Double Beta Decay and Neutrino Masses Amand Faessler Tuebingen

Amand Faessler, Tuebingen

1

Double Beta Decayand

Neutrino Masses

Amand FaesslerTuebingen

Neutrino Masses and the Neutrinoless Double Beta Decay: Dirac versus Majorana NeutrinosAccuracy of the Nuclear Matrix

Elements


2

Neutrinoless Double Beta Decay

The Double Beta Decay:

0+

0+

0+

β-

1+

2-

β-

e- e-

E>2me


3

2νββ-Decay (in SM allowed)

Thesis Maria Goeppert-Mayer1935 Goettingen

P P

n n


4

Oνββ-Decay (forbidden)

only for Majorana Neutrinos ν = νc

P

P

n n

Left

Leftν

Phase Space

106 x 2νββ


5

GRAND UNIFICATION

Left-right Symmetric Models SO(10)

Majorana Mass:


6

P P

νν

n n

e-

e-

L/R l/r


7

l/r

P

ν

P

l/r

n n

light ν

heavy N

Neutrinos


8

Supersymmetry

Bosons ↔ Fermions--------------------------------------------------------------------

---

Neutralinos

P P

e- e-

n n

u

u u

ud d

Proton Proton

Neutron Neutron


9

Theoretical Description:

Simkovic, Rodin, Haug, Kovalenko, Vergados, Kosmas, Schwieger, Raduta, Kaminski, Gutsche, Bilenky, Vogel et al.

0+

0+

0+

1+

2-

k

k

ke1

e2PP

ν Ek

Ein n

0νββ


10


11

The best choice:

Quasi-Particle-

(a) Quasi-Boson-Approx.:

(b) Particle Number non-conserv.(important near closed shells)

(c) Unharmonicities(d) Proton-Neutron Pairing

Pairing


12


13

Nucleus 48Ca 76Ge 82Se 96Zr 100Mo 116Cd 128Te 130Te 134Xe 136Xe

150Nd

T1/2 (exp)[years]

>9.51021

>1.91025

>1.41022

>1.01021

>5.51022

>7.01022

>8.61022

>1.41022

>5.81022

>7.01023

>1.71021

Ref.: You Klap-dor

Elli-ott

Arn. Ejiri Dane-vich

Ales.

Ales. Ber. Staudt

Klimenk.

<m>[eV] <22.

<0.47

<8.7

<40.

<2.8 <3.8 <17.

<3.2 <27. <3.8

<7.2

η~m(p)/M(

<200.

<0.79

<15.

<79.

<6.0 <7.0 <27.

<4.9 <38. <3.5

<13.

λ‘(111)[10-4] <8.9

<1.1 <5.0

<9.4

<2.8 <3.4 <5.8

<2.4 <6.8 <2.1

<3.8

Only for Majorana ν possible.


14

gPP fixed to 2νββ; M(0) [MeV**(-1)]

Each point: (3 basis sets) x (3 forces) = 9 values


15


16

Neutrinoless Double Beta Decay and the Sensitivity to the Neutrino Mass

of planed Experiments


17

Neutrino-Masses from the 0ν

and Neutrino Oscillations

Solar Neutrinos (CL, Ga, Kamiokande, SNO)Atmospheric ν (Super-Kamiokande)Reactor ν (Chooz; KamLand)

with CP-Invariance:


18

Solar Neutrinos (+KamLand):

(KamLand)

Atmospheric Neutrinos: (Super-Kamiok.)


19

Reactor Neutrinos (Chooz):

CP


20

ν1, ν2, ν3 Mass States

νe, νμ, ντ Flavor States

Theta(1,2) = 32.6 degrees Solar + KamLandTheta(1,3) < 13 degrees ChoozTheta(2,3) = 45 degrees S-Kamiokande


21

OSCILLATIONS AND DOUBLE BETA DECAY

Hierarchies: mν

Normal

m3

m2

m1

m1<<m2<<m3

Inverted m2

m1

m3

m3<<m1<<m2

Bilenky, Faessler, Simkovic P. R. D 70(2004)33003


22

(Bild)


23

Summary:Accuracy of Neutrino

Masses from 0

Fit the g(pp) by in front of the proton-neutron Gamow-Teller NN matrixelement include exp. Error of .

Calculate with these g(pp) for three different forces (Bonn, Nijmegen, Argonne) and three different basis sets the

Use QRPA and R-QRPA (Pauli principle)

Use: g(A) = 1.25 and 1.00

Error of matrixelement 20 to 50 % (large errors from experim value of T(1/2, 2))


24

Summary:Results from

<m()>(GeExp. Klapdor) 0.47 [eV]

<M(heavy >[GeV]

<M(heavy Vector B)> > 5600 [GeV]

SUSY+R-Parity: ‘(1,1,1) < 1.1*10**(-4)

Mainz-Troisk: m(2.2 [eV]

Astro Physics (SDSS): Sum{ m() } < 1 to 2 [eV]

Klapdor et al. from Ge76 with R-QRPA (no error of theory included):

0.15 to 0.72 [eV], if confirmed.

THE END

THE END 25

Summary:Accuracy of Neutrino

Masses by the Double Beta Decay

Dirac versus Majorana NeutrinosGrand Unified Theories (GUT‘s), R-Parity violatingSupersymmetry

→Majorana-Neutrino = Antineutrinos

<m(eV; ‘ < 1.1*10**(-4)

Direct measurement in the Tritium Beta Decay in Mainz and Troisk

Klapdor et al.: <mββ> = 0.1 – 0.9 [eV] ; R-QRPA: 0.15 – 0.72 [eV]

n n

nn

PP

P P

d

d

d

d

u u

u

u u

u


26

3. Neutrino Masses and Supersymmetry

R-Parity violating Supersymmetry mixes Neutrinos with Neutrinalinos (Photinos, Zinos, Higgsinos) and Tau-Susytau-Loops, Bottom-Susybottom-Loops → Majorana-Neutrinos (Faessler, Haug, Vergados: Phys. Rev. D )

m(neutrino1) = ~0 – 0.02 [eV] m(neutrino2) = 0.002 – 0.04 [eV] m(neutrino3) = 0.03 – 1.03 [eV]

0-Neutrino Double Beta decay <mββ> = 0.009 - 0.045 [eV]

ββ Experiment: <mββ> < 0.47 [eV]

Klapdor et al.: <mββ> = 0.1 – 0.9 [eV]

Tritium (Otten, Weinheimer, Lobashow) <m> < 2.2 [eV]

THE END


27

ν-Mass-Matrix by Mixing with:

Diagrams on the Tree level:

Majorana Neutrinos:


28

Loop Diagrams:

Figure 0.1: quark-squark 1-loop contribution to mv

X

X

Majorana

Neutrino


29

Figure 0.2: lepton-slepton 1-loop contribution to mv

(7x7) Mass-Matrix:

X

X

Block

Diagonalis.


30

7 x 7 Neutrino-Massmatrix:

Basis: Eliminate Neutralinos in 2. Order:

separabel

{ Mass Eigenstate

Vector in

flavor space

for 2 independent

and possible


31

Super-K:


32

Horizontal U(1) Symmetry

U(1) FieldU(1) chargeR-Parity breaking terms must be without U(1) charge change (U(1) charge

conservat.)Symmetry Breaking:


33

How to calculate λ‘i33 (and λi33) from λ‘333?

U(1) charge conserved!

1,2,3 = families

Double Beta Decay and Neutrino Masses Amand Faessler Tuebingen

Documents

Transcript of Double Beta Decay and Neutrino Masses Amand Faessler Tuebingen