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Neutrino Physics. Part 3: Absolute neutrino mass Introduction beta decay double beta decay. Caren Hagner Universität Hamburg. Neutrinos have mass! m lightest v ?. Evidence f o r Neutrino Oscillations:. (3).

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Neutrino physics

Neutrino Physics

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

Caren Hagner

Universität Hamburg


Evidence f o r neutrino oscillations

Neutrinos have mass! mlightest v ?

Evidence for Neutrino Oscillations:

(3)

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 ≈ 1eV2 (Tested by MiniBooNE)


Nature of neutrino mass i

4 component spinor

The left-handed and right-handed components are:

2 components each

This leads to a system of two coupled equations:

With m=0 one obtains the decoupled Weyl equations:

Nature of Neutrino Mass I

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

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.


Neutrino physics

m

Dirac Mass Term

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

Dirac mass term

Lepton number is conserved!

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

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


Neutrino physics

particle

anti-particle (charge conjugate field):

for a Majorana particle:

observed!

Neutrinos (solar):

not observed!

Anti-neutrinos(reactor):

Majorana Particles

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

Majorana particle

But what about experiments?

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


Neutrino physics

mL

vL

(vL)c

right handed field

left handed field

Majorana Mass Term

is a left-handed field

Note that

is a right-handed field

and

ok!

Let’s try

Lepton number violation!

works too!

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


Neutrino physics

Construct the Majorana fields:

Eigenstates of the interaction: vL and vR

Mass eigenstates: Φ1 (mass mL), Φ2 (mass mR)


Neutrino physics

Dirac-Majorana Mass Term

with

with the mass eigenstates:

and mass eigenvalues:

mass term for each flavor:

mass matrix M

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

find unitary U with


Neutrino physics

What if…

mD

mR

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

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

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

per neutrino flavor: one very light Majorana neutrino v1L = vL one very heavy Majorana neutrino v2L = (vR)c

mD of the order of lepton masses, mR reflects scale of new physics⇒ explains small neutrino masses!


Lower limit of neutrino mass

Lower Limit of Neutrino Mass

Super-K (atmospheric neutrinos): m2atm = 2.5 × 10-3 eV2  m(νi) ≥ 0.05 eV

This sets the energy scalefor mass search!


Which mass hierarchy

v1

v2

v3

v2

Δmsolar

v1

≲ 2 eV

Δmatm

v3

0

quasi-degenerate

inverted hierarchy

Which mass hierarchy?

  • Lightest neutrino mass not known

  • Δm2atm < 0 or >0 ?

v3

Δmatm

0.05 eV

v2

Δmsolar

v1

?

0

normal hierarchy


Neutrino physics

β decay kinematics:

- Microcalorimeters- MAC-E spectrometers

0nbb decay:

76Ge @ LNGS ´90-´03

(71.7 kg×y)

2nbb

NEMO3

|mee|=0.44+0.13-0.2 eV

<m>e < 2eV

astrophysics: supernova time of flight measurements

cosmology &structure formation

187Re

3H

SuperK, SNO, OMNIS + grav.waves:

potential for ~1eV sensitivity?

D.N. Spergel et al:Smn < 0.69 eV (95%CL)

S.W. Allen et al:Smn = 0.56 eV (best fit)

Neutrino Mass Measurements

Strategies

?


Decay

ve

Total kinetic energy Q≈ maximal kinetic energy of electron

β-decay

u

u

n

p

d

d

u

d

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

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

W-

e-


Tritium decay mainz troitsk

Tritium β-Decay: Mainz/Troitsk

E0 = 18.6 keV

dN/dE = K × F(E,Z) × p × Etot × (E0-Ee) × [ (E0-Ee)2 – mn2]1/2


Neutrino physics

Problem: All experiments measured negative Δm2!

Only recently solved by electrostatic spectrometers with MAC-E filter


Neutrino physics

principle of an electrostatic filter with

magnetic adiabatic collimation (MAC-E)

adiabatic magnetic guiding

of b´s along field lines

in stray B-field of

s.c. solenoids:

Bmax = 6 T

Bmin = 3×10-4 T

energy analysis by

static retarding E-field

with varying strength:

high pass filter with

integral b transmission

for E>qU


Neutrino physics

results from the MAINZ experiment

Mainz Data (1998,1999,2001)


Neutrino physics

TheKArlsruhe TRItium Neutrino

Experiment

KATRIN

~70 m beamline, 40 s.c. solenoids


Katrin main spectrometer

Ziel:

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

Commissioning 2008

UHV requirements:

outgassing < 10-13 mbar l/s

inner surface ~ 800m2

volume to pump ~ 1500m3


Neutrino physics

187Re b-decay: m-calorimeters

E0 = 2.46 keV

MIBETA experiment

(Milano, Como, Trento)

array of 10 AgReO4 crystals

M.Sisti et al, NIM A520(2004)125

A.Nucciotti et al, NIM A520(2004)148

C. Arnaboldi et al, PRL 91, 16802 (2003)

Top ~ 70-100mK


Neutrino physics

fit range: 0.9 to 4 keV

fit function

187Re b decay m-calorimeters

Kurie plot of 6.2 ×106187Re b decay events above 700 eV

dN/dE = K × F(E,Z) × p × Etot × (E0-Ee) × [ (E0-Ee)2 – mn2 ]1/2

free fit parameters:

  • b endpoint energy

  • mn2

  • b spectrum normal.

  • pile-up amplitude

  • background level

mn2 = -112 ± 207 ± 90 eV2

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


Double beta decay

-

-

e

-

e

u

e

0n - bb decay

2n - bb decay

d

W

u

W

d

W

d

n

e

u

d

n

e

W

-

e

u

n

n

e

e

Summenenergie der Elektronen (E/Q)

Double-beta decay

Lepton number violation

ΔL = 2


Neutrinoless double beta decay

p

u

0v Double Beta Decay:

n

d

e

W

v = v

W

e

d

n

u

p

Majorana-neutrino:

neutrino  anti-neutrino

(A,Z) (A,Z+2) + 2e-

Neutrinoless Double Beta Decay

only forMajorana-neutrinoandmV > 0!


Neutrinoless double beta decay1

Phase space factor

Effective neutrino mass

Transition matrix element

Effective neutrino mass in 0νββ-decay:

Compare to β-decay:

Neutrinoless Double Beta Decay


Neutrino physics

Cancellation possible!

Complex phases in the mixing matrix

Majorana CP-Phases

Dirac CP-Phase


Neutrino physics

invertierte Hierarchie

in eV

normale Hierarchie

Masse des leichtesten Neutrinos in eV


0v doppel beta experimente ergebnisse

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

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

HM-K

IGEX

2.1 × 1023

all 90%CL

0.85 – 2.1

0v Doppel-Beta Experimente: Ergebnisse


Neutrino physics

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

?

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


Neutrino physics

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


Neutrino physics

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 1/20v (130Te) > 7.5 x 1023 y <mv> < 0.3 - 1. 6 eV

CUORICINO

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


Il progetto cuore

IL PROGETTOCUORE

array of 988 bolometers

grouped in 19 colums with 13 flours of 4 crystals

750 kg TeO2 => 600 kg Te

= 203 kg 130Te


Neutrino physics

20 sectors

B(25 G)

3 m

Magnetic field: 25 Gauss

Gamma shield: Pure Iron (e = 18 cm)

Neutron shield: 30 cm water (ext. wall)

40 cm wood (top and bottom)

(since march 2004: water + boron)

4 m

Able to identify e-, e+, g and a

The NEMO3 detector

Fréjus Underground Laboratory : 4800 m.w.e.

Source: 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


Neutrino physics

Transverse view

Run Number: 2040

Event Number: 9732

Date: 2003-03-20

Longitudinal

view

Vertex

emission

Vertex

emission

Drift distance

Deposited energy:

E1+E2= 2088 keV

Internal hypothesis:

(Dt)mes –(Dt)theo = 0.22 ns

Common vertex:

(Dvertex) = 2.1 mm

(Dvertex)// = 5.7 mm

Criteria to select bb 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 (g rejection)

  • No delayed track (214Bi rejection)

bb events selection in NEMO-3

Typical bb2n event observed from 100Mo

Transverse view

Run Number: 2040

Event Number: 9732

Date: 2003-03-20

Longitudinal

view

100Mo foil

100Mo foil

Geiger plasma

longitudinal

propagation

Scintillator

+ PMT


Neutrino physics

bb2n measurement

bb0n search

bb decay isotopes in NEMO-3 detector

116Cd405 g

Qbb = 2805 keV

96Zr 9.4 g

Qbb = 3350 keV

150Nd 37.0 g

Qbb = 3367 keV

48Ca 7.0 g

Qbb = 4272 keV

130Te454 g

Qbb = 2529 keV

External bkg

measurement

natTe491 g

100Mo6.914 kg

Qbb = 3034 keV

82Se0.932 kg

Qbb = 2995 keV

Cu621 g

(All the enriched isotopes produced in Russia)


Neutrino physics

PRELIMINARY

100Mo

6914 g

216.4 days

4.10 kg.y

Data

-Log(Likelihood)

bb2n

Monte-Carlo

Radon

Monte-Carlo

Data

Nbb0n

bb2n

Monte-Carlo

xbb0n=

Ntot

Radon

Monte-Carlo

Ec1+Ec2 (keV)

bb0n

T1/2 = 3.5 1023

V-A: T1/2(bb0n) > 3.5 1023 y (90% C.L.)

Previous limit V-A: T1/2(bb0n) > 5.5 1022 y (Elegant V, Ejiri et al., 2001)

100Mo bb0n likelihood analysis

100Mo

6914 g

216.4 days

4.10 kg.y

Ec1+Ec2 (keV)

<mv>ee < 0.7 – 1.2 eV

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


Double beta decay future

Double Beta Decay: Future

to t13


Neutrino physics

End part 3


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