Dark Matter Search with the Nuclear Isomer Ta-180m

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Björn Lehnert Valencia (virtual) TAUP 2021

Ⅹ Ⅹ’

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Dark Matter Candidates

neutrino

in te ra c ti o n s tr e n g th w ith SM m a tte r

particle mass 10

^-6

neutrino

10

^-12

neutrino

10

^-18

neutrino

gravity

meV eV keV MeV GeV TeV 10

⁹

-10

¹³

TeV

𝛍 eV

Neutrino

WIMP (neutralino, KK photon)

W IMPZ IL L A

Axion Sterile

Neutrino SuperWIMP

(gravitino, axion, KK, graviton) Hidden sector

Cartoon from L. Baudis

Dark Matter Candidates

• Dark matter (DM) well motivated by many astrophysical observations

• Large variety of theoretical DM candidates proposed

• WIMPs are favorite model

• Multiple DM types possible - fraction of observed density 0.3 GeV/cm 3

• Too strongly interacting DM might not interact in traditional underground

direct detection experiments

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Strongly Interacting Dark Matter

• Dark matter thermalizes in overburden

• No signal in underground WIMP detectors

• Existing limits from surface, balloon and rocket experiments with limited sensitivity

• Limits only valid if all DM is strongly interacting

• Unconstraint parameter space for sub component

New idea: Measure thermal WIMPs underground with nuclear isomers

PRD 100, 063013 (2019) surface

rocket

balloon

underground lab e.g. SNOLAB WIMP detector

e.g. DEAP-3600

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180m Ta: Longest lived nuclear isomer

www.nndc.bnl.gov

• Longest lived isomeric state >10 14 yr

• Spin trapped: 9

^-

- 2

⁺

• 3-fold forbidden non-unique β-decay / EC

• Rarest known “stable” isotope

• Elemental abundance 1-2 ppm

•

^180m

Ta isotopic abundance 0.012%

• Origin not well known

• survival not explained in stellar explosions

neutron number N

pr oto n number Z

EC

β -

isomer excited state

half-life

180m

Ta 77 keV >10

¹⁴

yr

137m

Ba 661 keV 2.55 min

177m

Lu 970 keV 160 d

178m

Hf 2.4 MeV 31 yr

examples of nuclear isomers

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180 W

180 Ta

0 + 2 + 4 + 6 +

1 +

0 keV

103.5 keV 337.5 keV 688.4 keV

103.5 keV 234.0 keV

350.9 keV

2 + 9 -

40 keV 77 keV

0 keV 93.3 keV 308.6 keV 640.9 keV

93.3 keV 215.3 keV 332.3 keV

EC

EXP > 2.0x10

¹⁷

yr

PRC 95, 044306 (2017)

TH = 1.4x10

²⁰

yr

JPG, 44 065101 (2017)

β - decay

EXP > 5.8x10

¹⁶

yr

PRC 95, 044306 (2017)

TH = 5.4x10

²³

yr

JPG, 44 065101 (2017)

180 Hf

0 + 2 + 4 + 6 +

37.7 keV

39.5

keV 0 keV

β - decay

(15%) 702 keV

EC

(85%) 845.6 keV

T

1/2

= 8.1 h

180m Ta Decay Modes

𝛾 -decay / IC

EXP > 1.3x10

¹⁴

yr

PRL 124, 181802 (2020)

TH 𝛾 = 1.4x10

³¹

yr TH

IC

= 8.0x10

¹⁸

yr

JPG, 44 065101 (2017)

• Intermediate nucleus in double beta decay system

• All natural 180 Ta trapped in

meta-stable state

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Search for 180m Ta Decay

Ta

HPGe

ɣ

HPGe

• Combined 4 datasets (≈ 400 d)

• Bayesian analysis

• No signal found

excluded: bg from

214

Pb 351.9 keV signal

signal signal excluded: low

detection efficiency

excluded signal at 90% credibility

1.5 kg Ta, 180 mg

^180m

Ta

sa n d w ich co n fig u ra ti o n

HADES underground lab

Mol, Belgium

PRC 95, 044306 (2017)

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• Heavy DM can de-excite 180m Ta absorbing large angular momentum

• Not competitive for standard WIMP DM

• Focus on DM not accessible by large

underground direct detection experiments Two Dark Matter models:

(1) Strongly interacting dark matter (2) Inelastic dark matter

• Same datasets / analysis

• No signal found

Search for Dark Matter Induced 180m Ta Decay

Ⅹ

Ⅹ’

PRL 124, 181802 (2020)

signal (0.9%)

excluded: bg line from

224

Th 92.4 + 92.8 keV

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Limits on Strongly Interacting Dark Matter

σ χ,Ta < ln(2) ⋅ M χ T 1/2 ⋅ ρ lab

• Half-life to cross section:

ρ lab

ρ solar = v solar

v terminal ≈ 10 8

223 m overburden

ρ solar ρ lab

p e r-n u cl e o n cro ss se ct io n

DM density gradient

@100 GeV, 10^-30 cm²

• Cross section enhancement:

dark matter mass fraction of strongly interacting DM compared to all DM

new

exclusion

realistic exclusion in future

f DM = 1

f DM = 0.01 f DM = 10 −4

PRL 124, 181802 (2020)

more info in PRD 101, 055001 (2020)

= 0.3 GeV/cm³

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4

FIG. 2: Region of interest in each dataset for the 103.5 keV peak search in the channel. The best fit is shown in blue and the best fit with the signal peak set to the 90% C.I. half-life limit is shown in red. The arrows indicated

the 93.3 keV peak of the EC channel (not used in fit) as well as the named background -lines.

� ��

�� -��

� χ [��]

σ � [ �� ]

� �� =�� -�

�� (��+��)

�� (�� + �� )

��

�� (�� )

��

�� -��

δ� χ [��]

σ � [ �� ]

� χ =� ��

��

�� (�� + �� )

�� ( �� + �� )

�� (�� )

��

FIG. 3: Left: 90% credibility limits on the per-nucleon cross-section for DM that interacts strongly with nuclei from lifetime limit of 180m Ta corresponding to T 1/2 > 1.3 ⇥ 10 14 a are shown in red. Also shown are limits from existing

experiments adapted from [15] in gray. Projections for limits from an experiment that can measure

T 1/2 > 1 ⇥ 10 18 a in the (3a)+(3b) decay mode are shown in dashed orange and for T 1/2 > 4 ⇥ 10 19 a in the (3a) only mode in dashed purple. Right: Limits and projections with the same color coding for inelastic DM with mass

splitting M . Also shown are limits from existing experiments adapted from [17] in gray.

h Ta v i = Min

✓

n

µ Ta,

q 0 , 4⇡R 2 Ta

◆

S f (q 0 ). (4) Here, µ Ta, is the tantalum-DM reduced mass, q 0 =

267

p

E ⇥ µ Ta, is the momentum exchange, and R Ta is

268

the radius of tantalum nuclei. The quantity S f (q 0 ) is

269

the nuclear form factor that captures the inelastic ma-

270

trix element for the down-scatter of the isomeric state

271

to one of the lower states. Following [10] it is estimated

272

from the Weisskopf estimates and includes the hindrance

273

factors prescribed in [12].

274

Since it is an exothermic reaction, the counting rate

275

depends on the local DM density and not the flux. We

276

can use Eq. 4 along with ⌘ calculated in [10], the relation

277

in Eq. 3 and the limit in Eq. 2 to set limits on n . This

278

limit will depend on f DM , the fraction of solar system DM

279

in particles. Limit contours are plotted in the n vs

280

limits from existing experiments which are adapted from

282

[15]. Stringent new limits are set for M > 50 GeV in the

283

strongly interacting regime. There is a drastic reduction

284

in parameter space ruled out by existing direct detection

285

(DD) experiments for such small dark matter fractions.

286

However, 180m Ta has a much slower drop-o↵ in sensitivity

287

owing to its unique ability to look for slowed down DM

288

that has a large local number density. Limits for di↵erent

289

f DM are discussed in Supplementary Material. V.

290

B. Inelastic Dark Matter

291

DM could have dominantly non-diagonal couplings

292

with the SM, i.e. scattering relevant to DD is deter-

293

mined by the operator L (G F ) 2 ¯ 0 N N ¯ , where N

294

is the target nucleus, 0 is non-degenerate with and

295

M = M

⁰

M . As a result this energy di↵erence

296

Limits on Inelastic Dark Matter

• Composite dark matter with excited state: δM χ = M χ′ − M χ

p e r-n u cl e o n cro ss se ct io n

• Energy difference needs to be supplied for scatter

• Traditional: Maximum of DM velocity limits access to

• New 180m Ta: Stored energy in metastable state can access higher

• Overburden has no stopping below E kin threshold

δM χ

δM χ < 400 keV δM χ

dark matter mass splitting

DM Mass new

exclusion

realistic exclusion in future

Ⅹ

Ⅹ’

ground state excited state

δM χ

9

0 500 1000 1500 2000 2500 3000 10^-37

10^-35 10^-33 10^-31 10^-29

δM_χ[keV]

σN[cm2 ]

M_χ=1 TeV

1 g. year¹⁸⁰Ta

1μg. year¹⁷⁸Hf 1 mg. year¹⁷⁷Lu

100 kg. 2.6min¹³⁷Ba CRESST

FIG. 4. Per-nucleon cross-section reach for di↵erent Isomeric nuclei for corresponding exposure. Also shown are ”inelastic frontier” limits from LZ/PANDAX and CRESST. The sensitivity is derived assuming 3 detectable interactions per year.

These limits are for illustrative purposes only. Limits on con- crete models with detection signature are displayed in Fig. 5 and Fig. 6

its from conventional detectors are strongest purely from exposure considerations. Among these CRESST is dom- inant due to having the heaviest element element used in DD, tungsten (¹⁸⁷W). However these limits disappear altogether at M >400 keV. Projections for limits from metastable nuclei extend well above that, with the maximum splitting given by Eqn.(22). Potential limits from

178Hf are weak due to small mass of target but extend the farthest in M . ^180mTa could have only nominal im- provements in the splitting due its modest energy splitting (77 keV). ¹⁷⁷Lu and¹³⁷Ba have theoretically a good reach in cross-section and should also be able to probe splittings above 1 MeV.

In practice, the lifetime and scattering rate of the excited state ₂ will determine the feasibility of this reach. These quantities, as well as the corresponding elastic loop-induced scattering cross-section are model- dependent, and will be considered for specific models next.

A. Dark Photon Mediator

We start with the terms in the Lagrangian relevant to the dark photon [21],

L ig_{D 2} ^µ ₁A⁰_µ+ h.c + 1

2✏F_µ⌫⁰ F^µ⌫. (26) The di↵erential cross-section for inelastic scattering is given by [7],

d

dq² = 4⇡↵↵_D✏²

(mA⁰)⁴v². (27) where m_A0 is the mass of the dark photon. This can be substituted in Eqn.(8) to obtain the event rate.

FIG. 5. Reach for di↵erent Isomeric nuclei for dark photon DM model. Limits from LZ/PANDAX and CRESST do not have any reach for M > 450keV. Also shown in gray are loop constraints from LZ/Icecube and limits on the dark photon mediator from BABAR and projections for Belle II (dashed). Contours of constant mean-free-path for excited DM in a conventional DM detector are also marked.

The elastic process at one loop level is given by [7] (see also [22]),

n,loop = ↵²_D↵²✏⁴m⁴_nf_q²

⇡(m_A0)⁶ , (28) for m_A⁰ > 100 MeV. For lower masses, there will be coherence across the nucleus. This formula is rather ap- proximate, and the hadronic matrix elements are estimated to be f_q ⇠0.1 [7].

The mass splitting considered are always smaller than the mediator mass. The excited state can only decay through an o↵-shell A⁰ to e⁺e if the splitting is above threshold, or through 3 which is a loop process. Both of these are highly suppressed. As a result some other decay mechanism might be required to deplete the excited state in the first place. We will assume that excited DM is long-lived on the detector scale. As a result, the observable is either ground state decay (^180mTa) or end-point (^178mHf). For large statistics, we can also en- vision placing the isomer in the vicinity of a conventional DM detector. Thus if ₁ transitions into ₂ by scattering with the isomer, it now has enough energy to deposit its excess inside a conventional detector.

To this end we plot in Fig. 5the reach for 3 scattering events for various isomer target options as a function of the dark photon model parameters i.e. the mixing ✏ vs dark photon mass m_A0. Also shown are contours of the subsequent mean-free-path of the excited state ₂ in a

Other isomers more powerful but experimentally very challenging

models with predominantly inelastic interactions

PRL 124, 181802 (2020)

DM Search with ^180mTa, Bjoern Lehnert, TAUP 2021

9

PRD 101, 055001 (2020)

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(1) Gamma spectroscopy

• Direct detection

• 180m Ta decay gammas

• T 1/2 overburden dependent

(2) WIMP detectors

• Direct detection

• Nuclear recoil

• Source on-off

(3) Geological

• Indirect detection

• Excess daughters 180 W, 180 Hf

• T 1/2 overburden dependent

• Ratio of 180 W to 180 Hf

Ta sample

HPGe

ɣ

Ⅹ

Ⅹ’

Ⅹ

Ⅹ’

Ⅹ’’

WIMP detector

NR

Ta Ta

sh ie ld in g

^180m

Ta

¹⁸⁰

W

180m

Ta

¹⁸⁰

Hf

180m

Ta

¹⁸⁰

W

180m

Ta

¹⁸⁰

Hf

Ⅹ Ⅹ

thermal DM

fast DM

Three Types of 180m Ta Dark Matter Experiments

thermal DM

thermal

DM

fast DM

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Tantalum Minerals

• Ta present in tantalite

• Old minerals O(10 9 yr)

• Accumulation of decay products

• 180m Ta → 180 Hf

• 180m Ta → 180 W

• Hf and W potentially in low concentrations in tantalite

• Measurement with mass spectroscopy on different samples

natural isotopic abundance

abundance ratio to

reference isotope

increase abundance due to

^180m

Ta decay

Example with realistic inputs - not a measurement

significant discovery

After discovery of decay:

• Daughter ratio depends on decay mode

• 180m Ta: 180 Hf / 180 W = 4000 (th. prediction)

• 180 Ta: 180 Hf / 180 W = 5.7

• Decay can occur via normal processes or dark matter interactions

• Smoking gun: T 1/2 overburden

dependent for dark matter interactions

• Measure different tantalite samples

from different deposits / depth

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Systematics over 1 Billion Years

Milky way rotation:

• Change in local DM density?

• Solar system period: 0.24 Gyr

• Solar system passing through different DM substructures?

Plate techtonics:

• Ta minerals move around earth in cratons

• Formation and break-up of supercontinents

• Pangaea 0.17 - 0.34 Gyr

• Pannotia 0.57 - 0.63 Gyr

• Rodinia 0.75 - 1.13 Gyr

• Significant change of overburden?

• Moving up and down in crust

• Atmospheric changes

0.24 Gyr

Earth-Sci. Rev. 214, 103477 (2021)

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Conclusions

180m Ta can be used for dark matter detection

• DM can de-excite 180m Ta,

• DM can get a kinetic boost / gets excited

• New parameter space excluded for

• Strongly interacting dark matter

• Inelastic dark matter

Three types of experiments

• (1) Gamma spectroscopy

• (2) Around WIMP detectors

• (3) Geological

• Smoking gun: Overburden dependent 180m Ta half-life