Towards reliable nuclear matrix elementsfor neutrinoless ββ decay
Javier Menéndez
Center for Nuclear Study, The University of Tokyo
Center for Experimental Nuclear Physics and Astrophysics, CENPA
Seattle, 15th March 2018
Nuclear physics and neutrinoless ββ decay
Neutrinos, dark matter studied inexperiments using nuclei
Nuclear matrix elementsdepend on nuclear structurecrucial to anticipate reachand fully exploit experiments
0νββ decay:(T 0νββ
1/2
)−1∝∣∣M0νββ
∣∣2m2ββ
Dark matter:dσχNdq2 ∝
∣∣∣∑i
ci ζi Fi
∣∣∣2M0νββ : Nuclear matrix elementFi : Nuclear structure factor
2 / 42
Neutrinoless ββ decay
Lepton-number violation, Majorana nature of neutrinos
Second order process only observable in rare caseswith β-decay energetically forbidden or hindered by ∆J
-76
-74
-72
-70
-68
-66
30 31 32 33 34 35 36 37
Bin
din
g e
ne
rgy (
Me
V)
Atomic number, Z
76Se
76Ge
76As
76Br
76Kr
76Ga
β-
β+
β+
β-β
-
Present best limits T 0νββ1/2 &1025 y:
76Ge (GERDA, Majorana), 130Te (CUORE), 136Xe (EXO, KamLAND-Zen)3 / 42
Signature of neutrinoless ββ decayVery different signatures for neutrinoless and two-neutrino ββ decays
2νββ : Ee1 + Ee2 + Eν1 + Eν2 = Qββ
0νββ : Ee1 + Ee2 = Qββ
because only the electrons are detected in experiments
KamLAND-Zen, PRL110 062502 (2013)4 / 42
Next generation experiments: inverted hierarchy
The decay lifetime is T 0νββ1/2
(0+ → 0+
)−1= G01
∣∣M0νββ∣∣2 m2
ββ
sensitive to absolute neutrino masses, mββ = |∑U2ek mk |, and hierarchy
(eV)lightestm4−10 3−10 2−10 1−10
3−10
2−10
1−10
1
IH
NH
A50 100 150
Ca
Ge
SeZr
Mo
CdTe
Te
Xe
Nd
(eV)
m
Matrix elements needed to make sure KamLAND-Zen, PRL117 082503(2016)next generation ton-scale experiments fully explore "inverted hierarchy"
5 / 42
Outline
Present status of 0νββ decay nuclear matrix elements
Future prospects for 0νββ nuclear matrix element calculations
How can other nuclear experiments help 0νββ decay studies?
6 / 42
Outline
Present status of 0νββ decay nuclear matrix elements
Future prospects for 0νββ nuclear matrix element calculations
How can other nuclear experiments help 0νββ decay studies?
/
Calculating nuclear matrix elementsNuclear matrix elements needed to study fundamental symmetries
〈Final |Lleptons−nucleons| Initial 〉 = 〈Final |∫
dx jµ(x)Jµ(x) | Initial 〉
• Nuclear structure calculationof the initial and final states:Shell model Retamosa, Poves, JM, Horoi...Energy-density functional Rodríguez, Yao...QRPA Vogel, Faessler, Šimkovic, Suhonen...Interacting boson model Iachello, Barea...Ab initio many-body methodsGreen’s Function MC, Coupled-cluster, IM-SRG...
• Lepton-nucleus interaction:Study hadronic current in nucleus:phenomenological approaches,effective theory of QCD
CDMS Collaboration7 / 42
0νββ nuclear matrix elements: last 5 years
Comparison of nuclear matrix element calculations: 2012 vs 2017
0
1
2
3
4
5
6
7
8
48 76 82 96 100 116 124 130 136 150
M0
ν
A
SM St-M,Tk
SM Mi
IBM-2
QRPA CH
QRPA Tu
QRPA Jy
R-EDF
NR-EDF
Vogel, J. Phys. G 39 124002 (2012) Engel, JM, Rep.Prog.Phys. 80 046301(2017)
What have we learned in the last 5 years?8 / 42
Configuration spaceNuclear shell model configuration spaceonly keep essential degrees of freedom
• High-energy orbits: always empty
• Configuration space:where many-body problem is solved
• Inert core: always filled
H |Ψ〉 = E |Ψ〉 → Heff |Ψ〉eff = E |Ψ〉eff
|Ψ〉eff =∑α
cα |φα〉 , |φα〉 = a+i1a+
i2...a+iA |0〉
Shell model codes (1 major oscillator shell)∼1010 Slater dets. Caurier et al. RMP77 (2005)
QRPA calculations suggestlarger spaces (& 2 major shells) needed
Dimension ∼((p + 1)(p + 2)ν
N
)((p + 1)(p + 2)π
Z
)9 / 42
Shell model configuration space: two shells
For 48Ca enlarge configuration spacefrom pf to sdpf4 to 7 orbitals, dimension 105 to 109
increases matrix elementsbut only moderately 30%Iwata et al. PRL116 112502 (2016)
NM
E
QRPA IBM EDF SM SM SM(pf) (MBPT) (sdpf)
0
1
2
3
Ca48
Contributions dominated by pairing2 particle – 2 hole excitationsenhance the ββ matrix element,
Contributions dominated by1 particle – 1 hole excitationssuppress the ββ matrix element
10 / 42
76Ge matrix element in two shells: approximateLarge configuration space calculations in 2 major oscillator shellsInclude all relevant correlations: isovector/isoscalar pairing, deformationMany-body approach: generating coordinate method (GCM)
GCM approximatesshell model calculation
Degrees of freedom,or generating coordinates,validated againstexact shell modelin small configuration space
Jiao et al. PRC96 054310 (2017)
76Ge nuclear matrix element in 2 major shellsvery similar to shell model nuclear matrix element in 1 major shell
11 / 42
76Ge matrix element in two shells: exact
Dimension of the shell-model many-body Hilbert space
dimen
sion
year
abouttwiceperyear
ab initio type calculation
From T. Otsuka, INT-18-1a program12 / 42
76Ge matrix element in two shells: exact
0nbb decayNuclearMatrixElementbyMonteCarloshellmodel(MCSM)
0nbb
NME
Δ𝐻#Exactfor
JUN45
76Ge⇒ 76Se
Benchmark
f5pg9shell,JUN45int.(Honma2009)
MCSM:wavefunctioncomposedofa superpositionofselectedoptimalSlaterdeterminantswithprojectionontoJandP
extrapolation
Expectationvalueofenergyvariance(measureofapproximation)
GT-type
NME(total)
tensor-type
Fermi-type
From T. Otsuka, INT-18-1a program13 / 42
76Ge matrix element in two shells: exact
0nbb decay Nuclear Matrix Element by the Monte Carlo shell model
0nbb
NME
Δ𝐻#
76Ge->76Se
pf-shell+0g9/2+1d5/2A3DA-mint.
Theexactvaluebytheconventional shellmodelcalculationcannotbeobtainedduetotheprohibitivelylargedimensionoftheHamiltonianmatrix.ca.3.17x1017 dim.againstcurrentlimit
1010 dim.inprogress
GT-type
NME(total)
tensor-type
Fermi-type
JUN45
?
From T. Otsuka, INT-18-1a program14 / 42
Heavy-neutrino exchange nuclear matrix elements
Contrary to light-neutrino-exchange, for heavy-neutrino-exchange decayshell model, IBM, and EDF matrix elements agree reasonably!
0
1
2
3
4
5
6
7
M0
ν
shell model
EDF
0
50
100
150
200
250
48 76 82 96 100 116 124 130 136 150
M0
N
A
Song et al. PRC95 024305 (2017)JM, JPG 45 014003 (2018)
Neacsu et al. PRC100 052503 (2015)
Suggests differences in treatinglonger-range nuclear correlationsdominant in light-neutrino exchange
15 / 42
Heavy-neutrino matrix elementCompared tolight-neutrino exchange
heavy neutrino exchangedominated byshorter internucleon range,larger momentum transfers
heavy neutrino exchangecontributionfrom J > 0 pairs smaller:pairing most relevant
⇒Long-range correlations(except pairing)not under control
JM, JPG 45 014003 (2018)
-0.5
0
0.5
1
1.5
2
2.5
0 1 2 3 4 5
CG
T (
r) [fm
-1]
r [fm]
heavy N
light ν
0 200 400 600 800 1000
-0.002
0
0.002
0.004
0.006
0.008
0.01
136Xe
CG
T (q
) [MeV
-1]
q [MeV]
-2
0
2
4
6
0+
0-
1+
1-
2+
2-
3+
3-
4+
4-
5+
5-
6+
6-
7+
7-
8+
8-
9+
9-
10+10
--100
-50
0
50
100
150
200
136Xe
MG
T0
ν (
Jπ) M
GT
0N
(Jπ)
Jπ
light ν
heavy N
16 / 42
Pairing correlations and 0νββ decay0νββ decay favoured by proton-proton, neutron-neutron pairing,but it is disfavored by proton-neutron pairing
Ideal case: superfluid nucleireduced with high-seniorities
0
2
4
6
8
10
12
0 4 8 12
M0ν
ββ
sm
A=48A=76A=82
A=124A=128A=130A=136
Caurier et al. PRL100 052503 (2008)
Addition of isoscalar pairingreduces matrix element value
-10
-5
0
5
10
0 0.5 1 1.5 2 2.5 3
M0ν
gT=0/gT=1
GCM SkO′QRPA SkO′GCM SkM*
QRPA SkM*
Hinohara, Engel PRC90 031301 (2014)
Related to approximate SU(4) symmetry of the∑
H(r)σiσjτiτj operator17 / 42
IBM matrix elements with proton-neutron pairing
van Isacker et al. PRC96 064505 (2018)
Energy-density functional (EDF) theoryand interating boson model (IBM)calculated nuclear matrix elementsdo not include explicitlyproton-neutron pairing correlations
This effect (partially) accounted forby other degrees of freedompresent in these approaches
Include p-boson (L = 1) to IBMin addition to s and d bosons (L = 0,2)
First IBM results in calcium regionsuggest nuclear matrix elementscould be somewhat reduced
18 / 42
Matrix elements: theoretical uncertaintySystematic uncertainty hard to estimatefor phenomenological matrix elements
Effective theory for ββ decay:spherical core coupled to one nucleon
Couplings adjusted to experimental data,uncertainty given by effective theory(breakdown scale, systematic expansion)
Take β decay data to predict 2νββ
M2νββ =∑k
⟨0+
f
∣∣∑n σnτ
−n∣∣1+
k
⟩ ⟨1+
k
∣∣∑m σmτ
−m∣∣0+
i
⟩Ek − (Mi + Mf )/2
Good agreement with large errors(leading-order calculations)
Coello-Pérez, JM, Schwenk, arXiv:1708.0614019 / 42
Outline
Present status of 0νββ decay nuclear matrix elements
Future prospects for 0νββ nuclear matrix element calculations
How can other nuclear experiments help 0νββ decay studies?
/
Ab initio methods: No core shell modelNo core shell model
Many-body wave functionlinear combination ofSlater Determinantsfrom single particle states in the basis(3D harmonic oscillator)
|i〉 = |ni li jimji mti 〉|φα〉 = a+
i1a+j2...a
+kA |0〉
|Ψ〉 =∑α
cα |φα〉
H |Ψ〉 = E |Ψ〉
Dim ∼(
(p + 1)(p + 2)νN
)((p + 1)(p + 2)π
Z
) Dimensions increasecombinatorially...
20 / 42
Green’s function Monte CarloGreen’s function Monte CarloPieper, Wiringa, Carlson...
NN forcesdo not reproducebinding energiesand spectra:need 3N forces
Good agreementwith 3N forces
21 / 42
Coupled Cluster, In-Medium SRGCoupled Cluster method: operators (correlations) acting on referenceimpose no particle-hole excitations present in the reference stateHagen, Papenbrock, Hjorth-Jensen...
|Ψ〉 = e−(T1+T2+T3··· ) |Φ〉
with T1 =∑α,α
tαα{
a†α, aα},T2 =
∑αβ,αβ
tαβαβ{
a†αa†β, aαaβ
}, · · ·
solve⟨Φαα∣∣ e∑
Ti He−∑
Ti |Φ〉 = 0 ,⟨
Φαβαβ
∣∣∣ e∑Ti He−
∑Ti |Φ〉 = 0
In-medium similarityrenormalization group method:apply a similarity (unitary)transformationto decouple reference statefrom particle-hole excitationsBogner, Schwenk, Hergert, Stroberg...
〈i|H(0) |j〉 〈i|H(∞) |j〉
0p0h 1p1h 2p2h 3p3h 0p0h 1p1h 2p2h 3p3h
0p0h
1p1h
2p2h
3p3h
0p0h
1p1h
2p2h
3p3h
22 / 42
Ab initio many-body methods
Oxygen dripline using chiral NN+3N forces correctly reproducedab-initio calculations treating explicitly all nucleonsexcellent agreement between different approaches
No-core shell model(Importance-truncated)
In-medium SRGHergert et al. PRL110 242501(2013)
Self-consistent Green’sfunctionCipollone et al. PRL111 062501(2013)
Coupled-clustersJansen et al. PRL113 142502(2014)
16 18 20 22 24 26 28
Mass Number A
-180
-170
-160
-150
-140
-130
Ener
gy (
MeV
)MR-IM-SRG
IT-NCSM
SCGF
Lattice EFT
CC
obtained in large many-body spaces
AME 2012
23 / 42
Calcium isotopes with NN+3N forcesCalculations with NN+3N forces predict shell closures at 52Ca, 54Ca
28 29 30 31 32 33 34 35 36
Neutron Number N
0
2
4
6
8
10
12
14
16
18
20
22
S2
n (
MeV
)
MBPT
CC
SCGF
MR-IM-SRG
42 44 46 48 50 52 54 56
Mass Number A
0
1
2
3
4
5
2+ E
ner
gy (
MeV
)
MBPT
CC
51−54Ca masses [TRIUMF/ISOLDE]54Ca 2+
1 excitation energy [RIBF,RIKEN]Hebeler et al. ARNPS 65 457 (2015)
24 / 42
Chiral effective field theoryChiral EFT: low energy approach to QCD, nuclear structure energies
Approximate chiral symmetry: pion exchanges, contact interactions
Systematic expansion: nuclear forces and electroweak currents
2N LO
N LO3
NLO
LO
3N force 4N force2N force
N
N
e ν
N
N
e
N
π
N ν e ν
N
NN
N
Weinberg, van Kolck, Kaplan, Savage, Epelbaum, Kaiser, Meißner...
Park, Baroni, Krebs...
2b currents applied toνd scattering (SNO),3H β-decay, µ moment...25 / 42
Gamow-Teller transitions: quenchingSingle β decays well described by nuclear structure (shell model)
pn
W
ν
e
〈F |∑
i
geffA σiτ
−i |I〉
geffA = qgA, q ∼ 0.7− 0.8. 0.0 0.2 0.4 0.6 0.8 1.0
0.0
0.2
0.4
0.6
0.8
1.0
T(GT) Th.T
(GT
) E
xp.
0.77
0.744
Martínez-Pinedo et al. PRC53 2602 (1996)
Theory needs to “quench“ Gamow-Teller operator to reproduceGamow-Teller lifetimes: problem in nuclear many-body wf or operator?This puzzle has been the target of many theoretical efforts:Arima, Rho, Towner, Bertsch and Hamamoto, Wildenthal and Brown...
26 / 42
2b currents in medium-mass nucleiNormal-ordered 2b currents modify GT operatorJM, Gazit, Schwenk PRL107 062501 (2011)
Jeffn,2b ' −
gAρ
f 2π
τ−n σn
[I(ρ,P)
(2c4−c3)
3
]−
gAρ
f 2π
τ−n σn23
c3p2
m2π + p2
,
N
N
e
N
π
N ν
0 0.04 0.08 0.12
ρ [fm-3
]
0.5
0.7
0.9
1.1
p=0
1bc
2bc
0 100 200 300 400p [MeV]
0.6
0.7
0.8
0.9
1
1.1
0.5
GT
(1b+
2b)/
gA 1bc
2bc
2b currents predict gA quenching q = 0.85...0.66Quenching reduced at p > 0, relevant for 0νββ decay where p ∼ mπ
27 / 42
β decay in very light nuclei: GFMCAb initio Green Function Monte Carlo β decay matrix elements in A ≤ 10Pastore et al. PRC97 022501 (2018)
2.11.11
Ratio to EXPT
10C
10B
7Be
7Li(gs)
6He
6Li
3H
3He
7Be
7Li(ex)
gfmc 1b
gfmc 1b+2b(N4LO)
Chou et al. 1993 - Shell Model - 1b
Very good agreement to experiment in all casesexcept for 10C, very sensitive to nuclear structure details
Impact of 2b currents small (few %) enhancement of matrix elements28 / 42
β decay in very light nuclei: NCSM
0.95 1.00 1.05 1.10
ratio to experiment
14O0 !14 N1
10C0 !10 B1
7Be 32!7 Li 3
2
7Be 32!7 Li 1
2
6He0 !6 Li1
3H 12!3 He 1
2
GT only
GT + 2BC
Theory to experiment ratios for beta decays in light nuclei from NCSM
0.95 1.00 1.05 1.10
ratio to experiment
14O0 !14 N1
10C0 !10 B1
7Be 32!7 Li 3
2
7Be 32!7 Li 1
2
6He0 !6 Li1
3H 12!3 He 1
2
GT only
GT + 2BC
NNLOsat (cD =0.82)
From G. Hagen, INT-18-1a program29 / 42
β decay in medium-mass nuclei: IMSRG
“Quenching” of gA in Gamow-Teller Decays
VS-IMSRG calculations of GT transitions in sd, pf shells
Minor effect from consistent effective operator
Significant effect from neglected 2-body currents Ab initio calculations explain data with unquenched gA
From J. Holt, INT-18-1a program30 / 42
Nuclear matrix elements with 1b+2b currents
48Ca
76Ge
82Se
124Sn
130Te
136Xe
0
1
2
3
4
5
6
7
M0ν
ββ
1b Q0
1b Q2
1b+2b Q3 c
D=0
SM (2009)
0 100 200 300 400 500 600
p [MeV]C
GT(p
)
Q0
Q2
Q3
JM, Gazit, Schwenk PRL107 062501 (2011)
Order Q0+Q2 similar tophenomenological currentsJM, Poves, Caurier, NowackiNPA818 139 (2009)
N
N
e ν N
N
e
N
π
N ν
Order Q3 2b currentsreduce NMEs∼ 20%− 50%
Improved, ideally ab initio calculations are needed!
31 / 42
0νββ decay matrix elements in very light nucleiVariational Monte Carlo 0νββ decay matrix elements in A ≤ 12Pastore et al. PRC97 014606 (2018)
0
1
2
3
4
5
6
7
8
6 12 48 76 82 96 100 116 124 130 136 150
M0
ν
A
VMC
SM St-M,Tk
SM Mi
IBM-2
QRPA CH
QRPA Tu
QRPA Jy
R-EDF
NR-EDF
Larger/smaller matrix elements given by same/different nuclear isospinAnchor for other ab initio approaches that can extend to heavier nuclei
32 / 42
Outline
Present status of 0νββ decay nuclear matrix elements
Future prospects for 0νββ nuclear matrix element calculations
How can other nuclear experiments help 0νββ decay studies?
/
Tests of nuclear structureSpectroscopy well described: masses, spectra, transitions, knockout...
Theory Exp0
500
1000
1500
2000
2500
Ex
cita
tio
n e
ner
gy
(k
eV)
4+
6+
0+
3+
4+
6+
2+5
+
2+
0+
2+
4+
2+
6+
3+,4
+6+
2+ 2
+5(4
+)
136Xe
0
0
0.5
1
Ex (
MeV
)
0+2+
4+
6+
8+
0+2+
4+
6+
8+
0+
2+
4+
0+
2+
4+
6+
204
292
325
345
115(2)
175(1)
212(12)
236(11)
98
151
181
55.8(25)
112(12)
Theory Exp. Theory Exp.150Nd 150Sm
Schiffer et al. PRL100 112501(2009)Kay et al. PRC79 021301(2009)...Szwec et al., PRC94 054314 (2016)
Rodríguez et al. PRL105 252503 (2010)...Vietze et al. PRD91 043520 (2015)
33 / 42
Two-neutrino ββ decayTest of 0νββ decay: comparison of predicted 2νββ decay vs data
Shell modelreproduce 2νββ dataincluding "quenching"common to β decaysin same mass region
Shell model predictionprevious to48Ca measurement!
Table 2
The ISM predictions for the matrix element of several 2ν double beta decays
(in MeV−1). See text for the definitions of the valence spaces and interactions.
M2ν (exp) q M2ν (th) INT
48Ca→48Ti 0.047± 0.003 0.74 0.047 kb3
48Ca→48Ti 0.047± 0.003 0.74 0.048 kb3g
48Ca→48Ti 0.047± 0.003 0.74 0.065 gxpf1
76Ge→76Se 0.140± 0.005 0.60 0.116 gcn28:50
76Ge→76Se 0.140± 0.005 0.60 0.120 jun45
82Se→82Kr 0.098± 0.004 0.60 0.126 gcn28:50
82Se→82Kr 0.098± 0.004 0.60 0.124 jun45
128Te→128Xe 0.049± 0.006 0.57 0.059 gcn50:82
130Te→130Xe 0.034± 0.003 0.57 0.043 gcn50:82
136Xe→136Ba 0.019± 0.002 0.45 0.025 gcn50:82
Caurier, Nowacki, Poves PLB711 62(2012)
M2νββ =∑
k
⟨0+
f
∣∣∑n σnτ
−n∣∣1+
k
⟩ ⟨1+
k
∣∣∑m σmτ
−m∣∣0+
i
⟩Ek − (Mi + Mf )/2
34 / 42
µ-capture, ν-nucleus scatteringMomentum transfers very different in ββ decays:2νββ decay (q ∼ 1 MeV) and 0νββ decay (q ∼ 100 MeV)
X
M
M
W
p
Wp
ν
ν
n
e
e
n
ν
pe
ν
pe
W
W
n
n
Muon-capture,neutrino-nucleus scattering(to low-energy states)probe similar momentumtransfers than 0νββ decay
Several multipolarities (J values)contribute, like in 0νββ decay35 / 42
Gamow-Teller strength distributionsGamow-Teller (GT) distributions well described by theory (quenched)
Freckers et al.NPA916 219 (2013)
Iwata et al. JPSCP 6 03057 (2015)⟨1+
f
∣∣∑i
[σiτ±i ]eff
∣∣0+gs
⟩, [σiτ
±]eff ≈ 0.7σiτ±
M2νββ =∑
k
⟨0+
f
∣∣∑n σnτ
−n∣∣1+
k
⟩ ⟨1+
k
∣∣∑m σmτ
−m∣∣0+
i
⟩Ek − (Mi + Mf )/2
GT strengths combined related to 2νββ decay, but relative phaseunknown
36 / 42
Double Gamow-Teller strength distribution
Measurement of Double Gamow-Teller (DGT) resonancein double charge-exchange reactions 48Ca(pp,nn)48Ti proposed in 80’sAuerbach, Muto, Vogel... 1980’s, 90’s
Recent experimental plans in RCNP, RIKEN (48Ca), INFN CataniaTakaki et al. JPS Conf. Proc. 6 020038 (2015)Capuzzello et al. EPJA 51 145 (2015), Takahisa, Ejiri et al. arXiv:1703.08264
Promising connection to ββ decay,two-particle-exchange process,especially the (tiny) transitionto ground state of final state
Two-nucleon transfers related to0νββ decay matrix elementsBrown et al. PRL113 262501 (2014)
excitation energy increases. The cross section at the low excitation region of E=0-5 MeV is around 20 nb/sr/MeV, while the cross section at the high excitation region of E=20-30 MeV is around 100 nb /sr/MeV. Broad bumps around E=30 MeV and 45 MeV may correspond to the giant resonance built on isobaric analog states GDR*IAS and the double giant resonance DGDR observed in the double charge exchange ( ) reaction4 on 13C .
Figure 3. Cross-sections for the 13C(11B,11Li)13O reaction(upper) and the 56Fe(11B,11Li) 56Ni reaction(low).
Then we measured the (11B,11Li) reaction on 56Fe with N-Z=4 (TZ=2) (99% enriched in 56Fe, 11mg/cm2). So far the 56Fe( ) ( T=2, S=0) reaction has been measured3. In this reaction, DIAS and GDR*IAS were observed. In the present case of the 56Fe(11B,11Li)56Ni ( T=2) reaction, it is possible to excite not only DIAS and GDR*IAS, but also DGTR. A
37 / 42
48Ca Double Gamow-Teller distributionCalculate with shell model 48Ca 0+
gs Double Gamow-Teller distribution
B(DGT−;λ; i → f ) =1
2Ji + 1
∣∣∣∣⟨48Ti∣∣∣∣∣∣∣∣[∑
i
σiτ−i ×
∑j
σjτ−j
](λ)∣∣∣∣∣∣∣∣48Cags
⟩∣∣∣∣2
0 20 400 20 400
20
40
60
0 20 40
(c) SDPFMU-DB
B(D
GT
)
Ex (MeV)
Jf=2+
Jf=0+
Jf=0+
Jf=2+
(a) GXPF1B
Ex (MeV)
(b) KB3G
Jf=0+
Jf=2+
Ex (MeV)
Shell model calculation with Lanczos strength function method
Double GT resonances in one and two shells rather similar resultShimizu, JM, Yako, PRL accepted
38 / 42
48Ca double GT resonance and 0νββ decay
Correlation between Double Gamow-Teller resonance in 48Caand 0νββ decay nuclear matrix element
20 25 30
0
2
4
Ec (MeV)
NM
E
GT-type
DGT0
Fermi-type
Tensor-type
G(0
1) =
0 Total
Energy of DGT resonancewith accuracy to ∼1MeV,can give insight on the value of0νββ decay matrix element
Eav =
∑f Ef B(DGT−, i → f )∑
f B(DGT−, i → f )
Might be feasible in near futureat LNS Catania or RIBF RIKEN
Uesaka, Takaki, Cappuzzello, Ejiri...
Shimizu, JM, Yako, PRL accepted
39 / 42
Double Gamow-Teller and 0νββ decay
0
0.2
0.4
0.6
0.8
1
1.2 (a)
MD
GT(0
+ gs→
0+ gs)
EDF
GXPF1B
KB3G
Cr
Ti
Ca
0
0.2
0.4
0.6
0.8
1
1.2
1 2 3 4
(b)
MD
GT(0
+ gs→
0+ gs)
M0νββ
(0+gs→ 0
+gs)
QRPA
EDF
Xe
Te
Sn
Se
Ge
DGT transition to ground stateMDGT =⟨Fgs∣∣∣∣[∑
i σiτ−i ×∑
j σjτ−j
]0∣∣∣∣Igs⟩∣∣2
very good linear correlationwith 0νββ decaynuclear matrix elements
Correlation holdsacross wide range of nuclei,from Ca to Ge and Xe
Common to shell model andenergy-density functional theory0 . M0νββ . 5disagreement to QRPA
Shimizu, JM, Yako, PRL accepted40 / 42
Short-range character of DGT, 0νββ decay
Correlation between DGT and 0νββ decay matrix elementsexplained by transition involving low-energy states combined withdominance of short distances between exchanged/decaying neutronsBogner et al. PRC86 064304 (2012)
-0.2
0
0.2
0.4
0.6
0 3 6 9 12 15
(a)
CG
T (
r jk)
[fm
-1]
rjk [fm]
0νββ decay
DGT
0 200 400 600
-0.001
0
0.001
0.002
0.003136
Xe
(b)
CG
T (q
) [Me
V-1]
q [MeV]
0νββ decay matrix elementlimited to shorter range
Short-range part dominantin double GT matrix elementdue to partial cancellationof mid- and long-range parts
Long-range part dominant inQRPA DGT matrix elements
Shimizu, JM, Yako, PRL accepted
41 / 42
Summary
Reliable nuclear matrix elements needed to plan and fully exploitimpressive experiments looking for neutrinoless double-beta decay
• Matrix element differencesbetween present calculations, factor 2− 3besides addional "quenching"?
• 48Ca and 76Ge matrix elementsin large configuration space increase . 30%,missing correlations introduced in IBM, EDF
• First ab initio calculations of β decaysdo not need additional "quenching",stay tuned for ab initio 48Ca matrix elements
• 2νββ decay, µ-capture/ν-nucleus scatteringand double Gamow-Teller transitionscan give insight on 0νββ matrix elements42 / 42