Theory of DM-atom Interactions Oren Slone, Princeton University - - PowerPoint PPT Presentation

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Theory of DM-atom Interactions

Oren Slone, Princeton University

Non ΛCDM simulations

Theory of DM-“bound nucleus” Interactions

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Why Bound States?

In-elastic to extract more energy. Chemical bonds typically have

∆E ≈ O(eV)

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Extracting the Energy

Scattering Absorption

O(eV) O(eV)

Eextract > mχ matom Eχ

Eextract = mχ

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Eextract ≈ q2 matom ≈ mχ matom Eχ

Eextract ≈ q2 + ~ q · ∆~ p matom ≈ ✓ mχ matom + ∆p matomvχ ◆ Eχ

|0> |1>

How this works for Scattering

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An example: Di-Atomic Molecules

q m1 m2 m2 m1

Eextract = 0.1 − 10 eV

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Diatomic Molecules Potential Energy

Born Oppenheimer |Φ0

moli = |Φ0 nuci|Φ0 ei

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The Scattering Cross Section

hσvχi / ¯ σn Z qdq 2µ2

χn

f 2

P N|FDM(q)|2|Ftarget(q)|2η[vmin(q)]

V elocity Distribution DM Form Factor Target Form Factor ⌘[vmin(q)] ≡ Z ∞

vmin

d3vχ f(~ vχ) vχ

|FDM(q)|2 ≡ |M2→2(q)|2 |M2→2(q2 = q2

0)|2

¯ σn ≡ |M2→2(q2 = q2

0)|2

16π(mχ + mn)2

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The Form Factor

Eextract = ~ vχ · ~ q − q2 2µχtarget

| hΨf|Hint|Ψii |2 / |Ftarget(q)|2 ⌘

• Z

d3reiq·rΨ∗

f (r)Ψi(r)

• 2

2 3 4 5 6 r @a0D

• 0.4
• 0.2

0.2 0.4 0.6

WaveFunction Overlap for l=90

Energy Conservation:

• Prob. to Transition

with Eextract:

Dictates the q-E Relation

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Classical Picture

The Form Factor:

|Ftarget(q)|2 ∝ (3)(~ q − X~ ki)

The Cross Section:

⌧∂σvχ ∂q2

• =

¯ σn 4µ2

χnvχ

Eextract Ebind

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QM Picture

The Form Factor:

|Ftarget(q)|2 ≡

• Z

d3reiq·rΨ∗

f (r)Ψi(r)

• 2

Eextract ≈ Ebind

Essig, Figueroa, Perez-Rios, Ramani, OS, 2019

Eextract = ~ vχ · ~ q − q2 2µχtarget

The Classical Momentum T ransfer

Eextract ≈ q2 ± q · ∆p matom

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The Scattering Cross Section

Target FF summed

• ver all signal states

hσvχi / ¯ σn Z qdq 2µ2

χn

f 2

P N|FDM(q)|2

@ X

• sig. states

|Ftarget(q)|2 1 A η[vmin(q)]

The states included in the signal drastically affect the available phase space!

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Kinematics & Signal

Dissociation with Scattering

mχ ≈ 100 MeV

Eextract ≈ mχ matom 1 2mχv2

χ

q ≈ mχvχ ≈ 100 keV

mχ

¯ σn

Lots of phase space available

∼ 100 MeV

≈ 10 eV

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Kinematics & Signal

Excitation with Scattering

mχ

¯ σn

Phase space suppression for each final state

Eextract ≈ ✓ mχ matom + ∆p matomvχ ◆ 1 2mχv2

χ

q ≈ mχvχ ≈ 10 − 100 keV

Width ~

qr cos θ

≈ 1 − 10 eV

mχ ≈ 1 − 10 MeV

∼ 1 − 10 MeV

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The Absorption Cross Section

|Ftarget(q)|2 ≡

• Z

d3reiq·rΨ∗

f (r)Hint(r)Ψi(r)

• 2

(q = mχvχ)−1 aBohr

eiq·r ≈ 1 + O(q · aBohr)

Same as for scattering except: The momentum transfer is small: Additional (model dependent) interaction terms can be important: Eextract = mχ ≈ 1 eV

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Kinematics & Signal

Excitation with Absorption

mχ

Phase space VERY suppressed for each final state Eextract = mχ ≈ 1 eV

q ≈ mχvχ ≈ 1 meV

Width ~ h∆Ei

∼ 1 eV

✏

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The Migdal Effect

|Φ0

eci = eime P

i v·ri|Φeci

P = |hΦ⇤

ec|Φ0 eci|2

Using all this to plan real experiments

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Using all this to plan real experiments

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Dissociation via Scattering: Detecting Color Center Defects in a Crystal Lattice (Ranny’s Talk) Excitation via Scattering: Detecting Multiple Coincident IR Photons in a Molecular Gas Excitation via Bosonic DM Absorption: Detecting Single IR-UV Photons in a Multi- Component Molecular Gas (Ken’s Talk) Migdal Efgect: Reinterpret TPC results

eV

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Budnik, Chesnovsky, OS, Volansky, 2017

Crystal Defects

Proposed Setup

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Crystal Defects

Prospective Reach (also Solar Neutrinos)

• χ []

σ [] [(·)-]

=

χ=ν

• χ []

σ [] [(·)-]

=

• χ=ν
• []

ν/ [(·)-]

• []

ν/ [(·)-]

• Budnik, Chesnovsky, OS, Volansky, 2017

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Essig, Figueroa, Perez-Rios, Ramani, OS, 2019

Molecular Excitation via Scattering

Proposed Setup

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Molecular Excitation via Scattering

Basic Proposal

Detect IR Photons from a low pressure gas at ~55 K

Consider molecules with large spontaneous emission rates and suppressed quenching rates Use of MKIDs, TESs or SNSPDs Search for all excitations which produce multiple coincident photons (for BG discrimination, BBR and DC) Optimize Temperature and Pressure for different DM masses and target molecules Sensitive to SI as well as SD Interactions

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Molecular Excitation via Scattering

Two Types of Multi Photon Signals

Less efficient for large v V-V transfer (resonant quenching)

|v0i + |0i ! |v0 1i + |1i

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Essig, Figueroa, Perez-Rios, Ramani, OS, 2019

Molecular Excitation via Scattering

Two Types of Multi Photon Signals

a3Π Energetically available Experimentally unobserved v J Co-Quench signal Cascade signal vb

• γ

[(·)-] (=)

= σ=·-

(-)

Huge MFP Easy to collect Tiny MFP Difficult to collect Sensitivity to MeV DM

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Essig, Figueroa, Perez-Rios, Ramani, OS, 2019

Molecular Excitation via Scattering

Expected Reach - SI Coupling

+

• χ []

σ []

()=

=() =

• =

(

• )
• =

(

• )
• =() =
• =
• μ
• +
• χ []

σ []

()=(/)

• =

(

• )
• =
• =

(

• )
• =

(

• )
• =

(

• )
• =
• =μ

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Essig, Figueroa, Perez-Rios, Ramani, OS, 2019

Molecular Excitation via Scattering

Expected Reach - SD Coupling

+

• χ []

σ []

• ()=

=() = =() =() =() =

• χ []

σ []

• ()=

=()

• =
• =() =()

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Arvanitaki, Dimopoulos, KVT, 2017

Molecular Excitation via Absorption

Proposed Setup (Study by Ken Van Tilburg et. al.)

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Molecular Excitation via Absorption

• f Bosonic DM

Basic Proposal and Features

Detect single IR-UV photons from a low pressure gas Resonant enhancement of the cross section when DM mass matches excitation energy Constructive interference for emission of photons in stack setup Scan over DM masses by varying target molecules

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Arvanitaki, Dimopoulos, KVT, 2017

Molecular Excitation via Absorption

Expected Reach for a Light Hidden Photon Mediator

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The Migdal Effect

|Φ0

eci = eime P

i v·ri|Φeci

P = |hΦ⇤

ec|Φ0 eci|2

Akerib, et. al., 2019

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SUMMARY

In-elastic states allow DD to access light DM with nuclear couplings Dissociation / Scattering / Absorption achieve sensitivity to different masses, models and interaction strengths Much of the technology will soon be available

THANK YOU

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Backup

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An irreducible BG Nine Solar neutrino families - uncertainties in flux Neutrino BG reduction depends on 2 parameters: Exposure Threshold DM spectrum can mimic neutrino spectrum Cross section reach saturates for large exposure

Solar Neutrinos

Background

ArXiv:1608.02940 - Essig, Slone, Mardon, Volansky

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Solar Neutrinos

Background Reduction

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Sommerfeld Enhancement

Escaping particle “feels” the binding potential Phase space grows Larger effect for smaller p F(p) ~ p-1 Equivalent to the improved FF