Neutrino PhysicsNeutrino PhysicsCaren Hagner

Universität Hamburg

Caren Hagner

Universität Hamburg

Part 3: Absolute neutrino mass Introduction beta decay double beta decay

Part 3: Absolute neutrino mass Introduction beta decay double beta decay

Evidence for Neutrino Oscillations:Evidence for Neutrino Oscillations:

Neutrino oscillations were observed in 2 regions:

• Solar neutrinos and reactor neutrinosve → vμ,τ with Δm2 ≈ 8·10-5 eV2, large mixing

• Atmospheric neutrinos and accelerator neutrinosvμ → vτ,(s) mit Δm2 ≈ 2·10-3 eV2, maximal mixing

• LSND? Anti-vμ → Anti-ve with Δm2 ≈ 1 eV2

(Tested by MiniBooNE)

Neutrino oscillations were observed in 2 regions:

• Solar neutrinos and reactor neutrinosve → vμ,τ with Δm2 ≈ 8·10-5 eV2, large mixing

• Atmospheric neutrinos and accelerator neutrinosvμ → vτ,(s) mit Δm2 ≈ 2·10-3 eV2, maximal mixing

• LSND? Anti-vμ → Anti-ve with Δm2 ≈ 1 eV2

(Tested by MiniBooNE)

Neutrinos have mass! mlightest v ?

(3)(3)

Nature of Neutrino Mass I

Neutrino fields v(x) with mass m are described by the Dirac equation: 0)()( xvmi

The left-handed and right-handed components are:

)(2

1)( 5 xvxvL

)(

2

1)( 5 xvxvR

This leads to a system of two coupled equations:

0 RL mvvi 0 LR mvvi

With m=0 one obtains the decoupled Weyl equations: 0, RLvi

From Goldhaber experiment one knows that vL is realized.With m=0 there is no need to have vR. Therefore there were no vR in the Standard Model.

4 component spinor

2 components each

Dirac mass term..chvvmL LRD

Dirac Mass Term

The neutrino mass term in L could have exactly the same formas the mass term of the quarks and charged leptons:

LvRvm

Must add vR (right handed SU(2) singlets) to standard model!Problem: When the mechanism is the same, why are the masses so small?

mt = 174.3 ± 5.1 GeV; mb = (4.0-4.5) GeV;mτ = 1776.99 ± 0.29 MeV; m3 < 2eV

Lepton number is conserved!

Footnote: A Lorentz invariant mass term must link a chirally left-handed field with a chirally right handed field

Majorana ParticlesBecause neutrinos carry no electric charge(and no color charge), there is the possibility: particle ≡ anti-particle

Majorana particle

particleanti-particle (charge conjugate field):

Tc C M

cM for a Majorana particle:

But what about experiments?

Anti-neutrinos(reactor):

Neutrinos (solar):

-3737 eArCl ev-3737 eArCl ev

observed!

not observed!

There are two different states per flavorbut the difference could be due to left-handed and right-handed states!

-3737 eArCl eRv

-3737 eArCl eLv

Majorana Mass Term

Lcc

R vv )()( Note that

is a left-handed field

Rcc

L vv )()( and is a right-handed field

Footnote: A Lorentz invariant mass term must link a chirally left-handed field with a chirally right handed field

cLLLc

LL

M vvvvm

LL

)()(2

Let’s try

vL

left handed field

(vL)c

right handed field

mL

ok!

cRRRc

RR

M vvvvm

LR

)()(2

works too!

Lepton number violation!

cLLLc

LL

M vvvvm

LL

)()(2

cRRRc

RR

M vvvvm

LR

)()(2

112 LM mLL

222 RM mLR

cLL vv )(1 c

RR vv )(2 Construct the Majorana fields:

c)( 2,12,1

Eigenstates of the interaction: vL and vRMass eigenstates: Φ1 (mass mL), Φ2 (mass mR)

Dirac-Majorana Mass Term

h.c. )(

)(,2

R

cL

RD

DLcRLDM

v

v

mm

mmvvL

mass matrix M

mass term for each flavor:

In order to obtain the mass eigenstates one must diagonalize M:

2

1

0

0~m

mMUUMfind unitary U

with

cossin

sincosU with

LR

D

mm

m

22tan

with the mass eigenstates:

c

R

L

L

L

v

vU

v

v

)(2

1

and mass eigenvalues:

222,1 4)()(

2

1DRLLR mmmmmm

What if…1. mL = mR = 0: pure Dirac case θ = 45, m1=m2=mD. 2 degenerate Majorana states can be combined to form 1 Dirac state.

2. mD = 0: pure Majorana case θ = 0, m1=mL m2=mR

3. mR≫ mD, mL= 0: seesaw model θ = mD/mR≪ 1

,2

1R

D

m

mm Rmm 2

per neutrino flavor: one very light Majorana neutrino v1L = vL

one very heavy Majorana neutrino v2L = (vR)cmD of the order of lepton masses, mR reflects scale of new physics⇒ explains small neutrino masses!

mR

mD

Lower Limit of Neutrino MassLower Limit of Neutrino Mass

Super-K (atmospheric neutrinos): m2

atm = 2.5 × 10-3 eV2

m(νi) ≥ 0.05 eV

Super-K (atmospheric neutrinos): m2

atm = 2.5 × 10-3 eV2

m(νi) ≥ 0.05 eV

This sets the energy scalefor mass search!

This sets the energy scalefor mass search!

Which mass hierarchy?

v1

v2Δmsolar

v3

Δmat

m

inverted hierarchy

v3

v1

v2Δmsolar

Δmat

m

normal hierarchy

0.05 eV

- Lightest neutrino mass not known

- Δm2atm < 0 or >0 ?

?0

v3v1 v2

≲ 2 eV

quasi-degenerate

0

Neutrino Mass Measurements Strategies

cosmology &structure formation

D.N. Spergel et al: m < 0.69 eV (95%CL)S.W. Allen et al: m = 0.56 eV (best fit)

0 decay:

NEMO3

76Ge @ LNGS ´90-´03(71.7 kg×y)

|mee|=0.44+0.13-0.2 eV

2

SuperK, SNO, OMNIS + grav.waves: potential for ~1eV sensitivity?

astrophysics: supernova time of flight measurements

?3H

187Re

β decay kinematics:- Microcalorimeters- MAC-E spectrometers

<m>e < 2eV

β-decay

udd

udu

n p

W-

e-

ve

q = 2/3 - 1/3 -1/3 = 0

q = 2/3 + 2/3 -1/3 = 1

evepn

eve )1ZA,()ZA,(

Total kinetic energy Q≈ maximal kinetic energy of electron

Tritium β-Decay: Mainz/TroitskTritium β-Decay: Mainz/Troitsk

e -33 eHe H e -33 eHe H

222i

iei mUm

E0 = 18.6 keV

dN/dE = K × F(E,Z) × p × Etot × (E0-Ee) × [ (E0-Ee)2 – m2 ]1/2

Problem: All experiments measured negative Δm2!

Only recently solved by electrostatic spectrometers with electrostatic spectrometers with MAC-E filter MAC-E filter

principle of an electrostatic filter withprinciple of an electrostatic filter withmagnetic adiabatic collimation (MAC-E)magnetic adiabatic collimation (MAC-E)

adiabatic magnetic guiding of ´s along field lines in stray B-field of s.c. solenoids:Bmax = 6 TBmin = 3×10-4 T

energy analysis bystatic retarding E-fieldwith varying strength:

high pass filter withintegral transmissionfor E>qU

results from the MAINZ experimentresults from the MAINZ experiment

CL%95eV2.2eV1.22.22.1 22

mm

Mainz Data (1998,1999,2001)

KATRIN

~70 m beamline, 40 s.c. solenoids

The KArlsruhe TRItium Neutrino Experiment

KATRIN Main Spectrometer stainless steel vessel (Ø=10m & l=22m) on HV potential minimisation of bg UHV: p ≤ 10-11 mbar

„massless“ inner electrode system

UHV requirements:outgassing < 10-13 mbar l/sinner surface ~ 800m2

volume to pump ~ 1500m3

Ziel:eV20.0

m

Commissioning 2008

187187Re Re -decay: -decay: -calorimeters-calorimeters

MIBETA experiment(Milano, Como, Trento)array of 10 AgReO4 crystals

M.Sisti et al, NIM A520(2004)125A.Nucciotti et al, NIM A520(2004)148C. Arnaboldi et al, PRL 91, 16802 (2003)

E0 = 2.46 keV

Top ~ 70-100mK

free fit parameters:

endpoint energy

m2

spectrum normal.

pile-up amplitude

background level

187187Re Re decay decay -calorimeters -calorimeters Kurie plot of 6.2 ×106 187Re decay events above 700 eV

fit range: 0.9 to 4 keV

fit function

m2 = -112 ± 207 ± 90 eV2

m < 15 eV (90%CL) (2 eV in 2007?)

dN/dE = K × F(E,Z) × p × Etot × (E0-Ee) × [ (E0-Ee)2 – m2 ]1/2

Double-beta decayDouble-beta decay2 - decay

u e -

d

d

e -W

u

e

eW

0 - decay

e -

e -

d

du

u

W

We e

Lepton number violationΔL = 2

Lepton number violationΔL = 2

Summenenergie der Elektronen (E/Q)

Neutrinoless Double Beta DecayNeutrinoless Double Beta Decay

d

d

u

u

e

eW

W

n

n

p

p

v = v

0v Double Beta Decay:

(A,Z) (A,Z+2) + 2e- neutrino anti-neutrinoneutrino anti-neutrino

Majorana-neutrino:Majorana-neutrino:

only forMajorana-neutrino

andmV > 0!

Neutrinoless Double Beta DecayNeutrinoless Double Beta Decay

3

1

2

ieiiUmm

Effective neutrino mass in 0νββ-decay:

22

02

20

0010

2/1 ),(][

vF

A

VGT mM

g

gMZEGT

222 i

eii Umm

Compare to β-decay:

Phase space factor Transition matrix

element

Effective neutrino mass

3

2

1

132313231223121323122312

132313231223121323122312

1313121312

21

21

21

][

][

iiii

iiii

iiie

ecceescsscesccss

ecseesssccessccs

eesecscc

Dirac CP-PhaseDirac CP-Phase

Majorana CP-PhasesMajorana CP-Phases

Complex phases in the mixing matrixComplex phases in the mixing matrix

21 233

222

211

3

1

2

ie

iee

ieii eUmeUmUmUmm

Cancellation possible!

m

in eV

Masse des leichtesten Neutrinos in eV

normale Hierarchie

invertierte Hierarchie

22

02

20

0010

2/1 ),(][

vF

A

VGT mM

g

gMZEGT

0v Doppel-Beta Experimente: Ergebnisse0v Doppel-Beta Experimente: Ergebnisse

CL) (90% eV 35.0

mHeidelberg-Moskau Collaboration, Eur.Phys.J. A12 (2001) 147

IGEX Collaboration, hep-ex/0202026, Phys. Rev. C59 (1999) 2108

2.1 × 1023 0.85 – 2.1

all 90%CLall 90%CL

HM-K

IGEX

Jedoch: ein Teil der HdM Kollaboration veröffentlicht Evidenz für 0v Doppel-Beta Zerfall!

Jedoch: ein Teil der HdM Kollaboration veröffentlicht Evidenz für 0v Doppel-Beta Zerfall!

(Q = 2039 keV für 76Ge Doppel-Beta Zerfall)

?

Zukunft: Heidelberg Ge Initiative (MPIK Heidelberg)Zukunft: Heidelberg Ge Initiative (MPIK Heidelberg)

Phase I: 20kg angereichertes (86%) 76Ge, vgl. HDMPhase II: 100 kgJahre, 0.1 – 0.3 eVPhase III: O(1t) angereichertes 76Ge, 10meV

Phase I: 20kg angereichertes (86%) 76Ge, vgl. HDMPhase II: 100 kgJahre, 0.1 – 0.3 eVPhase III: O(1t) angereichertes 76Ge, 10meV

CUORICINOCUORICINO

11 modules, 4 detector each,crystal dimension 5x5x5 cm3

crystal mass 790 g

4 x 11 x 0.79 = 34.76 kg of TeO2

2 modules, 9 detector each,crystal dimension 3x3x6 cm3

crystal mass 330 g

9 x 2 x 0.33 = 5.94 kg of TeO2

2v Doppelbeta mit 130Te (Q=2529 keV)

18 crystals 3x3x6 cm3 + 44 crystals 5x5x5 cm340.7 kg of TeO2

Start in 2003

Suche nach 0v Doppelbeta:T 1/2 0v (130Te) > 7.5 x 1023 y <mv> < 0.3 - 1. 6 eV

2v Doppelbeta mit 130Te (Q=2529 keV)

18 crystals 3x3x6 cm3 + 44 crystals 5x5x5 cm340.7 kg of TeO2

Start in 2003

Suche nach 0v Doppelbeta:T 1/2 0v (130Te) > 7.5 x 1023 y <mv> < 0.3 - 1. 6 eV

array of 988 bolometersgrouped in 19 colums with 13 flours of 4 crystals

750 kg TeO2

=> 600 kg Te

= 203 kg 130Te

IL PROGETTO CUOREIL PROGETTO CUORE

3 m

4 m

B (25 G)

20 sectorsSource: 10 kg of isotopes cylindrical, S = 20 m2, e ~ 60 mg/cm2

Tracking detector: drift wire chamber operating in Geiger mode (6180 cells)Gas: He + 4% ethyl alcohol + 1% Ar + 0.1% H2O

Calorimeter: 1940 plastic scintillators coupled to low radioactivity PMTs

Magnetic field: 25 GaussGamma shield: Pure Iron (e = 18 cm)Neutron shield: 30 cm water (ext. wall)

40 cm wood (top and bottom) (since march 2004: water boron)

Able to identify e, e, and

The NEMO3 detector Fréjus Underground Laboratory : 4800 m.w.e.

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

100Mo 6.914 kg Q= 3034 keV

decay isotopes in NEMO-3 detector

82Se 0.932 kg Q= 2995 keV

116Cd 405 g Q= 2805 keV

96Zr 9.4 g Q= 3350 keV

150Nd 37.0 g Q= 3367 keV

Cu 621 g

48Ca 7.0 g Q= 4272 keV

natTe 491 g

130Te 454 g Q= 2529 keV

measurement

External bkg measurement

search (All the enriched isotopes produced in Russia)

100Mo likelihood analysis

Ec1+Ec2 (keV)

Data

Monte-Carlo

RadonMonte-Carlo

100Mo 6914 g

216.4 days4.10 kg.y

PRELIMINARY

Xavier Sarazin for the NEMO-3 Collaboration Neutrino 2004 Paris 14-19 June 2004

DataMonte-CarloRadonMonte-CarloT1/2 = 3.5 1023

100Mo 6914 g

216.4 days4.10 kg.y

Ec1+Ec2 (keV)

Previous limit V-A: T1/2() > 5.5 1022 y (Elegant V, Ejiri et al., 2001)

V-A: T1/2() > 3.5 1023 y (90% C.L.)

-Log

(Lik

elih

ood)

x NNtot

<mv>ee < 0.7 – 1.2 eV

Double Beta Decay: FutureDouble Beta Decay: Future

to t13

End part 3