Amand Faesler, University of Tuebingen, Germany. Short Range Nucleon-Nucleon Correlations, the Neutrinoless Double Beta Decay and the Neutrino Mass.

Why does the Neutrinoless Double Beta Decay depend on the Short Range Nucleon- Nucleon Correlations (SRC)? 1. Two-Neutrino Double Beta Decay does not depend on SRC. Why? 2. The Neutrinoless double beta Decay depends on the SRC. Why? Amand Faessler, October 2015

2 νββ -Decay (allowed in Standard Model) e1-e1-

Amand Faessler, October νββ -Decay (forbidden in Standard Model) e1-e1- Only possible for massive Majorana- Neutrinos c = m = 0 Short Range correlations are important ~ „Coulomb“.

Amand Faessler, October 2015 GRAND UNIFICATION Left-right Symmetric Models SO(10) Majorana Mass:

Amand Faessler, October 2015 P P ν ν nn e-e- e-e- L/R l/r

Amand Faessler, October 2015 l/r P ν P n n light ν heavy N Neutrinos l/r L/R p n e-e- p n e-e- W

Amand Faessler, October 2015 Uncorrelated and Correlated Relative N-N- (two neutrons  two protons) Wavefunction in the N-N-Potential Short Range Correlations; Bonn potential; Brueckner Theory

Miller+Spencer: Jastrow Correlations (Brueckner) Amand Faessler, October 2015 Distance: s = 0  f(0) = -1 Distance: s = ∞  f(∞) = 0

Amand Faessler, October 2015 Finite Nucleon size; Dipole Form Factor: M A = 1.09 GeV Jastrow-Function of Spencer and Miller [1+ f(s)] 

Different Short Range Correlations Amand Faessler, October 2015

Contributions at different distances for the 2v-decay Amand Faessler, October 2015

Neutrinoless Double Beta Decay Matrix Element: 82 Se  82 Kr Amand Faessler, October 2015

Uncorrelated and Correlated Relative N-N- (two neutrons  two protons) Wavefunction in the N-N-Potential Short Range Correlations; Bonn potential; Brueckner Theory

Different treatment of Short Range Correlations (SRC) NOW Sept Brückner Correlations: The same realistic force for Pairing, G-matrix elements, for the solution of the Many Body Problem and Short Range Correlations. All as solutions of the same relativistic Bethe-Goldstone Eq.. First fully consistent calculation. UCOM (Feldmeier et al.): Different forces and treatment for Nuclear Structure and SRC. SRC (AV18) fitted to an analytic function with about 3(plus) parameters to the Deuteron and suppression of the long range changes. Fermi Hypernetted chain: SRC parametrized by 3(plus) parameters fixed by the many body variational approach (Argonne). Jastrow: Fit of Gerry Miller and Spencer to Brückner results with two parameters to S-waves.

Amand Faessler, October 2015 Theoretical Description of Nuclei: Qusi-Particle Random Phase Approximation k k k e1e1 e2e2 P P ν EkEk EiEi n n 0 νββ

Amand Faessler, October 2015 Neutrinoless Double Beta- Decay Probability

Amand Faessler, October 2015 Effective Majorana Neutrino-Mass for the 0  Decay CP Tranformation from Mass to Flavor Eigenstates Time reversal CPT

Amand Faessler, October 2015 (Bild) Results from Oscillations: No Hierarchy, no absolute Mass Scale Fogli, Lisi, Marrone, Palazzo: Prog. Part. Nucl. Phys. 57(2006)742

Amand Faessler, October 2015 Normal Hierarchy: Double Beta Decay Majorana Mass m  versus lowest mass m 1

Amand Faessler, October 2015 Inverted Hierarchy: Double Beta Decay Majorana Mass m  versus lowest mass m 3

Amand Faessler, October 2015 The best choice: Quasi-Particle Random Phase Approximation (QRPA) and Shell Model QRPA starts with Pairing:

Up to now: Pairing for T=1: proton-proton and neutron-neutron adjusted to odd even mass differences: g pp ; g pp g pp = 1.1 for 9 levels; g pp = 0.9 for 23 levels g ph g ph = 1.0 fit to Gamow-Teller Resonance g pp +g pp Isospin conservation ??? Amand |p‘, October 2015

Partial Isospin Restoration (g pp T=1 different from g pp T=0 ): g pp T=1 ; g pp T=1 = g pair g pp T=0 from Fermi 2 Amand Faessler, October 2015

Fermi Transition forbidden!!! T-T- T-T- Isospin selection rules and Double Isobaric Analog State Amand Faessler, October 2015 |T,T> |T,T-1> |T, T-2> |T-2,T-2>

T = 1  S=0, L=0  M 2 FERMI ; T = 0  S=1, L=0  M 2 GT Amand Faessler, October Ge FERMI 76 Ge GT 130 Te FERMI 130 Te GT Changing g pp T=1 affects only the M 2 FERMI and leaves the M 2 GT unchanged. For M 2 FERMI = 0 on fits g pp T=1 ~ 1.0

Fit of the odd-even mass differences (pairing) for protons/neutrons and intial/final states (Argonne V18): d (i/f) p/n and g pp T=1 to M 2 FERMI = 0 Amand Faessler, October 2015 Nucleus Argonne V18 Number of levels Average d (i/f) p/n g pp T=1 M 2n Fermi = 0 76 Ge Te The two methods to determine the T=1 strength of the NN-interaction yield practically the same value for the renormalisation of the force and are close to 1, e.g. the bare Brückner NN-matrix element.

0 Half-Life  Amand Faessler, October 2015

The total 0 Matrix Element reduced by ~10% by isospin restoration (Bonn CD force). Amand Faessler, October 2015 Nucleus M 2 F M 2 GT M 0 F M 0 GT M 0 T M 0 total 76 Ge old Ge new Te old Te new

Source = Detector  10.9 kg - ( 86% from 8% nat.) 76 Ge  Gran Sasso Laboratory (Italy) HD claim for Detection of 0  DBD HD claim for Detection of 0  DBD HM collaboration claim the 0 DBD of 76 Ge Spectrum with 71.7 kgy Amand Faessler, October 2015 hep-ph/

Amand Faessler, October 2015 Summary: Neutrino Mass from  asuming the measurement of Klapdor et al. is correct: 8new) Theory with R-QRPA and g A =1.25  Exp. Klapdor et al. Mod. Phys. Lett. A21,1547(2006) ; 76 Ge  T(1/2; 0  ) = ( ) x years; 6  = 0.22 [eV] (exp+-0.02;theor+-0.01) [eV]  (new) 0.24 [eV] Bonn CD, Consistent Brückner Correlations = 0.24 [eV] (exp+-0.02; theor+-0.01)  (new) 2.6 [eV] Argonne, Consistent Brückner Correlations = 0.30 [eV] ( exp+-0.03;theor+-0.01) [eV]  (new) 0.33 [eV] Bonn CD, Fermi Hypernetted Chain (Argonne in nuclei) = 0.26 [eV] (exp+-0.02;thero+-0.01) Bonn CD, UCOM (AV18)  (new) 0.29 [eV] = 0.31 [eV] (exp ;theor+-0.02) [eV] Bonn CD, Jastrow  0.34 [eV] THE END