on the importance of neutrino mass is it really important? why? who cares? what is a neutrino ? what...
TRANSCRIPT
On the Importance of Neutrino Mass
Is it really important? Why? Who cares?
What is a Neutrino ? What is Mass ? Keys to the Puzzle ?
A. Para, Fermilab
More
questions
than
answers..
11 Greatest Unanswered Questions of Physics
What is dark matter ? What is dark energy ? How were the elements from iron to uranium
made? Do neutrinos have mass ? … Are protons unstable ? What is gravity ? Are there additional dimensions ? How did the Universe begin ?
Discover February 2002
Particle Physics at the End of the XX Century:Theory of Matter and Forces
Matter Forces
Periodic table of elementary particles
Expanding our Ignorance: Composition of the Universe
65+-10% Dark(vacuum) energy 30+-7% Dark matter
4.5+-0.5% Ordinary matter 0.5% Stars 0.5% Neutrinos
0.02% C,N,O,…,Fe,…
Unknown, not understood
Known, poorly understood
“Us”
N() >~109N(protons, neutrons, electrons)
Theory of Matter and Forces: the Right-handed Stuff?
, , ,
,
, ,
,
R R R R
R R R
R Ru d c s t b
e
• Left-handed SU(2) doublets
• Quark <-> lepton symmetry (anomaly free)
•Right-handed SU(2) singlets
•No neutrinos!
•Do not participate in weak interactions, we know of their existence because of their strong/electromagnetic interactions
Neutrinos are special
Quarks and charged leptons
members of SU(2) doublets
(left-handed) and singlets (right handed)
Electric charges 1/3, 2/3, 1 4-component Dirac spinors Have antiparticles distinct
from particles
Neutrinos Members of SU(2) doublets
(left-handed), no singlets Electric charge = 0 obey Dirac equation?
Majorana equation? Do have anitparticles? Are
self-conjugate? Magnetic moments? Sterile neutrinos?
9 30.5 10mass eV
1 2 0.05 ?mass eV eV
Are these facts/questions related?
Enigma of Masses of Elementary Particles
Masses of all charged fermions within a given generation are the same within a factor of 10
Masses of neutrinos are a factor ~109 smaller
Why ??? What makes masses so different?
Notice: if m~me we would not be here to ask such questions !
The meaning of Mass:A Worldline of a Massive Particle in its
Rest Frame
5 51 2
1 1( ) ( ) ( )
2 2iu p Q t e Q t
51,2
1( )
sQ t
21,2 1,2
( )2
; 02
u p
p mst t
where
Q(t) is a spinor of a massless particle with momentum t
R.H.
L.H.
x ct
/ 2xx p
A Massive Particle in its Rest Frame
Interaction with vacuum changes left-handed particle into right-handed one
L
RWhat are R,L ?
Electron case
L = left handed electron
R = right handed electron (not positron! Because of charge conservation)
Neutrino case
L = left handed neutrino
R = right handed antineutrino??
right handed neutrino??
CPT transformation of a spinor
C
P
T
fL
f
f
fR
CPT Invariance implies:
fL fR
R
R
L
f
f
L
L
R
f
f
From Schrodinger to Dirac
2
02
it m
2
02
pE
m
2 2 2
2 2 2
10
m c
c t
22 2 2
20
Ep m c
c
0i mc
0 0
0
ii
i
o
o
I
I
1
2
3
4
2 2 2
2 2 2
10i
m c
c t
SchrodingerNon-relativistic
Klein-Gordon
Non-positive probabibility
Dirac
Square root of K-G
matrices, Weyl representation
2g I
1 2 30 1 0 1 0, ,
1 0 0 0 1
(1, )
i
i
OOOOOOOOOOOOOO
5 0 1 2 30,
0i
5
5
0 011
02
0 011
02
I
I
The ‘other’ square root
0mc
1
2
2 2 2
1,22 2 2
10
m c
c t
Majorana
Which equation describes neutrino? Dirac? Majorana?
This question arises only for neutral fermions
Dirac neutrino vs Majorana neutrino
Dirac Majorana
R
L
R
L
R
L
C
P
T
C
P
T
Lorentz
Boost,
E, B
A General Lagrangian (Neutral Fermions)
. .
. . . .2 2L R
D L R
c cL RL R
M M
L M hc
h c h c
, L D
D R
M M fL f f F F f F
M M F
,2 2
C C
L L R Rf F
Left, right handed fields
See-saw mechanism
,MN RN m M
2
,M D
R
Mm
M
D
R
L
R
L
R
L
L
R
N
N
The physical states are eigenstates of the mass matrix
Let all fermions have the same Dirac mass MD (~ mq or ml), ML=0 if MR>>MD than m<<ml
• Is neutrino a Majorana particle?
• Is a very heavy Majorana mass an explanation for the smallness of the observed mass eigenstate? Are we witnessing a first sign of the physics at very high energies?
Neutrino Masses: a Key to the Mass Generation Mechanism?
m1 : m2 : m3 = mu2 : mc
2 : mt2
m~ mq2/Mx
See-saw mechanism for Majorana neutrinos
New interactions at the scale Mx
m1 : m2 : m3 = mu : mc : mt
m~ mq
Top members of weak doublets couple to the same Higgs field
m1 : m2 : m3 = me : m : m
mml
‘Leptonic’ Higgs generates mass of leptons
Possible examples:
Direct measurements of neutrino mass
Techniques time of flight (SN1987a) particle decay kinematics
beta decay spectrum shape (e) muon momentum in pion decay () invariant mass studies of multiparticle semileptonic
decays () Advantages
sensitive to absolute mass scale purely kinematical observables no assumptions about properties
Neutrino Masses: Experimental Progress
100
101
102
103
104
Mas
s L
imit
(eV
, keV
, or
MeV
)
200019901980197019601950
Year
e (eV)
(keV)
(MeV)
e
J. Wilkerson
• points without error bars represent upper limits• note: different scale for different neutrinos types
Tritium beta decay spectrum
2
22
22cos
( ) ( , , )2 ee
F Ce
G In E dE F Z R E p Q T mE Q T
OOOOOOOOOOOOOO
3
0
( )
( )
Q
Q EQ
n E dEEQ
n E dE
3
103
102 10
18.6 10
eV
eV
n p+e-
+e
Two leading experiments: Troitsk and Mainz
2 2( ) 1.0 3.0 1.5
( ) 2.5 (95% )e
e
m eV
m eV CL
Troitsk
2 2( ) 1.6 2.5 2.1
( ) 2.2 (95% )e
e
m eV
m eV CL
Mainz
Breakthrough technique:MAC-E-Filter
•Magnetic Adiabatic Collimation followed by Electrostatic Filter
•Integrating high pass filter: high intensity
•Large acceptance ~ 2
•High resolution,
E~2-6 eV at E=20 keV
•Developed specifically for tritium beta decay experiments
New Twist: Neutrino Mixing (SuperK 1997)
3
2
1
321
221
321
UUU
UUU
UUUeee
e
Weak eigenstates are mixtures of mass eigenstates
23 23
23 2
12 12
12 12
1 3
33
3 1
13 1
01 0 00
0
0 0
10
1 0
0 0
0
i
i
c s
c s
s c
s c
c s e
s e
U
c
Large mixing angle 12 ~ 35o
Large mixing angle 23 ~ 45o
Mixing angle 13 ~ small
What is an electron neutrino?
n
p
e
e
1 1 2 2 3 3e e e eU U U
• Electron (muon,tau) neutrino is not a mass eigenstate
• Electron (muon, tau) neutrino is a coherent mixture of mass eigenstates
What do neutrino mass experiments measure?
An “effective mass” : m 2
= |Uei |2 mi
-decay spectrum and neutrino mixing
The beta spectrum shape depends on: the neutrino masses the number of neutrino mass eigenstates the leptonic mixing matrix elements
2
2
22
22cos
( ) ( , , )2 ee
F Ce
G In E dE F Z R E p Q T mE Q T
OOOOOOOOOOOOOO
2 2
2 22
2
cos( ) ( , , )
2 i
F Ce eei
i
G In E dE F Z R E Q TUp E Q mT
OOOOOOOOOOOOOO
Neutrino Oscillations: Tool for Measuring Mass Differences
If neutrinos have mass, then it is likely that flavor and mass eigenstates are different Neutrino Oscillations
Example: two families of neutrinos
1
2
cos sin
sin cose
2 2 212 1 2define m m m
222
si1.27
n i2 s nePm L
E
AmplitudeOscillation frequency
a ai iU
Neutrino Interferometry, or How do Neutrinos Oscillate?
i
Amplitude
Amplitude
2
* 2imi
i i
LE
i
U Ue
A
Components of the initial state have different time evolution => (t) (0)
3-slit interference Experiment: mass difference difference in optical path length
Oscillation Probability
2
2* * 2
2* *
( ) ( )
4 ( )sin4
2 ( )sin2
iji i j j
i j
iji i j j
i j
P
m LU U U U
E
m LU U U U
E
A
R
I
2 2 2ij i jm m m
where
Neutrino Oscillations Primer
if all masses are equal i.e. Neutrino oscillations are sensitive to mass differences only.
oscillates as a function of L/E
for Appearance experiment.
: disappearance experiment
:total number of neutrinos is conserved
If Ui is complex then hence T (or CP) violation
0P 2 0ijm
P
0P
1P
1P
P P
Neutrino Oscillations
Disappearance experiment: Start with neutrinos of type x (say ), detect
the flux at a distance L, (L)<
(0)
Appearance experiment: Start with neutrinos of type x (say ), detect
the neutrinos of type y (say ), at a distance L
Does really happen?
How does the Sun ‘work’? (H. Bethe)
Tiny fraction
2 4
33
13 2
14 ( )
2
4 10 /
4 (1.5 10 ) 14
10 2 16 10
Luminosity
r binding energy of He
erg s
cm MeV
cm s
Solar model
Detecting Solar Neutrinos
SuperKamiokande:
•Electron neutrino scatters elastically of an atomic electron
•Scattered electrons follow the direction of the incoming neutrino
R. Davis, Homestake:
•680 ton of CCl4
• ~ 15 atoms of 37Ar produced per month !!!
Solar Neutrino Results (~1999)
•Only about 50% of the predicted flux is detected
•Solar neutrino ‘problem’
Charged Current Reaction: � 6-9 events per day � e flux and energy spectrum � Some directional sensitivity (1 - 1/3cose)
e: 1.75(15) x 106 cm-2 s-1
SSM: 5.05 x 106 cm-2 s-1
Elastic Scattering Reaction: 1-2.5 events per day� Directional sensitivity (very forward peaked)�
e + d p + p + e Ethres= 1.4 MeV
CC
ESx + e x + e Ethres = 0 MeV
Reactions in heavy water (SNO)
e e-
n pW
e e-
e- e
W
e-W
e
e- e-
e
Ze-
: 3.69(113) x 106 cm-2 s-1
total: 5.44(99) x 106 cm-2 s-1
KamLAND: the ultimate proof of KamLAND: the ultimate proof of solar neutrino oscillations solar neutrino oscillations
Disappearing electron antineutrinos
Solar neutrino problem no longer a problem
Neutrinos oscillate
• Reactor neutrinos (== electron antineutrinos!!) disappear at distances ~ 100 km
• consistent with solar neutrino experiment
• m2 ~ 1-14 x 10-5 eV2
Atmospheric Neutrinos
Earth
SuperK
Results from Super-K Experiment
flux reduced by about 50% for long flight path
if it is a result of the neutrino oscillations, then :
the dominant mode is to
mixing angle is very large m2 :3 2 3 21.5 10 4 10 GeVm
Long Baseline Neutrino Oscillation Exp’s
Reproduce atmospheric effect using accelerator produced -beam
K2K (KEK to SuperK) L = 250 km Now
CNGS (Cern to Gran Sasso, Italy) L = 750 km 2005?
MINOS (Fermilab to Minnesota)
L = 730 km 2003
Det. 2
The MINOS Beamline
Two Detector NeutrinoOscillation Experiment
(Start 2005)
Det. 1
Far Detector (5.4 ktons) :- 8m diameter by 1” steel plates- 4cm wide solid scintillator strips- Steel magnetized at 1.5 T
Do Neutrinos Oscillate? Decay? Travel in Extra Dimensions
Observed energy distribution of CC interactions provide a measure of the survival probability as a function of E
Expected event spectrum
Observed (perhaps?) event spectrum
2232.54 m L
E
Three outstanding questions ~ 2003
1
2
3
e
sB B
B B B
B B B
• Neutrino mass pattern: This ? Or that?
• Electron component of 3 (sin2213)
• Complex phase of s CP violation in a neutrino sector (?) baryon number of the universe
The key: e oscillation experiment
A. Cervera et al., Nuclear Physics B 579 (2000) 17 – 55, expansion to second order in
2
2 2 2131 23 13
22 2 212
2 23 12
13 13123
13 13124
sin sin sin2
cos sin sin2
cos sin sin2 2 2
sin sin sin2
cos
in2 2
s
B LP
B
ALP
A
L B LALP J
A B
L B LALP J
A B
2
13
13 12 13 23
;2
2 ;
;
cos sin 2 sin 2 sin 2
ijij
F e
m
E
A G n
B A
J
1 2 3 4( )eP P P P P
12 1213 12
23
, , , LA
Neutrino Propagation in Matter
• Matter effects reduce mass of e and increase mass ofe
• Matter effects increase m2
23 for normal hierarchy and reduce m2
23 for inverted hierarchy
Anatomy of Bi-probability ellipses
sin2213
~sin
~cos
Observables are:•P •PInterpretation in terms of sin2213, and sign ofm2
23 depends on the value of these parameters and on the conditions of the experiment: L and E
Minakata and Nunokawa, hep-ph/0108085
NuMI Beam + Off-axis Detector(s)
•Search for nm to ne transition
•Measure mixing angle sin2213
•Search for CP violation in a neutrino sector
How about the nature of neutrino?
Dirac or Majorana particle? Does it have a distinct antiparticle? Is it its own antiparticle?
Masses of Nuclei: even A Case
Lowest energy state reachable only through two simultaneous weak beta decays very low rate, very long lifetimes (exceeding age of the Universe)
Neutrinoless Double decay: Key to the Nature of the Neutrino
Process allowed only for a Majorana neutrino
Two beta decays
If (neutrino=antineutrino) {they can ‘annihilate’ each other}
Electron Spectrum From Double Decay: from Theory to Practice
•Energy resolution
•High rates capabilities
Double Beta Decay Experiments: Results
Isotope Experiment48Ca HEP Beijing >1.1x102
2*23-50
76Ge Heidelberg-Moscow >5.7x102
52-8
IGEX >0.8x102
5
82Se Irvine >2.7x102
24-14
NEMO 2 >9.5x102
1
96Zr NEMO 2 >1.3x102
1
100Mo LBL >2.2x102
2*3-111
UCI >2.6x102
1
Osaka 5.5x1022 2
NEMO2 >5x1021
130Te Milano >1.4x102
32-5
136Xe Caltech/PSI/Neuchatel >4.4x102
32-5
150Nd UCI >1.2x102
15-6
01/ 2 ( )T yr ( )
ULm eV
Germ
an
ium
dio
de c
al.
Te0
2 c
ryo
calo
rim
.X
e
TPC
What do 0 Experiments Measure?
2 20
1/ 2
1( , )Rate G E Z
T M
Where:
a phase space factor
a nuclear matrix element (QRPA, NSM,..)
( , )G E Z2M
2ei
eff ei ii
m U m e 1eie Majorana phases
If CP is conserved
2 2 2max 2 ei i ei i ei i
i i
U m U m U mmeff
The quest for 20-50 meV sensitivity
CUORE – 210 kg of 130Te, Grand Sasso EXO - (liguid or gaseous) 136Xe WIPP?
Homestake? GENIUS - 1t of enriched 76Ge in liquid N2 shield MAJORANA – 500 kg of enriched segmented
76Ge detectors MOON – thin foils of (enriched?) 100 Mo
Homestake? Japan?•Large mass of the source material, enriched if possible
•Innovative background suppression
•Intermediate steps
Large scale clusters
•Large scale structures originate from fluctuations of the primordial mass/energy distribution
•Significant contribution of the mass/energy in a form of fast moving neutrinos would tend to wash out fluctuations
Weighing Neutrinos with Galaxy Surveys
Sloan Sky Survey of Bright Red Galaxies
W. Hu, D.J. Eisenstein, M. Tegmark, PRL80, p5255, 1998
Large scale cluster formation
Fraction of energy in neutrinos
The pattern and absolute scale of masses
Key issues in particle physics hierarchical or degenerate neutrino mass spectrum understanding the scale of new physics beyond SM potential insight into origin of fermion masses Nature of the neutrino
Cosmology and astrophysics connection
early universe, relic neutrinos (HDM), structure formation, anisotropies of CMBR
supernovae, r-process, origin of elements potential influence on UHE cosmic rays
(Instead of) Conclusions
We are living in interesting times.
It is fun to study neutrinos
Stellar Evolution
Supernova Explosion
Supernova 1987A
February 1984 March 8,1987Seven years later..
Supernova as a Neutrino Laboratory (Examples)
Neutrino mass:If neutrinos have mass m then neutrinos with different
energies will travel with different speed. Difference of arrival time of neutrinos with energy E1 and E2:
Neutrino lifetime:Neutrinos come from a distance L. Their lifetime must be
such, that:
22
21
22
212
2
1
EE
EELmt
Lcm
E
SN1987A: m<15 eV
SN1987A:
>5x1012 s
Neutrinos from Supernova 1987A
Energy spectrum of neutrinos
•total energy radiated (1.4 solar masses)
•size of the resulting neutron star (15 km)
Dec 1930: A Desperate Remedy
P h y s i k a l i s c h e s I n s t i t u t D e r E i d g . T e c h n i s c h e n H o c h s h u l e Z u r i c h
Z u r i c h 4 d e c . 1 9 3 0 G l o a r i a s t r .
D e a r R a d i o a c t i v e L a d i e s a n d G e n t l e m e n A s t h e b e a r e r p f t h e s e l i n e s w i l l e x p l a i n t o y o u i n m o r e d e t a i l – a n d I b e g y o u t o l i s t e n t o h i m w i t h b e n e v o l e n c e – I h a v e c o n s i d e r e d , i n c o n n e c t i o n w i t h t h e ‘ w r o n g ’ s t a t i s t i c s o f 1 4 N a n d 6 L i a s w e l l a s w i t h t h e c o n t i n u o u s s p e c t r u m , a w a y o u t f o r s a v i n g t h e ‘ l a w o f c h a n g e ’ o f s t a t i s t i c s a n d t h e c o n s e r v a t i o n o f e n e r g y : i . e . t h e p o s s i b i l i t y t h a t i n s i d e t h e n u c l e i t h e r e a r e p a r t i c l e s e l e c t r i c a l l y n e u t r a l , t h a t I w i l l c a l l n e u t r o n s , w h i c h h a v e s p i n ½ a n d f o l l o w t h e e x c l u s i o n p r i n c i p l e a n d t h a t i n a d d i t i o n d i f f e r f r o m p h o t o n s b e c a u s e t h e y d o n o t m o v e w i t h t h e v e l o c i t y o f l i g h t . T h e m a s s o f n e u t r o n s s h o u l d b e o f t h e s a m e o r d e r o f m a g n i t u d e o f t h a t o f t h e e l e c t r o n s a n d a n y h o w n o t g r e a t e r t h a n 0 . 0 1 p r o t o n i c m a s s e s . T h e c o n t i n u o u s s p e c t r u m w o u l d t h e n b e u n d e r s t a n d a b l e , a s s u m i n g t h a t i n t h e d e c a y t o g e t h e r w i t h t h e e l e c t r o n , i n a l l c a s e s , a l s o a n e u t r o n i s e m i t t e d , i n s u c h a w a y t h a t t h e s u m o f t h e e n e r g y o f t h e n e u t r o n a n d o f t h e e l e c t r o n r e m a i n s c o n s t a n t . T h e q u e s t i o n i s n o w t o s e e w h i c h f o r c e s a c t o n t h e n e u t r o n s . T h e m o s t p r o b a b l e m o d e l a p p e a r s t o m e t o b e , f o r w a v e m e c h a n i c a l r e a s o n s ( t h e d e t a i l c a n b e g i v e n t o y o u b y t h e b e a r e r o f t h e s e l i n e s ) , f o r t h e n e u t r o n a t r e s t t o b e a m a g n e t i c d i p o l e p f a c e r t a i n m o m e n t . T h e e x p e r i m e n t a l d a t a c e r t a i n l y r e q u i r e f o r t h e i o n i z i n g p o w e r o f s u c h a n e u t r o n t o b e n o t g r e a t e r t h a n t h a t o f a g a m m a r a y a n d t h e r e f o r e s h o u l d n o t b e g r e a t e r t h a n 1310 e c m . I d o n o t c o n s i d e r a d v i s a b l e , f o r t h e m o m e n t , t o p u b l i s h s o m e t h i n g a b o u t t h e s e i d e a s a n d f i r s t I a p p l y t o w i t h c o n f i d e n c e , d e a r R a d i o a c t i v e s , w i t h t h e q u e s t i o n : w h a t d o y o u t h i n k a b o u t t h e p o s s i b i l i t y o f p r o v i d i n g t h e e x p e r i m e n t a l p r o o f o f s u c h a n e u t r o n , i f i t w o u l d p o s s e s s a p e n e t r a t i n g p o w e r e q u a l o r t e n t i m e s g r e a t e r o f t h a t o f g a m m a r a y s ? I a d m i t t h a t m y s o l u t i o n m a y a p p e a r t o y o u n o t v e r y p r o b a b l e , b e c a u s e i t t h e n e u t r o n w o u l d e x i s t , t h e y w o u l d h a v e b e e n o b s e r v e d l o n g s i n c e . B u t o n l y w h o d a r e s w i n s , a n d t h e g r a v i t y o f t h e s i t u a t i o n i n r e g a r d t o t h e c o n t i n u o u s ? s p e c t r u m i s e n l i g h t e n e d b y t h e o p i n i o n o f m y p r e d e c e s s o r i n t h e c h a i r M r . D e b y e , w h o l o n g s i n c e t o l d m e i n B r u s s e l s : ‘ O h , t h e b e s t t h i n g t o d o i s n o t t o t a l k a b o u t , l i k e f o r n e w t a x e s ’ . F o r t h i s r e a s o n o n e s h o u l d c o n s i d e r s e r i o u s l y a n y w a y t o w a r d s s a f e t y . T h u s , d e a r R a d i o a c t i v e s , c o n s i d e r a n d j u d g e . U n f o r t u n a t e l y I c a n n o t c o m e p e r s o n a l l y t o T u b i n g e n , b e c a u s e I a m n e c e s s a r y h e r e f o r a b a l l t h a t w i l l t a k e p l a c e i n Z u r i c h t h e n i g h t f r o m 6 t o 7 D e c e m b e r . W i t h m a n y g r e e t i n g s t o y o u a s w e l l a s t o M r . B a c k . Y o u r d e v o t e d s e r v a n t , W . P a u l i
“I have done something very bad today by proposing a particle that cannot be detected; it is something no theorist should ever do.”
W. Pauli
A
A’
e
Weak Interactions
is a projection operator onto left-handed states for fermions and right-handed states for antifermions
Only left handed ferminos and right handed anti-fermions participate in weak interactions: Parity violation
5 51 . .2FG l cV A ff h
weakH
51/ 2 1LP
Current-current interaction :Fermi 1934. Paper rejected by ‘Nature’ because “it contained speculations too remote from reality to be of interest to the reader” Modern version:
2F
w
G wH J J
Reines and Cowan: an Audacious Proposal (1946)
•Nuclear reactor will do the same
•1956, Savannah River:”We are happy to inform you (Pauli) that we have definitely detected neutrinos…”
•1995 Nobel Prize for Reines
How Many Neutrinos?
2 2
12( ) e fpeak
e e fZ Z
fs
M
3Z had l N
Energy Spectrum of Solar Neutrinos
•Two body reaction: line
•Three body decay: phase space, like muon decay spectrum
Neutrino survival probability
Small Mixing
E(MeV)
P(
e →
e)
Large Mixing
LOW
Just-so
Night
DayDistortion of the observed energy spectrum differentiates between different oscillations scenarios