Double Gamow-Teller transitionsand its relation to neutrinoless ββ decays

Javier MenéndezCenter for Nuclear Study, The University of Tokyo

with N. Shimizu (CNS) and K. Yako (CNS)

Conference on Neutrinos and Nuclear Physics: CNNP2017Catania, 17th October 2017

Nuclear ββ decay

ββ decay second order process observable if β-decayis energetically forbidden or hindered by large ∆J

Neutrinoless double-beta decay (0νββ):Lepton-number violation, Majorana nature of neutrinos

-76

-74

-72

-70

-68

-66

30 31 32 33 34 35 36 37

Bin

din

g e

nerg

y (

MeV

)

Atomic number, Z

76Se

76Ge

76As

76Br

76Kr

76Ga

β-

β+

β+

β-β

-

Qββ > 2MeV

48Ca→ 48Ti76Ge→ 76Se82Se→ 82Kr96Zr→ 96Mo100Mo→ 100Ru110Pd→ 110Cd116Cd→ 116Sn124Sn→ 124Te130Te→ 130Xe136Xe→ 136Ba150Nd→ 150Sm

2 / 18

0νββ decay matrix elements and experiment

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"

3 / 18

0νββ decay nuclear matrix elementsLarge difference in nuclear matrix element calculations: factor ∼ 2− 3⟨0+

f

∣∣∑n,m

τ−n τ−m

∑X

HX (r) ΩX∣∣0+

i

⟩ ΩX = Fermi (1), GT (σnσm),TensorH(r) = neutrino potential

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

Engel, JM, Rep. Prog. Phys. 80 046301 (2017)

How cannuclear matrix elementscalculations improve?Talks bySimkovic, Coraggio (Mon),Suhonen, Barea (Tue)

Cannuclear structure experimentsguide 0νββ decay?Talks by Ejiri (Mon), Freckers (Sat)

4 / 18

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

)5 / 18

Shell model matrix elements in two shells48Ca→48Ti 0νββ decay

Enlarge configuration spacefrom pf to sdpf , 4 to 7 orbitals

Test excitation energy of 0+2 in

48Ca off by 1.3MeV in pf shell

NM

E

QRPA IBM EDF SM SM SM(pf) (MBPT) (sdpf)

0

1

2

3

Ca48

Nuclear matrix elementincreases moderately 30%Iwata et al. PRL116 112502 (2016)

Likewise, very mild effectfound in GCM calculations of 76GeJiao et al. arXiv:1707.03940

6 / 18

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)

7 / 18

Nuclear β decaysβ decays (e− capture) main decay model along nuclear chartIn general well described by nuclear structure theory: shell model...

pn

W

ν

e

0.0 0.2 0.4 0.6 0.8 1.00.0

0.2

0.4

0.6

0.8

1.0

T(GT) Th.

T(G

T)

Ex

p.

0.77

0.744

Martinez-Pinedo et al. PRC53 2602(1996)

〈F |∑

i

[gA σiτ−i ]eff |I〉 , [σiτ ]eff ≈ 0.7σiτ

Gamow-Teller transitions:theory needs σiτ "quenching"

8 / 18

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

9 / 18

Double Gamow-Teller strength distributionMeasurement 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:1703.08264Talks by Ejiri, Lenske (Mon), Yako, Lay (Tue), Carbone (Thu)

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

10 / 18

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, arXiv:1709.01088

11 / 18

Double Gamow-Teller distribution and pairingStudy the sensitivity of Double GT distribution to pairing correlations

Add/remove pairing

H ′ = H + GJT PJT

like-particle (T=1) orproton-neutron (T=0)

Position of theDGT giant resonancevery sensitive tolike-particle pairing

DGT resonance widthprobes isoscalar pairing

Shimizu, JM, Yako,arXiv:1709.01088

0

20

40

0

20

40

0

20

40

0

20

40

0 20 40 600

20

40

G(01)

= +0.5 MeV

B(D

GT

)

Ex (MeV)

Jf=2+

Jf=0+

G(01)

= +0.25 MeV

G(01)

= -0.25 MeV

G(01)

= -0.5 MeV

G(01)

= -1.0 MeV

0

20

40

0

20

40

0

20

40

0

20

40

0 20 40 600

20

40

G(10)

= +0.5 MeV

B(D

GT

)

Ex (MeV)

Jf=2+

Jf=0+

G(10)

= +0.25 MeV

G(10)

= -0.25 MeV

G(10)

= -0.5 MeV

G(10)

= -1.0 MeV

12 / 18

Pairing correlations and ββ decays0νββ decay favoured by (isovector) pairing, disfavored isoscalar pairingTalk by Hinohara (Fri)

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 operator13 / 18

48Ca DGT resonance and 0νββ decay

Correlation between Double Gamow-Teller resonance in 48Caand 0νββ decay nuclear matrix element

20 25 30 35

0

2

4

6

Eav (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 nuclear matrix element

Eav =

∑f Ef B(DGT−, i → f )∑

f B(DGT−, i → f )

Might be feasible in near future

Shimizu, JM, Yako, arXiv:1709.01088

In progress: sensitivity to other nuclear structure correlations14 / 18

DGT to ground state and 0νββ decayDGT transition to ground state of final nucleus:Ca, Ti, Cr isotopic chains MDGT =

⟨Finalgs

∣∣∣∣[∑i σiτ

−i ×∑

j σjτ−j

]0∣∣∣∣Initialgs⟩∣∣2

Very good linearcorrelation betweenDGT and 0νββ decaynuclear matrix elements

Linerar correlation holdsfor ∼ 25 transitions studiedfor simplified wf’s(seniority-zero),for different interactions

Shimizu, JM, Yako,arXiv:1709.01088

15 / 18

DGT and 0νββ decay: heavy nuclei

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 state

MDGT =√

B(DGT−; 0; 0+gs → 0+

gs)

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, arXiv:1709.0108816 / 18

Short-range character of DGT, 0νββ decayDGT transition to ground state same initial, final states with 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)

-0.5

0

0.5

1

0 2 4 6 8 10 12

CG

T (

r ij) [fm

-1]

rij [fm]

0νββ decayDGT

0 200 400 600

-0.002

0

0.002

0.00448Ca

CG

T (q

) [MeV

-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, arXiv:1709.0108817 / 18

Summary

Nuclear matrix elements are keyfor the design of next-generation tonne-scale 0νββ decay experimentsand for fully exploiting the experimental results

• Present matrix element calculations disagreeNeed improved calculations,guidance from other nuclear experiments

• Shell model nuclear matrix elementsin two shells for 48Ca, 76Ge,suggest moderate enhancement (. 30%)

• Double Gamow-Teller transitionspursued in RIKEN, INFN LNS, RCNP Osakacan provide very useful insight onvalue of 0νββ decay matrix elements

18 / 18

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

18 / 18