Graduiertenkolleg Bullay 12.9.2005 Caren Hagner, Uni Hamburg Neutrino Physics Caren Hagner Universität Hamburg Caren Hagner Universität Hamburg Part 3:

Graduiertenkolleg Bullay 12.9.2005 Caren Hagner, Uni Hamburg

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


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!


Majorana Particles

Because 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

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!


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

m1


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


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

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 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

Ziel:eV20.0

m


Double-beta decayDouble-beta decay

2 - decay

u e -

d

d

e -W

u

e

eW

0 - decay

e -

e -

d

du

u

W

We

e

Lepton number violationΔL = 2

Summenenergie der Elektronen (E/Q)


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


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!

(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


CUORICINO @ Gran Sasso (Start 2003)CUORICINO @ Gran Sasso (Start 2003)

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

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


End part 3

Boris Kayser:(at v2002)


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)

Graduiertenkolleg Bullay 12.9.2005 Caren Hagner, Uni Hamburg Neutrino Physics Caren Hagner Universität Hamburg Caren Hagner Universität Hamburg Part 3:

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