natTe + 130Te
100Mo
100Mo
2.6<E1+E2<3. 2.8<E1+E2<3.
2
2
22 M-C
Radon M-C
TOTAL Monte-Carlo
DATA
2.6<E1+E2<3. 2.8<E1+E2<3.
2
2
____
32.3  1.9
1.4  0.2
23.5  6.7
5.6  1.7
11.4  3.4
2.6  0.7
55.8  7.0
50
7.0  1.7
8
11.4  3.4
8
2.6  0.7
2
V-A:
T1/2(0) > 3 1023 y
V+A:
T1/2 > 1.8 1023 y
Majoron: T1/2 > 1.4 1022 y
Hideaki OHSUMI for the NEMO-3 Collaboration
____
with E1- E2> 800 keV
with Esingle > 700 keV
APN04 Osaka 12-14 July 2004
MOON
Osaka U. , U. of Washington etc.
100Mo
+ Plastic scintillator
CANDLES
Osaka U.
48Ca
+ CaF scintillator
Majorana Detector
ep+
p+
e-
n
e
n
• GOAL: Sensitive to effective Majorana
 mass near 50 meV
• 0  decay of 76Ge potentially
measured at 2039 keV
• Based on well known 76Ge detector
technology plus:
– Pulse-shape analysis
– Detector segmentation
• Requires:
–
–
–
–
–
–
Reference Configuration
Deep underground location
500 kg enriched 86% 76Ge
many crystals, segmentation
Pulse shape discrimination
Time/Spatial Correlation
Special low-background materials
Homework
Probability to have wrong helicity
Beta ray angular distribution
Seesaw mechanism
Neutrino oscillation
Beta ray energy spectrum