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