HEP2012, Valparaiso, January 3-9, 2012
Neutrinoless Double-Beta Decay and
Double-Electron capture
Fedor Šimkovic
JINR Dubna
and
Comenius University Bratislava)
4/8/2015
Fedor Simkovic
1
OUTLINE
• Introduction
• 0nbb-decay (present status)
- effective Majorana neutrino mass
- nuclear matrix elements
- distinguishing the 0nbb-decay mechanisms
•Resonant 0nee-decay
•Conclusion
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Amand Faessler, Vadim Rodin, Herbert Muether (University of Tuebingen)
Sergey Kovalenko (University of Valparaiso)
Mikhail Krivoruchenko (ITEP Moscow)
Petr Vogel (Caltech, Pasadena)
Walter Potzel (TU Muenchen)
Dieter Frekers (University of Muenster)
John Vergados (University of Ioannina)
Serguey Petcov (SISSA Trieste)
E. Lisi, G. Fogli, A. Rotunno (University of Bari)
…
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Sources of neutrinos
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The Sun is the most intense
detected source with a flux
on Earth of 6 1010 n/cm2s
Flux on Earth of neutrinos from different sources
as a Fedor
function
of energy
Simkovic
D. Vignaud and M. Spiro, Nucl. Phys.A 654 (1999) 350
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Fundamental properties of neutrinos
Like most people, physicists enjoy a good mystery. When
you start investigating a mystery you rarely know where it is going
After 55 years we know
• 3 families of light (V-A) neutrinos: ne, nm, nt
• n are massive: we know mass squared differences
• relation between flavor states and mass states
(neutrino mixing) only partially known
Claim for evidence of the 0nbb-decay
H.V. Klapdor-Kleingrothaus et al.,NIM A 522, 371 (2004); PLB 586, 198 (2004)
• Absolute n mass scale from the 0nbb-decay. (cosmology, 3H, 187Rh ?)
• n’s are their own antiparticles – Majorana.
No answer yet
• Is there a CP violation in n sector? (leptogenesis)
• Are neutrinos stable?
• What is the magnetic moment of n?
• Sterile
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• Statistical properties of n? Fermionic or partly bosonic?
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Standard Model
Lepton Family
Number Violation
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Lepton Universality
NEW PHYSICS
massive neutrinos, SUSY...
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Total Lepton
Number Violation
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Compelling evidence about new physics beyond the SM.
Reactor neutrinos
Solar neutrinos
1968
Atmospheric neutrinos
1957
Accelerator neutrinos
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Mass matrix of light neutrinos
Flavor
Large off
Mass
eigenstates diagonal elements ! eigenstates
0nbb-decay
Majorana condition
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Effective mass of
Majorana neutrinos
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Neutrinoless Double-Beta Decay
(A,Z)  (A,Z+2) + e- + e-
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The double beta decay process can be observed due to nuclear pairing
interaction that favors energetically the even-even nuclei over the
odd-odd nuclei
The NMEs for 0nbb-decay must be evaluated
using tools of nuclear theory
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The answer to the question whether neutrinos are their own antiparticles
is of central importance, not only to our understanding of neutrinos, but
also to our understanding of the origin of mass.
Absolute n
mass scale
Normal or inverted
Hierarchy of n masses
CP-violating phases
An accurate knowledge of the nuclear matrix elements, which is not available
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at present, is however a pre-requisite
for exploring neutrino properties.
Perspectives of the 0nbb-decay search
sin2 q13 < 5 10-2
Normal hierarchy
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Inverted hierarchy
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Quark-Lepton Complemenarity
QLC- relations:
H. Minakata, A.S.
Phys. Rev. D70: 073009 (2004)
ql12 + qq12 ~ p/4
q12 + qC = 46.5o +/- 1.3o
ql23 + qq23 ~ p/4
q23 + Vcb = 43.9o + 5.1 -3.6o
Qualitatively correlation:
• 2-3 leptonic mixing is close to maximal because 2-3 quark mixing is small
•1-2 leptonic mixing deviates from maximal substantially because
1-2 quark mixing is relatively large
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θ13 ≠ 0 : How Big or How Small?
Convincing flavor theory has been lacking—it is at present impossible to
predict fermion masses, flavor mixing angles and CP phases fundamental
level  the flavor problem
Bi-maximal mixing
As dominant structure?
Zero order?
Ubm = U23mU12m
θ13 has a role!
T2K: 0.03 < sin2 2q13< 0.34 (June 2011)
DOOBLE CHOOZ: sin2 2q13 =0.085±0.051 (9.11.2011)
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T2K: 0.03(0.04) < sin2 2q13< 0.28(0.34) for NH(IH)
Si=1,2,3=0.28 eV
0.084 eV
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DOOBLE CHOOZ: sin2 2q13 =0.085±0.051 (9.11.2011)
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Assumption MR » mD
See-Saw mechanism
Left-right symmetric
models SO(10)
Probability of
Neutrino Oscillations
As N increases, the formalism
gets rapidly more complicated!
large
small
N Dmij2
qij CP
--------------------------------------
small
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large
2
3
6
1
2
5
1
3
15
0
1
10
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Reactor neutrinos anomaly (January 2011)
Double Chooz re-evaluated reactor antineutrino flux (PRD 83, 073006 (2011))
• previous procedure used a phenomenological model based 30 effective beta
branches
• new analysis used detailed knowledge of the decays of 10,000 + fission products
New calculations
results in flux
increase of 3.5%
in reactor
antineutrinos
sin2(2qnew) ~ 0.14
Dmnew2 > 1.5 eV2
Reactor neutrinos anomaly and 0nbb-decay
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If (or when) the 0nbb decay
is observed two theoretical problems
must be resolved
S.R. Elliott, P. Vogel,
Ann.Rev.Nucl.Part.Sci. 52, 115 (2002)
1) What is the mechanism of the decay, i.e.,
what kind of virtual particle is exchanged
between the affected nucleons (quarks).
2)
How to relate the observed decay rate to
the fundamental parameters, i.e.,
what is the value of the corresponding
nuclear matrix elements.
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The 0nbb-decay NME
In double beta decay two neutrons bound in the ground state of an initial
even-even nucleus are simultaneously transformed into two protons that
are bound in the ground state or excited (0+, 2+) states of the final nucleus
It is necessary to evaluate, with a sufficient accuracy,
wave functions of both nuclei, and evaluate the matrix element of the
0nbb-decay operator connecting them
This can not be done exactly, some approximation and/or truncation
is always needed. Moreover, there is no other analogues observable
that can be used to judge directly the quality of the result.
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Many-body Hamiltonian
• Start with the many-body Hamiltonian
pi2
H 
+ VNN ri  rj 
2m i j
i
0f1p N=4

• Introduce a mean-field U to yield basis
 pi2

H  
+ Uri  + VNN ri  rj  U ri 
2m
 i j
i 
i
0d1s N=2
1p N=1
0s N=0
Residual interaction
The success of any nuclear structure calculation depends on
the choice of the mean-field basis and the residual interaction!
• The mean field determines the shell structure
• In effect, nuclear-structure calculations rely on perturbation theory
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The 0nbb-decay NMEs from literature - 2004
(mostly QRPA-like)
Uncertainties
in 0nbb-decay NME?
This suggest an uncertainty
of NME as much as factor 5 !!!
Is it really
so bad?!
Bahcall,
4/8/2015Murayama, Pena-Garay,
Phys. Rev. D 70, 033012 (2004)
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Nuclear structure approaches
Large Scale Shell Model: Caurier, Menendez,
Nowacki, Poves, PRL 100, 052503 (2008).
(Renormalized) QRPA: Šimkovic, Faessler,
Müther, Rodin, Stauf, PRC 79, 055501 (2009).
Projected Hartree-Fock-Bogoliubov:
Rath, Chandra, et al. PRC 82, 064310 (2010).
Interacting Boson Model: Barea, Iachello,
PRC 79, 044301 (2009).
Energy Dendity Functional appr.: Rodrígez,
Martínez-Pinedo, arXiv:1008.5260 [nucl-th].
gA=1.25, Jastrow s.r.c., r0=1.20 fm
The 0nbb-decay
NMEs
(Status:2012)
Differences: i) mean field; ii) residual interaction; iii) size of the model space
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iv) many-body approximation
Half-life T1/2 for mbb= 50 meV
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0nbb-decay and 2nbb-decay NMEs
F.Š., R. Hodák, A. Faessler, P. Vogel, PRC 83, 015502 (2011)
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2nbb-decay:
(A,Z)  (A,Z+2)+e-+e-+n- e+ n- e
Why the spread of the
2nbb NMEs is large
and of the 0nbb NMEs
is small?
Are both type of NMEs
related?
Differencies
among 2nbb-decay NMEs:
up to factor 10
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The cross sections of (t,3He) and (d,2He) reactions
give B(GT±) for b+ and b, product of the amplitudes
(B(GT)1/2) entering the numerator of M2nGT
Closure 2nbb-decay
NME
SSD hypothesis
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Grewe, …Frekers at al, PRC 78, 044301
(2008)
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Going to relative coordinates:
A connection between closure
2nbb and 0nbb GT NMEs
F.Š., R. Hodák, A. Faessler, P. Vogel, PRC 83, 015502 (2011)
r- relative distance
of two nucleons
Neutrino potential
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Neutrino potential prefer short distances
Closure 2nbb GT NME
The only non-zero contribution
from Jp=1+
=
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M0nGT depends weakly on gA/gpp
and QRPA approach unlike M2nGT
Nucleon
Nuclear physics
Nucleon
76Ge
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Different
Nuclear physics
76Ge
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Dependence
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on axial-vector coupling
Co-existence of few mechanisms
of the 0nbb-decay
It may happen that in year 201? (or 2???) the 0nbb-decay
will be detected for 2-3 or more isotopes …
F.Š., J.D. Vergados, A. Faessler, PRD 82, 113015 (2010)
A. Faessler, G. Fogli, E. Lisi, A. Rotunno, F. Š., Phys. Rev. D 83, 113015 (2011)
A. Faessler, A. Meroni, S.T. Petcov, F. Š., J.D. Vergados, Phys. Rev. D 83, 113003 (2011)
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Dominance of light n mass mechanism of the 0nbb-decay
H.V. Klapdor, I. Krivosheina,
Mod. Phys. Lett. A 21, 1547 (2006)
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Faessler, Fogli, Lisi, Rodin, Rotunno, F.Š., PRD 79, 053001 (2009)
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Probing the see-saw mechanism
There exist heavy Majorana neutral leptons Ni (singlet of SU(2)xU(1) group)
Effective interaction for processes
with virtual Ni at electroweak scale
After spontaneous violation of
the electroweak symmetry
the left-handed Majorana mass term is generated
Neutrino mixing
Inverted hierarchy
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Probe of
the see-saw mechanism
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Inverted
hierarchy
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Bilenky, Faessler, Potzel, F.Š, Eur. Phys. J. C 71 (2011) 1754
gluino/neutralino exchange R-parity breaking
SUSY mechanism of the 0nbbdecay
d+d → u + u + e- + eexchange of
squarks,
neutralinos
and
gluinos
l’111)2 mechanism
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Squark mixing SUSY mechanism
Mixing between
scalar superpartners
of the left- and
right-handed fermions
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M. Hirsch,
H.V. Klapdor-Kleingrothaus,
S.Fedor
Kovalenko
Simkovic
PLB 372 (1996) 181
A. Faessler,
Th. Gutsche,
S. Kovalenko,
L
R
F.Š.,
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PRD 77, 113012 (2008)
Co-existence of 2, 3 or more interferring mechanisms of 0nbb-decay
It is well-known that there exist many mechanisms that may contribute to the 0nbb.
Let consider 3 mechanisms: i) light n-mass mechanism, ii) heavy n-mass mechanism,
iii) R-parity breaking SUSY mechanism with gluino exchange and CP conservation
Claim of evidence:
We introduce
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Klapdor-Kleingrothaus, Krivosheina,
Mod. Phys. A 21, 1547 (2009)
ξTe < 1.2
ξMo < 2.6
ξ=0, non-observation (T2→∞)
ξ=1, solution for single active mech.
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is reproduced
4 sets of two linear eq.
2 different solutions CP-conservation assumed
F.Š., J.D. Vergados, A. Faessler, PRD 82, 113015 (2010)
2 active mechanisms
of the 0nbb-decay:
Light and heavy
n-mass mechanism
●
Non-observation of
the 0nbb-decay for some
isotopes might be
in agreement with
non- zero mbb
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● Fedor
Single
solution
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for light n-mass mech.
Non-observation
for 130Te
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Two non-interfering mechanisms of the 0nbb-decay
(light LH and heavy RH neutrino exchange)
Half-life:
Set of equations:
Solutions:
Fedor
Simkovic
A. 4/8/2015
Faessler, A. Meroni, S.T. Petcov, F. Š., J.D.
Vergados,
Phys. Rev. D 83, 113003 (2011)
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Two non-interfering mechanisms of the 0nbb-decay
(light LH and heavy RH neutrino exchange)
The positivity condition:
Very narrow ranges!
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Neutrinoless Double-Electron Capture
F.Š., M. Krivoruchenko, Phys.Part.Nucl.Lett. 6 (2009) 485
M. Krivoruchenko, F.Š., D. Frekers, A. Faessler, Nucl. Phys. A 859, 140171 (2011)
F.Š., Krivoruchenko, Faessler, PPNP 66, 446 (2011)
Eliseev, et al., F.Š, M. Krivoruchenko, PRL 106, 052504 (2011)
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Neutrinoless double electron capture
(resonance transitions)
(A,Z)→(A,Z-2)*HH’
J. Bernabeu, A. DeRujula, C. Jarlskog,
Nucl. Phys. B 223, 15 (1983)
Atom mixing amplitude
DM
Decay rate
Pertubation theory
Sujkowski,
Wycech,
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PRC 70, 052501 (2004)
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Oscillations of atoms
Oscillation of atoms
(lepton number violation)
F.Š., M. Krivoruchenko, Phys.Part.Nucl.Lett. 6 (2009) 485
In analogy with oscillations of
n-anti{n} (baryon number violation)
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OSCILLATIONS BETWEEN TWO STABLE ATOMS
 = 0 &   Mi - Mf)/2. Transition probability:
2
V
|  f | U (t ) | i |2  2 sin 2 (t ).

1/2
The exposure time of atoms in double-beta decay
experiments (months and years) is greater than 1/ by
many orders of magnitude.
Typically V = 10-30 MeV , and so
|  f | U (t ) | i |2  1060 ,
with no chances to observe the effect.
OSCILLATIONS & RESONANT TRANSITIONS
BETWEEN GROUND-STATE AND EXCITED ATOMS
To the lowest order in V:
i
i = (A,Z)
l+  M i + DM  1 ,
2
i
f = (A,Z - 2)**
l

M

D
M

(  1 ),
where

f
2
V 2 (M i  M f )
UNITARY LIMIT: MA,Z = M**A,Z-2
DM 
,
1 2
2
(M i  M f ) + 
2
4
V
4
max


.
1
2

V 
1 
 .
1
(M i  M f )2 +  2
4
Breit-Wigner factor
LIKELY RESONANT 0nee TRANSITIONS
Decay width of the parent atom:
1 
V 2
1
(M i  M f )2 +  2
4
.
Calculations:
1. Mass difference  Coulomb energy of electron holes.
2. Decay width   widths of the excited electron shells,
Auger & radiative transitions.
3. V  LT violating potential, electron w.f. & NME.
M. Krivoruchenko, F.Š., D. Frekers, A. Faessler, Nucl. Phys. A 859, 140171 (2011)
The process of the 0νεε has been revisited. New 0νεε transitions with parity
violation to ground and excited states of final atom/nucleus were found.
Selection rules for the 0νεε transitions were established.
The explicit form of corresponding NMEs was derived.
Assuming an effective Majorana neutrino mass of 1 eV, some half-lives has
been predicted to be as low as 1022 years in the unitary limit.
DECAY WIDTHS OF TWO-ELECTRON HOLES
Decays are dominated by
1. radiative transitions with the emission of X-rays,
2. the emission of Auger electrons.
X-rays are dominant in the decays of atoms with Z > 35.
The width of a two-hole state ab is represented by
ab  a + b + *.
nuclear de-excitation
electron shell
a are taken from: J. L. Campbell and T. Papp,
At. Data and Nuclear Data Tables, 77 (2001) 1.
Improved Q-value measurements
Klaus Blaum (MPI Heidelberg)
152Gd152Sm
(Eliseev, et al., F.Š, M. Krivoruchenko, PRL 106, 052504 (2011))
(F.Š., Krivoruchenko, Faessler, PPNP 66, 446 (2011)
Remeasured Q-value:112Sn, 74Se, 136Ce, 96Ru, 152Gd, 162Er, 168Yb, 106Cd, 156Dy
need to be remeasured: 124Xe, 130Ba, 180W, 184Os, 190Pt
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74Se
0nee experiment
in Bratislava
Muenster and Bratislava
groups
T1/2 > 4.3 1019 years
Frekers, Puppe, Thies, Povinec, F.Š.,
Staníček, Sýkora, NPA 860, 1 (2011)
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TGV experiment in Modane underground laboratory
New level
2737 keV
(Jp?
10 g of 106Cd
T1/2 2nee (106Cd) > 3.6 1020 y
T1/2 0nee
(106Cd) > 1.1 1020 y
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TGV Coll., Rukhadze et al., NPA 852, 197 (2011)
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Summary
(A,Z)  (A,Z+2) + e- + e-
e- + e- + (A,Z)  (A,Z-2)**
Perturbation theory
• 2nbb-decay background
•
can be a problem
•
• Uncertainty in NMEs
•
factor ~2, 3
•
+
+
+
• 0 0 ,2 transitions
•
• Large Q-value
• 76Ge, 82Se, 100Mo, 130Te, 136Xe …
•
• Many exp. in construction,
•
potential for observation in the
case
of inverted hierarchy (2020)Fedor Simkovic
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Breit-Wigner form
2nee-decay strongly suppressed
NMEs need to be calculated
0+0+ ,0 -, 1+, 1- transitions
Small Q-value
Q-value needs to be measured
at least with 100 eV accuracy
152Gd, looking for additional
small experiments yet
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We have no end of fun with neutrino physics.
Mathematics is Egyptian
Neutrino physics is Babylonian
We have to communicate more with neutrinos.
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