Nuclear structure for decay and dark matter searches...Nuclear physics, decay, dark matter detection...
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)
-τ
+τ
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