Outline
Weak interaction and neutrino propertyExercise: HelicityExercise: parity violation
Neutrino massExercise: Seesaw mechanism
Neutrino oscillationExercise; Neutrino oscillation
Oscillation experimentsNeutrino mass measurement
Beta decayExercise: Beta ray energy spectrum
Double beat decay
Neutrino
http://particleadventure.org/particleadventure/index.html
LeptonSpin ½No chargeThree generationsMass ??
32105 i
Pseudo Scalar operator
Chirality operator
Diagonal representation
0̂ˆ
ˆ0̂,
0̂1̂
1̂0̂,
ˆ0̂
0̂ˆ,
1̂0̂
0̂1̂5
In usual representation, βis diagonal
uThe solution of the Dirac equation is
mpE
mpE
p
p
p
p
,
Helicity operator and its eigen states
pE
pEu
pE
pEu
m
pENu
m
pENu
,
,
pE
pEu
pE
pEu ,
pE Is zero for mass-less particle
E
uE
u2
0,
0
2
Helicity eigenstate = chirality eigenstate for mass-less particle
Wrong helicitym
E
m
pE
pEpE
2
22
Chirality
5 +1: Right handed-1: Left handed
Weak interaction
Weak current
uue )1( 5
2
1 5LP
Projection operator of negative (left handed) chirality
In Weak interactionElectron and neutrino are always left handed
WhilePositron and anti-neutrino are always right handed
Parity violation
In Weak interactionElectron and neutrino are always left handed
WhilePositron and anti-neutrino are always right handed
mirror
spin spin
electron electronanti-neutrino anti-neutrino
We can know which is our world!
Beta decay of 60CoZ Z
560 Co 460 Ni
Electron and anti-neutron spin
Z
electron
Electron should be left handedElectron must have
21zs
Angular distribution
Z Z
1
0
22
22
cossin
sincos)(2
1
d
2
2
cos
sin
For angular momentum conservation, spin must be down.Angular distribution will be
cos1cos)( 21
22 W
Rotation of spin 1/2
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
..chmL
..chmmL RLLR
..chmL RC
R
Dirac mass
Majorana mass
CR Charge conjugate
Charged particle cannot have Majorana mass.
Neutrino mass
..2
..
chm
L
chmL
RC
RR
MAJORANA
LRDDIRAC
..),( chmm
mmL C
R
L
RD
DLR
CLmass
Neutrino may have both Dirac mass and Majorana mass.
Dirac mass breaks chiral symmetry.
Mass eigenvalue
RD
D
mm
m00)(det 2
DR
RD
D mmmm
m
R
DR
DRR
DDRR
DRR
m
mm
mmm
mmmm
mmm
2
22
222
22
,)4(2
4,
2
4
2
4
Seesaw mechanism
R
D
m
m Dirac mass will be the same order as the others. (0.1~10 GeV)
Right handed Majorana mass will be at GUT scale 1015 GeV
Rm
R
D
m
m 2
Mixing and oscillation
21 sincos)0( aAssuming
Probability to be at t is
tE
itE
ieet
21
21 sincos)(
a
2
22
2
2121
2
21
21
sincos
)sin)(cossin(cos)(
tEi
tEi
tEi
tEi
a
ee
eet
tEE
tEE
ee
ee
eeeet
tEE
itEE
i
tEE
itEE
i
tEi
tEi
tEi
tEi
a
1222
12222
22222
4224
22222
cos2sin1
sin1sincos21
21sincos2)sin(cos
sinsincoscos
sincossincos)(
1212
1212
2121
For small mass particle
p
mpE
2
2
For non relativistic limit
m
pmE
2
2
22 mpE
Lcp
mm
ctcp
mm
tEE
ta
2cos2sin1
2cos2sin1
cos2sin1)(
21
2222
21
2222
12222
Mixing angle⊿m2
c
Lcp
m
Lcp
mta
22
2cos2sin1)(
2
2222
0.2 GeV fm or 0.2x10-6 eVm
6
692
1012
102.010103
cpL
m
The value you have to remember
Atmospheric Neutrinos
Figures from Prof. Y. Suzuki at TAUP 2005
Super Kamiokande DATA
μ neutrino disappearance
Solar neutrino
Nuclear fusion reaction in the sun is WEAK interaction.
Electron neutrino disappearance
Δm2 (atmospheric)
Mass hierarchy
Δm2 (solar) m=0
Normal hierarchyInverted hierarchy
Mass hierarchy is not derived from the oscillation measurements.
Beta ray spectrum
The transition rate isffi nHR
22
the matrix elementthe density of final states
rdHGH eNiNNfWfi
3***
rkil e
V
1
rdeHV
GH rkki
NiNNfW
fie
3)(*
Assuming plane wave
dEdEEEQEnEnMV
GdR eeeefi
W )()()(2 2
2
2
Phase space volume
L
nkp x
xx
The number of state in momentum p in the volume V
nd
Vnd
Lpd 3
33
33 2
8
pdpdEEQ
VM
V
GdR eefi
W
336
22
2
2
)()2(
2
dpdpEEQppMG
dR eeefiW )(
)2(
)4(2 222
6
22
The transition rate will be
42222 cmcPE dppcEdE 222 gives
22
222
6
22
)()2(
)4(2
cp
dEE
cp
dEEEEQppM
GdR
e
eeeefi
W
The transition rate will be
dEdEEEQpEpEMc
GdR eeeefi
W )(2
2
473
2
eeeefiW dEEQcpEM
c
GdR 22
673
2
)(2
Assuming neutrino mass is zero,
Because of the coulomb potential, the electron wave function is not plane wave. It causes the modification of the result
eeeeefiW dEEQcpEEZFM
c
GdR 22
673
2
)(),1(2
Fermi-function
21
2),(
eEZF e
Z
c
Ze 1
4 0
2
pc
EZZEZF e
2
12),(
eeefiW dEEQEM
c
ZGdR 222
672
2
)( consequently
Neutrino mass in beta decay
dEEEQpE e )( 2
2 1)(
e
e EQ
mEQ
The end point of beta-ray depends on neutrino mass.
Beta decay experiments
KATRIN experiment
http://www-ik.fzk.de/~katrin/
3H beta decay, end point energy
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
2) 0 neutrino double beta decay
Neutrino has mass
Neutrino is Majorana particle
1) 2 neutrino double beta decay.
d(n)
d(n) u(p)
u(p)
W
W
e
eν
ν
T1/2 (): ~ 1.15 x 1019year
d(n)
d(n) u(p)
u(p)W
We
eνν
T1/2 (): > 1023year
Double beta decay
20
21
mT
Lepton number non-conservation
d(n)
d(n) u(p)
u(p)
W
W
e
eν
ν
T1/2 (): ~ 1.15 x 1019year
d(n)
d(n) u(p)
u(p)W
We
eνν
T1/2 (): > 1023year
Lepton number2 electron +22 anti neutrino -2
= Lepton number is conserved.
(Baryon number is conserved.)
Lepton number2 electron +2
= Lepton number is NOT conserved.
(Baryon number is conserved)
Mass measurement
electron electron
eiU eiU
i iW W
Mass term
Probability of helicity flip (wrong helicity) is proportional to m.
Beta decay observable
Double beta decay observable
It should be larger than that of double beta decay measurements.
It depends on the phase. Could be zero.
From NOON2004 summary by A. Yu. Smirnov
νe
νe
5meV
50meV
Next generation experiments are aiming to explore 50meV region
Double beta decay
S.Elliott, Annu.Rev.Nucl.Part.Sci. 52, 115(2002)
yT 260 102.12
1
2 )05.0(0 eVm
yT 192 108.02
1
100Mo
BackgroundNatural radio activitiesCosmogenic background2 neutrino double beta decay
Drift distance
100Mo foil100Mo foil
Transverse view Longitudinal view
Run Number: 2040Event Number: 9732Date: 2003-03-20
Geiger plasmalongitudinalpropagation
Scintillator + PMT
Deposited energy: E1+E2= 2088 keVInternal hypothesis: (t)mes –(t)theo = 0.22 nsCommon vertex: (vertex) = 2.1 mm
Vertexemission
(vertex)// = 5.7 mm
Vertexemission
Transverse view Longitudinal view
Run Number: 2040Event Number: 9732Date: 2003-03-20
Criteria to select events:• 2 tracks with charge < 0• 2 PMT, each > 200 keV• PMT-Track association • Common vertex
• Internal hypothesis (external event rejection)• No other isolated PMT ( rejection)• No delayed track (214Bi rejection)
events selection in NEMO-3
Typical 2 event observed from 100Mo
Hideaki OHSUMI for the NEMO-3 Collaboration APN04 Osaka 12-14 July 2004
Trigger: 1 PMT > 150 keV
3 Geiger hits (2 neighbour layers + 1)
Trigger rate = 7 Hz events: 1 event every 1.5 minutes
(Data 14 Feb. 2003 – 22 Mar. 2004)
T1/2 = 7.72 0.02 (stat) 0.54 (syst) 1018 y
100Mo 22 preliminary results
4.57 kg.y
Cos()
Angular Distribution
Background subtracted
22 Monte Carlo
• Data
145 245 events6914 g
241.5 daysS/B = 45.8
NEMO-3
100Mo
E1 + E2 (keV)
Sum Energy Spectrum
145 245 events6914 g
241.5 daysS/B = 45.8
NEMO-3
100Mo
• Data
Background subtracted
22 Monte Carlo
Hideaki OHSUMI for the NEMO-3 Collaboration APN04 Paris 12-14 July 2004
Analysis with 100Mo
V-A: T1/2() > 3 1023 y V+A: T1/2 > 1.8 1023 y with E1- E2> 800 keV
Majoron: T1/2 > 1.4 1022 y with Esingle > 700 keVHideaki OHSUMI for the NEMO-3 Collaboration APN04 Osaka 12-14 July 2004
100Mo
8
7.0 1.7
5.6 1.7
1.4 0.2
55.8 7.0TOTAL Monte-Carlo
2.6<E1+E2<3.2
50DATA
23.5 6.7Radon M-C
32.3 1.9100Mo 22M-C
100Mo
6914 g265 days
DataMonte-CarloRadonMonte-Carlo
E1+E2 (MeV)
arbitrary unit
PRELIMINARY
2.8<E1+E2<3.2
Cu + natTe + 130Te
265 days
RadonMonte-Carlo
Data
E1+E2 (MeV)
Cu + natTe + 130Te
8
11.4 3.4
11.4 3.4
____
2.6 0.7
2
2.6 0.7
____
2.6<E1+E2<3.2 2.8<E1+E2<3.2
Majorana Detector
• 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:– Deep underground location– 500 kg enriched 86% 76Ge– many crystals, segmentation– Pulse shape discrimination– Time/Spatial Correlation– Special low-background materials
n
n
p+ p+
e-
e-
e
Reference ConfigurationReference Configuration