Earth-Scattering of Dark Matter: from sub-GeV Dark Matter to - - PowerPoint PPT Presentation

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Earth-Scattering of Dark Matter: from sub-GeV Dark Matter to - - PowerPoint PPT Presentation

Nov 23, 2023 408 likes •943 views

Earth-Scattering of Dark Matter: from sub-GeV Dark Matter to WIMPzillas Bradley J. Kavanagh LPTHE - Paris VI Based (partly) on arXiv:1611.05453 with Riccardo Catena and Chris Kouvaris AmsterDark@GRAPPA - 24th May 2017

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NewDark

@BradleyKavanagh bkavanagh@lpthe.jussieu.fr

Bradley J. Kavanagh LPTHE - Paris VI AmsterDark@GRAPPA - 24th May 2017

Earth-Scattering of Dark Matter:

from sub-GeV Dark Matter to WIMPzillas

Based (partly) on arXiv:1611.05453 with Riccardo Catena and Chris Kouvaris

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Bradley J Kavanagh (LPTHE, Paris) AmsterDark@GRAPPA - 24th May 2017 Earth-scattering of DM

Direct Detection Landscape

10−1 100 101 102 103 104

mχ [GeV]

10−48 10−47 10−46 10−45 10−44 10−43 10−42 10−41 10−40 10−39 10−38 10−37 10−36

σSI

p [cm2]

8B

LUX (IDM-2016) CDMSlite (2015) CRESST-II (2015) Xenon1T (2017) Xe Neutrino Floor (O’Hare 2016)

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Bradley J Kavanagh (LPTHE, Paris) AmsterDark@GRAPPA - 24th May 2017 Earth-scattering of DM

Direct Detection Landscape

10−1 100 101 102 103 104

mχ [GeV]

10−48 10−47 10−46 10−45 10−44 10−43 10−42 10−41 10−40 10−39 10−38 10−37 10−36

σSI

p [cm2]

8B

LUX (IDM-2016) CDMSlite (2015) CRESST-II (2015) Xenon1T (2017) Xe Neutrino Floor (O’Hare 2016)

Sub-GeV DM

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Bradley J Kavanagh (LPTHE, Paris) AmsterDark@GRAPPA - 24th May 2017 Earth-scattering of DM

Direct Detection Landscape

10−1 100 101 102 103 104

mχ [GeV]

10−48 10−47 10−46 10−45 10−44 10−43 10−42 10−41 10−40 10−39 10−38 10−37 10−36

σSI

p [cm2]

8B

LUX (IDM-2016) CDMSlite (2015) CRESST-II (2015) Xenon1T (2017) Xe Neutrino Floor (O’Hare 2016)

Sub-GeV DM WIMPzillas

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Bradley J Kavanagh (LPTHE, Paris) AmsterDark@GRAPPA - 24th May 2017 Earth-scattering of DM

0.1 1 10 100 300

mχ [GeV]

10−46 10−45 10−44 10−43 10−42 10−41 10−40 10−39 10−38 10−37 10−36 10−35 10−34

ρ0.3 σp

SI [cm2]

LUX CRESST-II p = 5 % p = 10% p = 1%

DD Landscape - Sub-GeV DM

CRESST-II [1509.01515] LUX [1608.07648] + many others…

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Bradley J Kavanagh (LPTHE, Paris) AmsterDark@GRAPPA - 24th May 2017 Earth-scattering of DM

0.1 1 10 100 300

mχ [GeV]

10−46 10−45 10−44 10−43 10−42 10−41 10−40 10−39 10−38 10−37 10−36 10−35 10−34

ρ0.3 σp

SI [cm2]

LUX CRESST-II p = 5 % p = 10% p = 1%

DD Landscape - Sub-GeV DM

CRESST-II [1509.01515] LUX [1608.07648] + many others…

Focus on this region

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Bradley J Kavanagh (LPTHE, Paris) AmsterDark@GRAPPA - 24th May 2017 Earth-scattering of DM

Direct Detection of DM (in space?)

χ

Detector Unscattered (free) DM: f0(v)

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Bradley J Kavanagh (LPTHE, Paris) AmsterDark@GRAPPA - 24th May 2017 Earth-scattering of DM

Astrophysics of DM (the simple picture)

Standard Halo Model (SHM) is typically assumed: isotropic, spherically symmetric distribution of particles with . Leads to a Maxwell-Boltzmann (MB) distribution (in the lab frame): ρ(r) ∝ r−2 fLab(v) = (2πσ2

v)−3/2 exp

  • −(v − ve)2

2σ2

v

  • Θ(|v − ve| − vesc)

[But see e.g. 1705.05853]

f(v) = v2

  • f(v) dΩv

This is our ‘free’ distribution: f0(v)

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Bradley J Kavanagh (LPTHE, Paris) AmsterDark@GRAPPA - 24th May 2017 Earth-scattering of DM

Direct Detection of DM on Earth

χ

Detector Perturbed/scattered DM: But DM scattering in the Earth can distort the velocity distribution

˜ f(v)

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Bradley J Kavanagh (LPTHE, Paris) AmsterDark@GRAPPA - 24th May 2017 Earth-scattering of DM

Earth-Scattering - Attenuation

χ

Detector Previous calculations usually only consider DM attenuation

Kouvaris & Shoemaker [1405.1729,1509.08720] DAMA [1505.05336] Zaharijas & Farrar [astro-ph/0406531]

f(v) → f0(v) − fA(v)

Attenuation of DM flux:

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Bradley J Kavanagh (LPTHE, Paris) AmsterDark@GRAPPA - 24th May 2017 Earth-scattering of DM

Earth-Scattering - Deflection

χ

Detector

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Bradley J Kavanagh (LPTHE, Paris) AmsterDark@GRAPPA - 24th May 2017 Earth-scattering of DM

Emken, Kouvaris & Shoemaker [1702.07750] (see later)

Earth-Scattering - Deflection

χ

Detector

Collar & Avignone [PLB 275, 1992 and others]

Considered in early Monte Carlo simulations… Can treat (without MC) in the ‘single scatter’ approximation…

λ RE

Assuming DM mean free path As well as more recent ones… Can be very important for light DM.

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Bradley J Kavanagh (LPTHE, Paris) AmsterDark@GRAPPA - 24th May 2017 Earth-scattering of DM

˜ f(v) = f0(v) − fA(v) + fD(v) Earth-Scattering

Detector Total DM velocity distribution:

χ

altered flux, daily modulation, directionality…

λ RE

Assuming DM mean free path Consider both attenuation and deflection in an analytic framework (‘Single scatter’) Consider non-standard DM-nucleon interactions (e.g. NREFT)

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Bradley J Kavanagh (LPTHE, Paris) AmsterDark@GRAPPA - 24th May 2017 Earth-scattering of DM

deff,i = 1 ¯ ni

  • AB

ni(r)dl ¯ λi(v)−1 = ¯ ni σ(v)

Attenuation

Detector

A B

v = (v, cos θ, φ) f0(v) − fA(v) = f0(v) exp

  • −

species

  • i

deff,i(cos θ) ¯ λi(v)

  • Sum over 8 most abundant elements in the Earth: O, Si, Mg, Fe, Ca, Na, S, Al
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Bradley J Kavanagh (LPTHE, Paris) AmsterDark@GRAPPA - 24th May 2017 Earth-scattering of DM

Effective Earth-crossing distance

Most scattering comes from Oxygen (in the mantle) and Iron (in the core)

0.0 0.2 0.4 0.6 0.8 1.0 r/RE 0.0 0.5 1.0 1.5 2.0 n(r) [cm−3] ×1023

Oxygen Iron

NB: little Earth-scattering for spin-dependent interactions

π/4 π/2 θ 0.0 0.2 0.4 0.6 0.8 1.0 1.2 ¯ n deff(θ) [cm−2] ×1032

Oxygen Iron

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Bradley J Kavanagh (LPTHE, Paris) AmsterDark@GRAPPA - 24th May 2017 Earth-scattering of DM

Deflection

v = (v, cos θ, φ)

Detector

A B C

v = (v, cos θ, φ) ¯ λi(v)−1 = ¯ ni σ(v)

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Bradley J Kavanagh (LPTHE, Paris) AmsterDark@GRAPPA - 24th May 2017 Earth-scattering of DM

Deflection

v = (v, cos θ, φ)

Detector

A B C

v = (v, cos θ, φ) ¯ λi(v)−1 = ¯ ni σ(v) κi = v/v fD(v) =

species

  • i
  • d2ˆ

v deff,i(cos θ) λi(κiv) (κi)4 2π f0(κiv, ˆ v)Pi(cos α)

[Detailed calculation in the paper]

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Bradley J Kavanagh (LPTHE, Paris) AmsterDark@GRAPPA - 24th May 2017 Earth-scattering of DM

Deflection

v = (v, cos θ, φ)

Detector

A B C

v = (v, cos θ, φ) ¯ λi(v)−1 = ¯ ni σ(v) κi = v/v fD(v) =

species

  • i
  • d2ˆ

v deff,i(cos θ) λi(κiv) (κi)4 2π f0(κiv, ˆ v)Pi(cos α)

Depends on total cross section Depends on differential cross section

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Bradley J Kavanagh (LPTHE, Paris) AmsterDark@GRAPPA - 24th May 2017 Earth-scattering of DM

Deflection

v = (v, cos θ, φ)

Detector

A B C

v = (v, cos θ, φ) ¯ λi(v)−1 = ¯ ni σ(v) κi = v/v fD(v) =

species

  • i
  • d2ˆ

v deff,i(cos θ) λi(κiv) (κi)4 2π f0(κiv, ˆ v)Pi(cos α)

Depends on total cross section Depends on differential cross section

Focus on low mass DM:

mχ = 0.5 GeV

Fix couplings to give 10% probability of scattering in the Earth

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Bradley J Kavanagh (LPTHE, Paris) AmsterDark@GRAPPA - 24th May 2017 Earth-scattering of DM

DM deflection distribution

P(cos α) = 1 σ dσ dER dER d cos α

  • α

(α)

  • χ =
  • α

(α)

  • χ =

Forward Backward Standard SI interaction

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Bradley J Kavanagh (LPTHE, Paris) AmsterDark@GRAPPA - 24th May 2017 Earth-scattering of DM

  • α

(α)

  • χ =

DM deflection distribution

P(cos α) = 1 σ dσ dER dER d cos α O12 = Sχ · ( SN × v⊥) ⇒ d dER ∼ ER v2 O1 = 1 ⇒ dσ dER ∼ 1 v2 O8 = Sχ · v⊥ ⇒ d dER ∼ (1 − mN ER 2µ2

χN v2 )

Forward Backward Standard SI interaction Standard SI interaction

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Bradley J Kavanagh (LPTHE, Paris) AmsterDark@GRAPPA - 24th May 2017 Earth-scattering of DM

Deflection

v = (v, cos θ, φ)

Detector

A B C

v = (v, cos θ, φ) ¯ λi(v)−1 = ¯ ni σ(v) κi = v/v fD(v) =

species

  • i
  • d2ˆ

v deff,i(cos θ) λi(κiv) (κi)4 2π f0(κiv, ˆ v)Pi(cos α)

Depends on total cross section Depends on differential cross section

Now we have everything we need!

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Bradley J Kavanagh (LPTHE, Paris) AmsterDark@GRAPPA - 24th May 2017 Earth-scattering of DM

EARTHSHADOW Code

EARTHSHADOW code is available online at: github.com/bradkav/EarthShadow Including routines, numerical results, plots and animations…

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Bradley J Kavanagh (LPTHE, Paris) AmsterDark@GRAPPA - 24th May 2017 Earth-scattering of DM

Results

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Bradley J Kavanagh (LPTHE, Paris) AmsterDark@GRAPPA - 24th May 2017 Earth-scattering of DM

0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 ˜ f(v, γ) [10−3 km/s]

Operator O1 − mχ = 0.5 GeV

Free γ = 0 γ = π/2 γ = π

100 200 300 400 500 600 700 800 v [km/s] 0.7 0.8 0.9 1.0 1.1 ˜ f(v, γ)/f0(v)

Speed Distribution - Operator 1

Detector

Calculate DM speed distribution after Earth scattering: ve ˜ f(v, γ)

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Bradley J Kavanagh (LPTHE, Paris) AmsterDark@GRAPPA - 24th May 2017 Earth-scattering of DM

Comparison with Monte-Carlo

http://cp3-origins.dk/site/damascus

Monte-Carlo results from the DaMaSCUS code

[Emken & Kouvaris - paper appearing soon]

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Bradley J Kavanagh (LPTHE, Paris) AmsterDark@GRAPPA - 24th May 2017 Earth-scattering of DM

Comparison with Monte-Carlo

http://cp3-origins.dk/site/damascus

Monte-Carlo results from the DaMaSCUS code

[Emken & Kouvaris - paper appearing soon]

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Bradley J Kavanagh (LPTHE, Paris) AmsterDark@GRAPPA - 24th May 2017 Earth-scattering of DM

Speed Distribution - Operator 1

Detector

Calculate DM speed distribution after Earth scattering: ve

100 200 300 400 500 600 700 v [km/s]

π 4 π 2 3π 4

π γ = cos1(hˆ vχi · ˆ rdet)

  • 1 %
  • 10 %
  • 5 %
  • 1 %

1 %

Operator O1 mχ = 0.5 GeV

  • 30%
  • 20%
  • 10%

0% 10% 20% 30%

Percentage change in speed dist. ˜ f(v, γ)

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Bradley J Kavanagh (LPTHE, Paris) AmsterDark@GRAPPA - 24th May 2017 Earth-scattering of DM

Speed Distribution - O1 vs O8

Detector

100 200 300 400 500 600 700 v [km/s]

π 4 π 2 3π 4

π γ = cos1(hˆ vχi · ˆ rdet)

  • 1 %
  • 10 %
  • 5 %
  • 1

% 1 %

Operator O1 mχ = 0.5 GeV

  • 30%
  • 20%
  • 10%

0% 10% 20% 30%

100 200 300 400 500 600 700 v [km/s]

π 4 π 2 3π 4

π γ = cos1(hˆ vχi · ˆ rdet)

  • 1 %
  • 2

5 %

  • 10 %
  • 5 %
  • 1 %

1 % 5 %

Operator O8 mχ = 0.5 GeV

  • 30%
  • 20%
  • 10%

0% 10% 20% 30%

Operator 8 - preferentially forward deflection

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Bradley J Kavanagh (LPTHE, Paris) AmsterDark@GRAPPA - 24th May 2017 Earth-scattering of DM

Speed Distribution - O1 vs O12

Detector

100 200 300 400 500 600 700 v [km/s]

π 4 π 2 3π 4

π γ = cos1(hˆ vχi · ˆ rdet)

  • 1 %
  • 10 %
  • 5 %
  • 1

% 1 %

Operator O1 mχ = 0.5 GeV

  • 30%
  • 20%
  • 10%

0% 10% 20% 30%

Operator 12 - preferentially backward deflection

100 200 300 400 500 600 700 v [km/s]

π 4 π 2 3π 4

π γ = cos1(hˆ vχi · ˆ rdet)

  • 50 %
  • 25 %
  • 10 %
  • 5

%

  • 1 %

1 % 5 % 1 %

Operator O12 mχ = 0.5 GeV

  • 30%
  • 20%
  • 10%

0% 10% 20% 30%

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Bradley J Kavanagh (LPTHE, Paris) AmsterDark@GRAPPA - 24th May 2017 Earth-scattering of DM

Γout =

  • v·r>0

d2r

  • d3v ˜

f(v, r) (v · r)

Sanity check

Compare rate of DM particles entering the Earth… Γin = πR⊕v …and rate of DM particle leaving the Earth…

Detector

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Bradley J Kavanagh (LPTHE, Paris) AmsterDark@GRAPPA - 24th May 2017 Earth-scattering of DM

0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 ˜ f(v, γ) [10−3 km/s]

Operator O1 − mχ = 0.5 GeV

Free γ = 0 γ = π/2 γ = π

100 200 300 400 500 600 700 800 v [km/s] 0.7 0.8 0.9 1.0 1.1 ˜ f(v, γ)/f0(v)

Event Rate

Calculate number of signal events in a CRESST-II like experiment, with and without the effects of Earth-Scattering, and . Npert Nfree Scattering predominantly with Oxygen and Calcium. DM particles within of the energy threshold 3 σE Eth ∼ 300 eV

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Bradley J Kavanagh (LPTHE, Paris) AmsterDark@GRAPPA - 24th May 2017 Earth-scattering of DM

Mapping the CRESST-II Rate

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Bradley J Kavanagh (LPTHE, Paris) AmsterDark@GRAPPA - 24th May 2017 Earth-scattering of DM

Operator 1 - isotropic deflection

LNGS - Operator 1

LNGS - Gran Sasso Lab, Italy

6 12 18 24 time [hours] 0.9 1.0 1.1 1.2 Npert/Nfree LNGS (42.5 N)

  • Atten. only

Atten.+Defl. O1

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Bradley J Kavanagh (LPTHE, Paris) AmsterDark@GRAPPA - 24th May 2017 Earth-scattering of DM

Operator 8 - forward deflection

LNGS - Operator 8

LNGS - Gran Sasso Lab, Italy

6 12 18 24 time [hours] 0.9 1.0 1.1 1.2 Npert/Nfree LNGS (42.5 N)

  • Atten. only

Atten.+Defl. O1 O8

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Bradley J Kavanagh (LPTHE, Paris) AmsterDark@GRAPPA - 24th May 2017 Earth-scattering of DM

LNGS - Operator 12

LNGS - Gran Sasso Lab, Italy

6 12 18 24 time [hours] 0.9 1.0 1.1 1.2 Npert/Nfree LNGS (42.5 N)

  • Atten. only

Atten.+Defl. O1 O8 O12

Operator 12 - backward deflection

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Bradley J Kavanagh (LPTHE, Paris) AmsterDark@GRAPPA - 24th May 2017 Earth-scattering of DM

Operator 1 - isotropic deflection

6 12 18 24 time [hours] 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 Npert/Nfree SUPL (37.1 S)

O1 O8 O12

SUPL - Operator 1

SUPL - Stawell Underground Physics Lab, Australia

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Bradley J Kavanagh (LPTHE, Paris) AmsterDark@GRAPPA - 24th May 2017 Earth-scattering of DM

Around the world

6 12 18 24 time [hours] 0.9 1.0 1.1 1.2 Npert/Nfree LNGS (42.5 N)

  • Atten. only

Atten.+Defl. O1 O8 O12

6 12 18 24 time [hours] 0.9 1.0 1.1 1.2 Npert/Nfree CJPL (28.2 N)

O1 O8 O12

6 12 18 24 time [hours] 0.8 0.9 1.0 1.1 1.2 Npert/Nfree INO (9.7 N)

O1 O8 O12

6 12 18 24 time [hours] 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 Npert/Nfree SUPL (37.1 S)

O1 O8 O12

India-based Neutrino Observatory China Jinping Lab

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Bradley J Kavanagh (LPTHE, Paris) AmsterDark@GRAPPA - 24th May 2017 Earth-scattering of DM

Implications of Earth-Scattering

Smoking gun signature: daily modulation + location dependence could confirm DM nature Possibility to distinguish different interactions with different amplitude and phase of modulation Careful calculation (including deflection and attenuation) in the ‘single-scatter’ regime

6 12 18 24 time [hours] 0.9 1.0 1.1 1.2 Npert/Nfree LNGS (42.5 N)

  • Atten. only

Atten.+Defl. O1 O8 O12

BJK, Catena & Kouvaris [1611.05453]

EARTHSHADOW code available online to include these effects: 
 github.com/bradkav/EarthShadow

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Bradley J Kavanagh (LPTHE, Paris) AmsterDark@GRAPPA - 24th May 2017 Earth-scattering of DM

WIMPzillas!

PRELIMINARY

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Bradley J Kavanagh (LPTHE, Paris) AmsterDark@GRAPPA - 24th May 2017 Earth-scattering of DM

Direct Detection Landscape - zoomed out

Mack, Beacom & Bertone [0705.4298] Albuquerque & Baudis [astro-ph/0301188]

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Bradley J Kavanagh (LPTHE, Paris) AmsterDark@GRAPPA - 24th May 2017 Earth-scattering of DM

Direct Detection Landscape - zoomed out

Mack, Beacom & Bertone [0705.4298] Albuquerque & Baudis [astro-ph/0301188]

Earth’s heat flow from DM capture + annihilation

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Bradley J Kavanagh (LPTHE, Paris) AmsterDark@GRAPPA - 24th May 2017 Earth-scattering of DM

Direct Detection Landscape - zoomed out

Mack, Beacom & Bertone [0705.4298] Albuquerque & Baudis [astro-ph/0301188]

Assume e.g. asymmetric DM: no heat flux from annihilation

Focus on this region

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Bradley J Kavanagh (LPTHE, Paris) AmsterDark@GRAPPA - 24th May 2017 Earth-scattering of DM

Earth-scattering for super-heavy DM

Deflection of DM (per scatter) goes as Can show that

mA/mχ 1 v⊥(t)2 ∼ σnA m2

A

m2

χ

v4

0t v2

Deflection is almost always negligible Only need to consider stopping of ultra-heavy DM:

dv dx = −vσSI

p species

  • i

ni(r) mi mχ

  • A4

i Ci(v)

‘Correction factor’ due to nuclear form factors

Solve to find final DM speed given initial DM speed and incoming direction :

vi vf ˆ v vf = φ(vi, ˆ v)

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Bradley J Kavanagh (LPTHE, Paris) AmsterDark@GRAPPA - 24th May 2017 Earth-scattering of DM

Distribution of DM reaching the detector with velocity :

Earth-stopping for super-heavy DM

χ

Detector

vf

is the initial velocity the particle must have had

˜ f(vf) = f0(φ−1(vf, ˆ v), ˆ v) vi = φ−1(vf, ˆ v)

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Bradley J Kavanagh (LPTHE, Paris) AmsterDark@GRAPPA - 24th May 2017 Earth-scattering of DM

Preliminary Results

Consider scattering only from Silicon in the Earth, and a detector at a depth of ~11m.

CDMS I at the Stanford Underground Facility [astro-ph/0203500] From below From above

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Bradley J Kavanagh (LPTHE, Paris) AmsterDark@GRAPPA - 24th May 2017 Earth-scattering of DM

Preliminary Results

Consider scattering only from Silicon in the Earth, and a detector at a depth of ~11m.

CDMS I at the Stanford Underground Facility [astro-ph/0203500] 10 keV CDMS I threshold Assume on average that the DM flux comes from about 40 degrees off vertical

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Bradley J Kavanagh (LPTHE, Paris) AmsterDark@GRAPPA - 24th May 2017 Earth-scattering of DM

Preliminary Results

Mack, Beacom & Bertone [0705.4298] Albuquerque & Baudis [astro-ph/0301188]

Possible gain of about 3 orders of magnitude in cross section

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Bradley J Kavanagh (LPTHE, Paris) AmsterDark@GRAPPA - 24th May 2017 Earth-scattering of DM

Caveats

Need to include all Earth elements (but expect Silicon to dominate) Need to perform full careful rate calculation Need to take into account energy losses in the detector shielding (e.g. 1cm thick lead shield) Expect ~2 orders of magnitude improvement in limits (rather than 3),

  • nce I’ve calmed down and done everything properly…
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Bradley J Kavanagh (LPTHE, Paris) AmsterDark@GRAPPA - 24th May 2017 Earth-scattering of DM

Direct Detection Landscape

10−1 100 101 102 103 104

mχ [GeV]

10−48 10−47 10−46 10−45 10−44 10−43 10−42 10−41 10−40 10−39 10−38 10−37 10−36

σSI

p [cm2]

8B

LUX (IDM-2016) CDMSlite (2015) CRESST-II (2015) Xenon1T (2017) Xe Neutrino Floor (O’Hare 2016)

Sub-GeV DM WIMPzillas Still interesting parts of the landscape where Earth-scattering can be explored…

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Bradley J Kavanagh (LPTHE, Paris) AmsterDark@GRAPPA - 24th May 2017 Earth-scattering of DM

Backup Slides

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Bradley J Kavanagh (LPTHE, Paris) AmsterDark@GRAPPA - 24th May 2017 Earth-scattering of DM

Monte Carlo Simulations

State-of-the-art MC simulations are currently in development -

see Emken, Kouvaris & Shoemaker [1702.07750]

Takes deflection into account in a thin portion of Earth’s crust: But still need analytic calculations to test and calibrate!