Amand Faessler, GERDA, 11. November 20051 Double Beta Decay and Neutrino Masses Amand Faessler...

31
Amand Faessler, GERDA, 1 1. November 2005 1 Double Beta Decay and Neutrino Masses Amand Faessler Tuebingen Accuracy of the Nuclear Matrix Elements. It determines the Error of the Majorana Neutrino Mass extracted

Transcript of Amand Faessler, GERDA, 11. November 20051 Double Beta Decay and Neutrino Masses Amand Faessler...

Page 1: Amand Faessler, GERDA, 11. November 20051 Double Beta Decay and Neutrino Masses Amand Faessler Tuebingen Accuracy of the Nuclear Matrix Elements. It determines.

Amand Faessler, GERDA, 11. November 2005

1

Double Beta Decayand

Neutrino MassesAmand Faessler

Tuebingen

Accuracy of the Nuclear Matrix Elements.

It determines the Error of the Majorana Neutrino Mass extracted

Page 2: Amand Faessler, GERDA, 11. November 20051 Double Beta Decay and Neutrino Masses Amand Faessler Tuebingen Accuracy of the Nuclear Matrix Elements. It determines.

Amand Faessler, GERDA, 11. November 2005

4

Oνββ-Decay (forbidden)

only for Majorana Neutrinos ν = νc

P

P

n n

Left

Leftν

Phase Space

106 x 2νββ

Page 3: Amand Faessler, GERDA, 11. November 20051 Double Beta Decay and Neutrino Masses Amand Faessler Tuebingen Accuracy of the Nuclear Matrix Elements. It determines.

Amand Faessler, GERDA, 11. November 2005

5

GRAND UNIFICATION

Left-right Symmetric Models SO(10)

Majorana Mass:

Page 4: Amand Faessler, GERDA, 11. November 20051 Double Beta Decay and Neutrino Masses Amand Faessler Tuebingen Accuracy of the Nuclear Matrix Elements. It determines.

Amand Faessler, GERDA, 11. November 2005

6

P P

νν

n n

e-

e-

L/R l/r

Page 5: Amand Faessler, GERDA, 11. November 20051 Double Beta Decay and Neutrino Masses Amand Faessler Tuebingen Accuracy of the Nuclear Matrix Elements. It determines.

Amand Faessler, GERDA, 11. November 2005

7

l/r

P

ν

P

l/r

n n

light ν

heavy N

Neutrinos

l/r

L/R

Page 6: Amand Faessler, GERDA, 11. November 20051 Double Beta Decay and Neutrino Masses Amand Faessler Tuebingen Accuracy of the Nuclear Matrix Elements. It determines.

Amand Faessler, GERDA, 11. November 2005

8

Supersymmetry

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

---

Neutralinos

Neutralinos

P P

e- e-

n n

u

u u

ud d

Proton Proton

Neutron Neutron

Page 7: Amand Faessler, GERDA, 11. November 20051 Double Beta Decay and Neutrino Masses Amand Faessler Tuebingen Accuracy of the Nuclear Matrix Elements. It determines.

Amand Faessler, GERDA, 11. November 2005

9

Theoretical Description:Simkovic, Rodin, Benes, Vogel, Bilenky,

Salesh, Gutsche, Pacearescu, Haug, Kovalenko, Vergados, Kosmas, Schwieger,

Raduta, Kaminski, Stoica, Suhonen, Civitarese, Tomoda et al.

0+

0+

0+

1+

2-

k

k

ke1

e2PP

ν Ek

Ein n

0νββ

Page 8: Amand Faessler, GERDA, 11. November 20051 Double Beta Decay and Neutrino Masses Amand Faessler Tuebingen Accuracy of the Nuclear Matrix Elements. It determines.

Amand Faessler, GERDA, 11. November 2005

10

Neutrinoless Double Beta-

Decay Probability

Page 9: Amand Faessler, GERDA, 11. November 20051 Double Beta Decay and Neutrino Masses Amand Faessler Tuebingen Accuracy of the Nuclear Matrix Elements. It determines.

Amand Faessler, GERDA, 11. November 2005

11

Effective Majorana Neutrino-Mass

for the 0Decay

CP

Tranformation from Mass to Flavor Eigenstates

Page 10: Amand Faessler, GERDA, 11. November 20051 Double Beta Decay and Neutrino Masses Amand Faessler Tuebingen Accuracy of the Nuclear Matrix Elements. It determines.

Amand Faessler, GERDA, 11. November 2005

12

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:

Page 11: Amand Faessler, GERDA, 11. November 20051 Double Beta Decay and Neutrino Masses Amand Faessler Tuebingen Accuracy of the Nuclear Matrix Elements. It determines.

Amand Faessler, GERDA, 11. November 2005

13

ν1, ν2, ν3 Mass States

νe, νμ, ντ Flavor States

Theta12 = 32.6 degrees Solar + KamLand

Theta13 < 13 degrees Chooz

Theta23 = 45 degrees S-Kamiokande

m 212(solar

8eV

m223atmosphericeV

Page 12: Amand Faessler, GERDA, 11. November 20051 Double Beta Decay and Neutrino Masses Amand Faessler Tuebingen Accuracy of the Nuclear Matrix Elements. It determines.

Amand Faessler, GERDA, 11. November 2005

14

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

Page 13: Amand Faessler, GERDA, 11. November 20051 Double Beta Decay and Neutrino Masses Amand Faessler Tuebingen Accuracy of the Nuclear Matrix Elements. It determines.

Amand Faessler, GERDA, 11. November 2005

15

Bilenky, Faessler, Simkovic:, Phys.Rev. D70:033003(2004) : hep-ph/0402250

Page 14: Amand Faessler, GERDA, 11. November 20051 Double Beta Decay and Neutrino Masses Amand Faessler Tuebingen Accuracy of the Nuclear Matrix Elements. It determines.

Amand Faessler, GERDA, 11. November 2005

17

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

Page 15: Amand Faessler, GERDA, 11. November 20051 Double Beta Decay and Neutrino Masses Amand Faessler Tuebingen Accuracy of the Nuclear Matrix Elements. It determines.

Amand Faessler, GERDA, 11. November 2005

18

Page 16: Amand Faessler, GERDA, 11. November 20051 Double Beta Decay and Neutrino Masses Amand Faessler Tuebingen Accuracy of the Nuclear Matrix Elements. It determines.

Amand Faessler, GERDA, 11. November 2005

20

Contribution of Different Multipoles to M(0)

Page 17: Amand Faessler, GERDA, 11. November 20051 Double Beta Decay and Neutrino Masses Amand Faessler Tuebingen Accuracy of the Nuclear Matrix Elements. It determines.

Amand Faessler, GERDA, 11. November 2005

21

g(A)**4 = 1.25**4 = 2.44 fit to 2

Rodin, Faessler, Simkovic, Vogel, Mar 2005 nucl-th/0503063

Page 18: Amand Faessler, GERDA, 11. November 20051 Double Beta Decay and Neutrino Masses Amand Faessler Tuebingen Accuracy of the Nuclear Matrix Elements. It determines.

Amand Faessler, GERDA, 11. November 2005

27

2.76 (QRPA) 2.34 (RQRPA) Muto corrected

Page 19: Amand Faessler, GERDA, 11. November 20051 Double Beta Decay and Neutrino Masses Amand Faessler Tuebingen Accuracy of the Nuclear Matrix Elements. It determines.

Amand Faessler, GERDA, 11. November 2005

28

M0ν (QRPA)

O. Civitarese, J. Suhonen, NPA 729 (2003) 867

Nucleus their(QRPA, 1.254) our(QRPA, 1.25)

76Ge 3.33 2.68(0.12) 100Mo 2.97 1.30(0.10) 130Te 3.49 1.56(0.47) 136Xe 4.64 0.90(0.20)

g(pp) fitted differently

Higher order terms of nucleon Current included differently with Gaussian form

factors based on a special quark model ( Kadkhikar, Suhonen, Faessler, Nucl. Phys. A29(1991)727). Does neglect pseudoscalar coupling (see eq. (19a)), which is an effect of 30%.

We: Higher order currents from Towner and Hardy.

What is the basis and the dependence on the size of the basis?

Short-range Brueckner Correlations not included. But finite size effects included.

We hope to understand the differences. But for that we need to know their input parameters ( g(pp), g(ph),basis, …)!

Page 20: Amand Faessler, GERDA, 11. November 20051 Double Beta Decay and Neutrino Masses Amand Faessler Tuebingen Accuracy of the Nuclear Matrix Elements. It determines.

Amand Faessler, GERDA, 11. November 2005

29

Neutrinoless Double Beta Decay

The Double Beta Decay:

0+

0+

0+

β-

1+

2-

β-

e- e-

E>2me

x x x

xxx Gamov-Teller single beta decay in the second leg fitted with g(pp) by Suhonen et al.. Underestimates the first leg.

We fit the full 2decay by adjusting g(pp).

Page 21: Amand Faessler, GERDA, 11. November 20051 Double Beta Decay and Neutrino Masses Amand Faessler Tuebingen Accuracy of the Nuclear Matrix Elements. It determines.

Amand Faessler, GERDA, 11. November 2005

30

Fit of g(pp) to the single beta (2. leg) and the 2 double beta decay (small and large basis).

Fit to 2

Fit to 1+ to 0+

Page 22: Amand Faessler, GERDA, 11. November 20051 Double Beta Decay and Neutrino Masses Amand Faessler Tuebingen Accuracy of the Nuclear Matrix Elements. It determines.

Amand Faessler, GERDA, 11. November 2005

32

Uncorrelated and Correlated Relative N-N-

Wavefunctionin the N-N-Potential

Short Range Correlations

Page 23: Amand Faessler, GERDA, 11. November 20051 Double Beta Decay and Neutrino Masses Amand Faessler Tuebingen Accuracy of the Nuclear Matrix Elements. It determines.

Amand Faessler, GERDA, 11. November 2005

33

Jastrow-Function multiplying the relative

N-N wavefunction

(Parameters from Miller and Spencer, Ann. Phys 1976)

Page 24: Amand Faessler, GERDA, 11. November 20051 Double Beta Decay and Neutrino Masses Amand Faessler Tuebingen Accuracy of the Nuclear Matrix Elements. It determines.

Amand Faessler, GERDA, 11. November 2005

34

Influence of Short Range Correlations

(Parameters from Miller and Spencer, Ann. Phys 1976)

Page 25: Amand Faessler, GERDA, 11. November 20051 Double Beta Decay and Neutrino Masses Amand Faessler Tuebingen Accuracy of the Nuclear Matrix Elements. It determines.

Amand Faessler, GERDA, 11. November 2005

35

Contribution of Different Multipoles to the zero Neutrino

Matrixelements in QRPAs.r.c. = short range correlations

h.o.t. = higher order currents

Different Multipoles

a) 76Ge small model space ( 9 levels) b) 76Ge large model space (21 levels)

C) 100Mo small model space ( 13 levels) d) 100Mo large model space ( 21 levels)

Page 26: Amand Faessler, GERDA, 11. November 20051 Double Beta Decay and Neutrino Masses Amand Faessler Tuebingen Accuracy of the Nuclear Matrix Elements. It determines.

Amand Faessler, GERDA, 11. November 2005

36

Comparison of 2Half Lives with Shell model Results from Strassburg

Page 27: Amand Faessler, GERDA, 11. November 20051 Double Beta Decay and Neutrino Masses Amand Faessler Tuebingen Accuracy of the Nuclear Matrix Elements. It determines.

Amand Faessler, GERDA, 11. November 2005

46

Neutrinoless Double Beta Decay and the Sensitivity to the Neutrino Mass

of planed Experiments

expt. T1/2

[y]

<mv>

[eV]DAMA (136Xe)

1.2 X 1024 2.3

MAJORANA (76Ge)

3 X 1027 0.044

EXO 10t (136Xe)

4 X 1028 0.012

GEM (76Ge)

7 X 1027 0.028

GERDA II(76Ge)

1 X 1026 0.16

CANDLES (48Ca)

1 X 1026 0.2

MOON (100Mo)

1 X 1027 0.058

Page 28: Amand Faessler, GERDA, 11. November 20051 Double Beta Decay and Neutrino Masses Amand Faessler Tuebingen Accuracy of the Nuclear Matrix Elements. It determines.

Amand Faessler, GERDA, 11. November 2005

47

Neutrinoless Double Beta Decay and the Sensitivity to the Neutrino Mass

of planed Experiments

expt. T1/2

[y]

<mv>

[eV]XMASS (136Xe)

3 X 1026 0.10

CUORE (130Te)

2 X 1026 0.10

COBRA (116Cd)

1 X 1024 1

DCBA (100Mo)

2 X 1026 0.07

DCBA (82Se)

3 X 1026 0.04

CAMEO (116Cd)

1 X 1027 0.02

DCBA (150Nd)

1 X 1026 0.02

Page 29: Amand Faessler, GERDA, 11. November 20051 Double Beta Decay and Neutrino Masses Amand Faessler Tuebingen Accuracy of the Nuclear Matrix Elements. It determines.

Amand Faessler, GERDA, 11. November 2005

54

Summary:Accuracy of Neutrino

Masses from 0

Fit the g(pp) by in front of the particle-particle NN matrixelement include exp. Error of .

Calculate with these g(pp) for three different forces (Bonn, Nijmegen, Argonne) and three different basis sets (small about 2 shells, intermediate 3 shells and large 5 shells) the

Use QRPA and R-QRPA (Pauli principle)

Use: g(A) = 1.25 and 1.00

Error of matrixelement 20 to 40 % (96Zr larger; largest errors from experim. values of T(1/2, 2))

Core overlap reduction by ~0.85 (preliminary)

Page 30: Amand Faessler, GERDA, 11. November 20051 Double Beta Decay and Neutrino Masses Amand Faessler Tuebingen Accuracy of the Nuclear Matrix Elements. It determines.

Amand Faessler, GERDA, 11. November 2005

55

Summary:Results from

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

Klapdor et al. from Ge76 with R-QRPA (no error of theory included): 0.15 to 0.72 [eV].

<M(heavy >[GeV]

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

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

Mainz-Troisk, Triton Decay: m(2.2 [eV]

Astro Physics (SDSS): Sum{ m() } < ~0.5 to 2 [eV]

Do not take democratic averaged matrix elements !!!

THE END

Page 31: Amand Faessler, GERDA, 11. November 20051 Double Beta Decay and Neutrino Masses Amand Faessler Tuebingen Accuracy of the Nuclear Matrix Elements. It determines.

Amand Faessler, GERDA, 11. November 2005

56

Open Problems:1. Overlapping but slightly different

Hilbert space in intermediate Nucleus for QRPA from intial and from final nucleus.

2. Pairing does not conserve Nucleon

number. Problem at closed shells. Particle projection. Lipkin-Nogami <N>, <N2>

3. Deformed nuclei?