Nuclear structure for decay and dark matter searches...Nuclear physics, decay, dark matter detection...

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Nuclear structure for ββ decay and dark matter searches Javier Menéndez JSPS Fellow, The University of Tokyo International Workshop on "Double Beta Decay and Underground Science" (DBD16) Osaka University, 9 th November 2016

Transcript of Nuclear structure for decay and dark matter searches...Nuclear physics, decay, dark matter detection...

Nuclear structurefor ββ decay and dark matter searches

Javier Menéndez

JSPS Fellow, The University of Tokyo

International Workshop on"Double Beta Decay and Underground Science" (DBD16)

Osaka University, 9th November 2016

Nuclear physics, ββ decay, dark matter detection

Nuclear structure crucial for designand interpretation of experiments

Neutrinos, dark matter studied inlow-energy experiments using nucleiAbundant material, long observation timewith very low background sensitive torarest decays and tiny cross-sections!

0νββ decay:(

T 0νββ1/2

)−1∝∣∣M0νββ

∣∣2 m2ββ

Dark matter:dσχNdq2 ∝

∣∣∣∑i

ci ζi Fi

∣∣∣2M0νββ : Nuclear matrix elementFi : Nuclear structure factor

2 / 19

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

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, arXiv: 1610.065483 / 19

Application to experiment: inverted hierarchy

The decay lifetime is(

T 0νββ1/2

(0+ → 0+

))−1= G01

∣∣M0νββ∣∣2(mββ

me

)2

,

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"4 / 19

Spin-dependent scattering: 1b+2b currents

0 1 2 3 4 5 6 7 8 9 10

u

0.0001

0.001

0.01

0.1

Si(u

)

Sp(u) 1b currents

Sn(u) 1b currents

1 2 3 4 5 6 7 8 9

0.0001

0.001

0.01

0.1

Si(u

)

Sp(u) 1b currents

Sn(u) 1b currents

131Xe

129Xe

In 129,13154 Xe 〈Sn〉 � 〈Sp〉,

Neutrons carry most nuclear spin

1b current: couple to proton or neutron

S(q = 0) ∝∣∣∣ap〈Sp〉+ an〈Sn〉

∣∣∣22b current: involve neutrons + protons

N

N

χ

χ

N

NN

π

N χ

χ

Dramatic Sp(u) increase due to neutronsJM, Gazit, Schwenk, PRD86 103511(2012)Klos, JM, Gazit, Schwenk, PRD88 083516(2013)

5 / 19

Spin-dependent scattering: 1b+2b currents

0 1 2 3 4 5 6 7 8 9 10

u

0.0001

0.001

0.01

0.1

Si(u

)

Sp(u) 1b currents

Sn(u) 1b currents

Sp(u) 1b + 2b currents

Sn(u) 1b + 2b currents

1 2 3 4 5 6 7 8 9

0.0001

0.001

0.01

0.1

Si(u

)

Sp(u) 1b currents

Sn(u) 1b currents

Sp(u) 1b + 2b currents

Sn(u) 1b + 2b currents

131Xe

129Xe

In 129,13154 Xe 〈Sn〉 � 〈Sp〉,

Neutrons carry most nuclear spin

1b current: couple to proton or neutron

S(q = 0) ∝∣∣∣ap〈Sp〉+ an〈Sn〉

∣∣∣22b current: involve neutrons + protons

N

N

χ

χ

N

NN

π

N χ

χ

Dramatic Sp(u) increase due to neutronsJM, Gazit, Schwenk, PRD86 103511(2012)Klos, JM, Gazit, Schwenk, PRD88 083516(2013)

5 / 19

Application to experiment: LUX SD analysis2b contributions make LUX results (xenon, more sensitive to neutrons)competitive also for the spin-dependent WIMP-proton cross-section

)2WIMP Mass (GeV/c1 10 210

310 410

510

)2

SD

WIM

P-p

roto

n c

ross-s

ectio

n (

cm

-4310

-4210

-4110

-4010

-3910

-3810

-3710

-3610

-3510

-3410

DAMA

ZEPLIN-IIICDMS

KIMSPICASSO

)bSuperK (b

)-

W+SuperK (W)

SuperK (

PICO-2L PICO-60

XENON100

XENON10

LZ Projected

)b

IceCube (b

)-W+

IceCube (W

)-τ+

τ

IceCube (

LUX 90% C.L.

LUX Collaboration, PRL116 161302 (2016)6 / 19

Nuclear matrix elements and structure factorsNuclear 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:Ab initio, shell model,energy density functional...

• Lepton-nucleus interaction:Evaluate (non-perturbative)hadronic currents inside nucleus:phenomenology, effective theory

CDMS Collaboration7 / 19

Test of initial and final nuclear statesRelevant nuclear states spectra very good agreement with experimentElectromagnetic transitions, knockout data... also good agreement

SDPFMU-dbExp.

Excitation E

nerg

y (

MeV

)

0

1

2

3

4

5

SDPFMU-dbExp.

Ca48

0+1

2+1

0+2

4+1

2+1

0+2

4+1

0+1

3(+)1 3

+1

0+1

2+1

0+2

4+1

2+2

0+1

2+1

0+2

4+1

2+2

Ti48

Theory Exp0

500

1000

1500

2000

2500

Exci

tati

on e

ner

gy (

keV

)

4+

6+

0+

3+

4+

6+

2+5

+

2+

0+

2+

4+

2+

6+

3+,4

+6+

2+ 2

+5(4

+)

136Xe

Iwata et al. PRL116 112502 (2016) Vietze et al. PRD91 043520 (2015)

Single-β decay Gamow-Teller, need quenching of transition operator

Phenomenological calculations, uncertainties difficult to quantify8 / 19

Improving nuclear matrix element calculations

For 48Ca enlarge configuration spacefrom pf to sdpf (4 to 7 orbitals)increases matrix elementbut only moderately ∼ 30%Iwata et al. PRL116 112502 (2016)

Enlarge further configuration spacewith Monte Carlo shell modelTogashi et al. PRL117 172502 (2016)

0νββ decay very sensitive toproton-neutron (isoscalar) pairingMatrix element too large if neglectproton-neutron correlations:density functional, IBM valuesJM et al. PRC93 014305 (2016)

9 / 19

Nuclear structure ab initio calculationsGreat sucess prediction of oxygen dripline, calcium separation energies

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

Hergert et al. PRL110 242501 (2013)Cipollone et al. PRL111 062501 (2013)Jansen et al. PRL113 142502 (2014)

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

Gallant et al. PRL 109 032506 (2012)Wienholtz et al. Nature 498 346 (2013)Hagen et al. PRL 109 032502 (2012)Somà et al. PRC 89 061301 (2014)Hergert et al. PRC 90 041302 (2014)10 / 19

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, Gazit, Klos, Hoferichter...

Short-range couplingsfitted to experiment once

11 / 19

Gamow-Teller decay: "quenching" and 2b currentsSingle-β decays well described by nuclear theory (shell model),but need to “quench“ στ operator to predict Gamow-Teller half-lives

N

N

e ν

〈F |∑

i

geffA σiτ

−i |I〉

geffA = (0.7− 0.8)gA

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

0 0.04 0.08 0.12

ρ [fm-3

]

0.5

0.7

0.9

1.1

p=0

1bc

2bc

N

N

e

N

π

N ν Anything missingin transition operator?

2b currents predict quenchinggeff

A = (0.66...0.85)gA

12 / 19

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)JM arXiv:1605.05059, updated 2b currents

Quenching reduced in 0νββ decaylarge momentum transfer p ∼ mπ =⇒

2b currentsreduce matrix elements∼ 20%− 50%

N

N

e ν N

N

e

N

π

N ν

0 100 200 300 400p [MeV]

0.6

0.7

0.8

0.9

1

1.1

0.5

GT

(1b

+2

b)/

gA 1bc

2bc

13 / 19

WIMP scattering off nuclei: standard analysisStandard direct detection analyses consider two very different cases

Spin-Independent (SI) interaction:WIMPs couple to the nuclear density (1χ1N)

Coherent sum over neutrons and protonsCross section enhancement by factor|∑A 〈N‖1N |N 〉 |2 = A2

Spin-Dependent (SD) interaction:WIMP spins couple to the nuclear spin (Sχ · SN )Pairing interaction: spins couple to S = 0Cross section scale set bysingle-proton/neutron spin expectation value|∑A 〈N‖SN |N 〉 |2 = 〈Sn〉2, 〈Sp〉2 ∼ 0.1

How can direct detection analyses be generalized?

0 1 2 3 4 5 6u

10-4

0.001

0.01

0.1

1

10

100

1000

SS(u

)

Structure factorFit

130Xe

dσSIχN

dq2 ∝∣∣∣∑

i

ci ζi Fi

∣∣∣214 / 19

Non-relativistic / Chiral effective field theoryNon-relativistic effective field theory: set of operators Oiin the non-relativistic basis spanned by 1χ, 1N , SN , Sχ, q, v⊥All terms taken to be independent⇒ nucleon (hadronic) physics missingFitzpatrick et al. JCAP02 004(2013), Anand et al. PRC89 065501 (2014)

Chiral EFT: low energy approach to QCD, includes hadronic physicsSet hierarchy on Oi operators, and incorporate 2b effects

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

15 / 19

1b corrections: O3 operatorIn addition to standard spin-independent operator O1,contribution from coherent O11,8,5, quasi-coherent O3 operator

0 0.05 0.1 0.15 0.2 0.25 0.31e-08

1e-06

0.0001

0.01

1

100

10000

|q| [GeV]

|ξ OiF +

|2+

interferen

ceterm

s 132XeO1O1–O3O3O11O8O5

Hoferichter, Klos, JM, SchwenkPRD94 063505 (2016)

O3 → Φ′′ response ∼ nucleon spin orbit operator, interference with O1

O11,8,5 suppressed by 1/mχ or v ∼ 10−3, no O1 interference16 / 19

2b contributions to coherent scattering

Two coherent contributions from 2b currents:π coupling via scalar current, energy-momentum trace anomaly (θµµ)

0 0.05 0.1 0.15 0.2 0.25 0.3

0.01

1

100

10000

|q| [GeV]

|ξ OiF +

|2+

interferen

ceterm

s 132XeO1O1–O3

O1–2b scalarO1–2b θ

O3–2b scalarO3–2b θ2b scalar

2b θ2b interference

Hoferichter, Klos, JM, SchwenkPRD94 063505 (2016)

2b structure factors more important than leading 1b corrections (O3)17 / 19

Minimal extension of spn-independent analysesThe hierarchy in structure factors suggests a minimal extension:

dσSIχN

dq2 =1

4πv2

∣∣∣cM+FM

+ (q2) + cM−FM− (q2) + cπFπ(q2) + cθπFθπ(q2)

∣∣∣2

0 0.05 0.1 0.15 0.2 0.25 0.3

0.01

1

100

10000

|q| [GeV]

structure

factors

132Xe|FM

+ |2 [O1]

q2/m2N |FM

+ FΦ′′+ | [O1–O3]

2|FM+ Fπ| [O1–2b scalar]

2|FM+ F θ

π | [O1–2b θ]

|Fπ|2 [2b scalar]

|F θπ |2 [2b θ]

2q2/m2N |FM

+ |2 [O1 radius]

2|FM+ FM

− | [O1 IS–IV]

|FM− |2 [O1 IV]

N

N

χ

χ NN

N

π

N

Hoferichter, Klos, JM, Schwenk PRD94 063505 (2016)

Constrain each ci , 4 combinations of new-physics parametersAll structure factors for xenon available, other nuclei (argon...) very soon

18 / 19

SummaryNuclear matrix elements and structure factors key forfully exploiting ββ decay and direct dark matter detection experiments

Neutrinoless ββ decay:

Improved matrix elementsin larger configuration spaceswith all relevant correlationsand 2b current contributions

Outlook: ab initio calculationswith controlled uncertainties

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

Direct dark matter detection:

Coupling to protons and neutronscan be same (usual) or different2b currents (scalar, θ coupling)1b corrections (O3) subleading

Each contribution constrainsnew-physics models differently

0 0.05 0.1 0.15 0.2 0.25 0.3

0.01

1

100

10000

|q| [GeV]

structure

factors

132Xe|FM

+ |2 [O1]

q2/m2N |FM

+ FΦ′′+ | [O1–O3]

2|FM+ Fπ| [O1–2b scalar]

2|FM+ F θ

π | [O1–2b θ]

|Fπ|2 [2b scalar]

|F θπ |2 [2b θ]

2q2/m2N |FM

+ |2 [O1 radius]

2|FM+ FM

− | [O1 IS–IV]

|FM− |2 [O1 IV]

19 / 19

CollaboratorsT. OtsukaT. Abe

Y. IwataN. Shimizu

Y. Utsuno M. Honma

P. Klos, A. SchwenkG. Martínez-PinedoJ. Simonis, L. Vietze

J. D. Holt

D. Gazit

A. PovesT. R. Rodríguez

E.CaurierF. Nowacki

L. BaudisG. Kessler

J. Engel

N. Hinohara

R. F. LangS. Reichard

19 / 19