1. Double-beta decay and BSM physics: shell model nuclear matrix elements for competing mechanisms
Mihai Horoi
Department of Physics, Central Michigan University, Mount Pleasant, Michigan 48859, USA
Support from NSF grant PHY and DOE/SciDAC grants DE-SC /SC is acknowledged
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2. Overview Neutrino physics within and beyond the Standard Model (BSM)
DBD mechanisms: light Majorana neutrino exchange, right-handed currents, heavy neutrinos, SUSY R-parity violation,…
48Ca: 2v and 0v shell-model matrix elements
Beyond closure approximation
76Ge, 82Se, 130Te, and 136Xe results
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3. Classical Double Beta Decay Problem
A.S. Barabash, PRC 81 (2010)
2-neutrino double beta decay
neutrinoless double beta decay
Adapted from Avignone, Elliot, Engel, Rev. Mod. Phys. 80, 481 (2008) -> RMP08
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4. Neutrino Masses Tritium decay:
Cosmology: CMB power spectrum, BAO, etc,
Two neutrino mass hierarchies
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5. Neutrino bb effective mass
Cosmology constraint
76Ge Klapdor claim 2006
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6. The Minimal Standard Model?
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7. Too Small Yukawa Couplings?
arXiv:
Standard Model fermion masses
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8. The origin of Majorana neutrino masses
Type I see-saw
arXiv: v3
SU2eimi term dominates in most cases
TeV collider Majorana tests not relevant
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9. The origin of Majorana neutrino masses
See-saw mechanisms
Left-Right Symmetric model
arXiv: v3
WR search at CMS arXiv:
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10. Majorana neutrino masses
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11. Low-energy contributions to 0vbb decay
Low-energy effective Hamiltonian
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12. Contributions to 0vbb decay: no neutrinos
See-saw type III
GUT/SUSY R-parity violation
Squark exchange
Gluino exchange
Hadronization /w R-parity v.
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13. The Black Box Theorem
J. Schechter and J.W.F Valle, PRD 25, 2951 (1982)
E. Takasugi, PLB 149, 372 (1984)
J.F. Nieves, PLB 145, 375 (1984)
M. Hirsch, S. Kovalenko, I. Schmidt, PLB 646, 106 (2006)
0nbb observed 
at some level
(i) Neutrinos are Majorana fermions.
(ii) Lepton number conservation is violated by 2 units
Regardless of the dominant 0nbb mechanism!
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14. DBD signals from different mechanisms
arXiv:
2b0n rhc(h)
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15. The 0vDBD half-life
PRD 83, (2011)
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16. Two Non-Interfering Mechanisms
Assume T1/2(76Ge)=22.3x1024 y
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17. Is there a more general description?
Long-range terms: (a) - (c )
Short-range terms: (d)
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18. Summary of 0vDBD mechanisms
The mass mechanism (a.k.a. light-neutrino exchange) is likely, and the simplest BSM scenario.
Low mass sterile neutrino would complicate analysis
Right-handed heavy-neutrino exchange is possible, and requires knowledge of half-lives for more isotopes.
h- and l- mechanisms are possible, but could be ruled in/out by energy and angular distributions.
Left-right symmetric model may be also (un)validated at LHC/colliders.
SUSY/R-parity, KK, GUT, etc, scenarios need to be checked, but validated by other means.
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19. 2v Double Beta Decay (DBD) of 48Ca
The choice of valence space is important!
ISR
48Ca
48Ti pf
24.0
12.0
f7 p3
10.3
5.2
Ikeda satisfied in pf !
Horoi, Stoica, Brown,
PRC 75, (2007)
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20. Double Beta Decay NME for 48Ca
M. Horoi, PRC 87, (2013)
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21. Closure Approximation and Beyond in Shell Model
Challenge: there are about 100,000 Jk states in the sum for 48Ca
Much more intermediate states for heavier nuclei, such as 76Ge!!!
No-closure may need states out of the model space (not considered).
Minimal model spaces
82Se : 10M states
130Te : 22M states
76Ge : 150M states
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22. 82Se: PRC 89, (2014)
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23. New Approach to calculate NME: New Tests of Nuclear Structure
Brown, Horoi, Senkov
arXiv: ,
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24. 136Xe bb Experimental Results
Publication
Experiment
T2n1/2
T0n1/2(lim)
T0n1/2(Sens)
PRL 110,
KamLAND-Zen
> 1.9x1025 y
1.1x1025 y
PRC 89,
EXO-200
( )x1021 y
Nature 510, 229
>1.1x1025 y
1.9x1025 y
PRC 85,
( )x1021 y
EXO-200
arXiv: , Nature 510, 229
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25. 136Xe 2nbb Results np - nh 0g7/2 1d5/2 1d3/2 2s5/2 0h11/2 model space
New effective interaction,
0h11/2
2s5/2
1d3/2
1d5/2
0g7/2
0h9/2
0g9/2
0h11/2
2s5/2
1d3/2
1d5/2
0g7/2
0h9/2
0g9/2
0g7/2 1d5/2 1d3/2 2s5/2 0h11/2 model space
0h11/2
2s5/2
1d3/2
1d5/2
0g7/2
0h9/2
0g9/2
0h11/2
2s5/2
1d3/2
1d5/2
0g7/2
0h9/2
0g9/2
0g9/2 0g7/21d5/2 1d3/2 2s5/2 0h11/2 0h9/2
n (0+)
n (1+)
M(2v)
0.062 1
0.091
0.037 2
0.020
np - nh
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26. S. Vigdor talk at LRP Town Meeting, Chicago, Sep 28-29, 2014
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27. IBA-2 J. Barea, J. Kotila, and F. Iachello, Phys. Rev
IBA J. Barea, J. Kotila, and F. Iachello, Phys. Rev. C 87, (2013).
QRPA-En M. T. Mustonen and J. Engel, Phys. Rev. C 87, (2013).
QRPA-Jy J. Suhonen, O. Civitarese, Phys. NPA –232 (2010).
QRPA-Tu A. Faessler, M. Gonzalez, S. Kovalenko, and F. Simkovic, arXiv:
ISM-Men J. Menéndez, A. Poves, E. Caurier, F. Nowacki, NPA –151 (2009). SM M. Horoi et. al. PRC 88, (2013), PRC 89, (2014), PRC 90, PRC 89, (2014), in preparation, PRL 110, (2013).
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28. IBA-2 J. Barea, J. Kotila, and F. Iachello, Phys. Rev
IBA J. Barea, J. Kotila, and F. Iachello, Phys. Rev. C 87, (2013).
QRPA-Tu A. Faessler, M. Gonzalez, S. Kovalenko, and F. Simkovic, arXiv:
SM M. Horoi et. al. PRC 88, (2013), PRC 90, PRC 89, (2014), in preparation, PRL 110, (2013).
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29. Take-Away Points
Observation of 0nbb will signal New Physics Beyond the Standard Model.
Black box theorem (all flavors + oscillations)
0nbb observed 
at some level
(i) Neutrinos are Majorana fermions.
(ii) Lepton number conservation is violated by 2 units
Regardless of the dominant 0nbb mechanism!
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30. Take-Away Points
The analysis and guidance of the experimental efforts need accurate Nuclear Matrix Elements.
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31. Take-Away Points
Extracting information about Majorana CP-violation phases may require the mass hierarchy from LBNE, cosmology, etc, but also accurate Nuclear Matrix Elements.
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32. Take-Away Points
Alternative mechanisms to 0nbb need to be carefully tested: many isotopes, energy and angular correlations.
These analyses also require accurate Nuclear Matrix Elements.
SuperNEMO; 82Se
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33. Take-Away Points
Accurate shell model NME for different decay mechanisms were recently calculated.
The method provides optimal closure energies for the mass mechanism.
Decomposition of the matrix elements can be used for selective quenching of classes of states, and for testing nuclear structure.
76Ge
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34. Experimental info needed
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35. Collaborators: Alex Brown, NSCL@MSU Roman Senkov, CMU and CUNY
Andrei Neacsu, CMU
Jonathan Engel, UNC
Jason Holt, TRIUMF
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36. Summary and Outlook
Observation of neutrinoless double beta decay would signal physics beyond the Standard Model: massive Majorana neutrinos, right-handed currents, SUSY LNV, etc
48Ca and 136Xe cases suggest that 2 double-beta decay can be described reasonably within the shell model with standard quenching, provided that all spin-orbit partners are included.
Higher order effects for 0 NME included: range 1.0 – 1.4
Reliable 0bb nuclear matrix elements could be used to identify the dominant mechanism if energy/angular correlations and data for several isotopes become available.
The effects of the quenching and the missing spin-orbit partners are important (see the 136Xe case), and they need to be further investigated for 76Ge, 82Se and 130Te.
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37. Effective Field Theory for BSM
V. Cirigliano talk at LPR Town Meeting, Chicago, Sep 28-29, 2014
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38. Effective Field Theory for BSM
M. Hirsch talk at NEUTRINO 2014
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39. Comparisons of M0n 0nbb Results
From T. Rodriguez, G. Martinez-Pinedo,
Phys. Rev. Lett. 105, (2010)
Present Shell Model results:
Phys. Rev. Lett. 110, (2013)
PRC 89, & 88, (2013)
PRC 89, (2014), submitted
(MS)
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40. Shell Model GT Quenching
empty
valence
frozen core
core polarization: Phys.Rep. 261, 125 (1995)
J. Menendez, D. Gazit and A. Schwenk, arXiV: , PRL 107
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41. The Minimal Standard Model?
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42. The effect of larger model spaces for 48Ca
M(0v)
SDPFU
SDPFMUP
0.941
0.623
0+2
1.182 (26%)
1.004 (61%)
M(0v)
/ GXPF1A
0.733
nd ord./GXPF1A
1.301 (77%)
arXiv: , PRC 89, (2014)
SDPFU: PRC 79, (2009)
PRC 87, (2013)
SDPFMUP: PRC 86, (R) (2012)
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43. Other Shell Model Results
0g7/2 1d5/2 1d3/2 2s5/2 0h11/2 valence space
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44. S. Vigdor talk at LPR Town Meeting, Chicago, Sep 28-29, 2014
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45. The Black Box Theorem
J. Schechter and J.W.F Valle, PRD 25, 2951 (1982)
E. Takasugi, PLB 149, 372 (1984)
J.F. Nieves, PLB 145, 375 (1984)
M. Hirsch, S. Kovalenko, I. Schmidt, PLB 646, 106 (2006)
However:
M. Duerr et al, JHEP 06 (2011) 91
0nbb observed 
at some level
(i) Neutrinos are Majorana fermions.
(ii) Lepton number conservation is violated by 2 units
Regardless of the dominant 0nbb mechanism!
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46. ACFI-FRIB
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47. Neutrino OscillationsNH IH
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48. Low-energy contributions to 0vbb decay
Low-energy effective Hamiltonian
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49. Some mechanisms tested at LHC
PRD 86, (2012)
Left-right symmetric model
arXiv:
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50. Some mechanisms tested at LHC
Broken D-parity left-right symmetric model: arXiv:
Recent CMS results a 2.8s effect arXiv:
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51. Neutrino Oscillations
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52. Consequences of Majorana Neutrinos
- Leptogenesis (DL=2) => (SM sphalerons) => Baryogenesis
- Exotic (DL=2) decays:
- Larger magnetic moments => Larger decay rates of heavy neutrino
- Different neutrino contribution to Supernovae explosion mechanism => different signals measured on Earth detectors
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53. Fermion masses in and beyond the Standard Model
Standard Model photon (m=0)
Standard Model Dirac fermions (m>0)
Standard Model neutrino (m=0)
Beyond Standard Model Dirac neutrino (m>0)
Beyond Standard Model Majorana neutrino (m>0)
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54. Matrix Elements: Light Neutrinos
Present Interacting Shell-Model
PRL 109, (2012)
PRD 83, (2011)
NPA 818, 139 (2009)
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55. Matrix Elements: Heavy Neutrinos
Present Interacting Shell-Model
PRL 109, (2012)
PRD 83, (2011)
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56. Fermions masses in the Standard Model
Standard Model photon (m=0)
Standard Model Dirac fermions (m>0)
Standard Model neutrino (m=0)
Extended Standard Model Dirac neutrino (m>0)
Beyond Standard Model Majorana neutrino (m>0)
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57. Beyond Closure in Shell Model
Challenge: there are about 100,000 Jk states in the sum for 48Ca !!!
Senkov & Horoi, PRC 88, (2013)
About 300 intermediate states for each spin are (more than) enough
GT dominates, and exhibits the largest change
A 8-12% increase from closure was found
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58. 76Ge
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59. DBD signals from different mechanisms
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