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

Collaborators

T. OtsukaT. Abe

N. ShimizuY. TsunodaK. Yako

Y. Utsuno M. Honma

E. A. Coello PérezG. Martínez-PinedoA. Schwenk

D. Gazit

A. PovesT. R. Rodríguez

E.CaurierF. Nowacki

J. Engel

N. Hinohara

Y. Iwata

42 / 42