[PPT] - Looking for Dark Matter in the Earth's Shadow Bradley J. Kavanagh PowerPoint Presentation

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Looking for Dark Matter in the Earth's Shadow

Bradley J. Kavanagh LPTHE (Paris) & IPhT (CEA/Saclay)

NewDark

IDM - Sheffield - 19th July 2016

@BradleyKavanagh bradley.kavanagh@lpthe.jussieu.fr with Riccardo Catena (Chalmers) and Chris Kouvaris (CP3-Origins)

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Bradley J Kavanagh (LPTHE & IPhT) DM in the Earth’s Shadow IDM - Sheffield - 19th July 2016

Earth Shadowing

χ

Detector Unscattered (free) DM: f0(v)

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Bradley J Kavanagh (LPTHE & IPhT) DM in the Earth’s Shadow IDM - Sheffield - 19th July 2016

Earth Shadowing

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:

λ RE

Assuming DM mean free path

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Bradley J Kavanagh (LPTHE & IPhT) DM in the Earth’s Shadow IDM - Sheffield - 19th July 2016

Earth Shadowing

χ

Detector

λ RE

Assuming DM mean free path

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Bradley J Kavanagh (LPTHE & IPhT) DM in the Earth’s Shadow IDM - Sheffield - 19th July 2016

Earth Shadowing

χ

Detector

Collar & Avignone [PLB 275, 1992 and others]

Considered in early Monte Carlo simulations Enhancement of DM flux: f(v) → f0(v) + fD(v)

λ RE

Assuming DM mean free path

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Bradley J Kavanagh (LPTHE & IPhT) DM in the Earth’s Shadow IDM - Sheffield - 19th July 2016

Earth Shadowing

Detector Total DM velocity distribution:

χ

f(v) = f0(v) − fA(v) + fD(v)

altered flux, daily modulation, directionality…

λ RE

Assuming DM mean free path

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Bradley J Kavanagh (LPTHE & IPhT) DM in the Earth’s Shadow IDM - Sheffield - 19th July 2016

Earth scattering calculation

Calculate perturbed DM velocity distribution analytically to first order

in (‘Single scatter’ approximation)

Include both contributions to DM flux (both attenuation and

deflection)

Include 9 most abundance elements in the Earth (O, Si, Mg, Fe, Ca,

Na, S, Ni, Al)

Include radial density profile of nuclei in the Earth
Calculate for 14 non-relativistic DM-nucleon interactions (not just

standard SI/SD)

Valid for all DM masses (but focus for now on light DM)

RE/λ ni(r)

Total DM velocity distribution: f(v) = f0(v) − fA(v) + fD(v)

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Bradley J Kavanagh (LPTHE & IPhT) DM in the Earth’s Shadow IDM - Sheffield - 19th July 2016

f0(v) − fA(v) = f0(v) exp

−deff(cos θ)

¯ λ(v)

≈ f0(v)(1 − deff(cos θ)

¯ λ(v) ) ¯ λ = (σ¯ n)−1

DM attenuation

χ

θ v = (v, cos θ, φ)

deff(cos θ)

v

Sum over Earth nuclei

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Bradley J Kavanagh (LPTHE & IPhT) DM in the Earth’s Shadow IDM - Sheffield - 19th July 2016

fD(v) = 1

1

d cos θ 2π dφ deff(cos θ) ¯ λ(κv) (κ)4 2π P(cos α) f(κv, cos θ, φ)

DM deflection

χ

θ v = (v, cos θ, φ)

κ = v/v

v = (v, cos θ, φ) α v v

¯ λ = (σ¯ n)−1

fixed by kinematics

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Bradley J Kavanagh (LPTHE & IPhT) DM in the Earth’s Shadow IDM - Sheffield - 19th July 2016

α

(α) χ=

DM deflection

α

(α) χ=

Forward Backward

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Bradley J Kavanagh (LPTHE & IPhT) DM in the Earth’s Shadow IDM - Sheffield - 19th July 2016

O12 = Sχ · ( SN × v⊥) ⇒ d dER ∼ ER v2

DM deflection

O1 = 1 ⇒ dσ dER ∼ 1 v2 O8 = Sχ · v⊥ ⇒ d dER ∼ (1 − mN ER 2µ2

χN v2 )

α

(α) χ=

Forward Backward

Standard SI

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Bradley J Kavanagh (LPTHE & IPhT) DM in the Earth’s Shadow IDM - Sheffield - 19th July 2016

Size of effect depends

n mean free path:

O12 = Sχ · ( SN × v⊥) ⇒ d dER ∼ ER v2

DM deflection

O1 = 1 ⇒ dσ dER ∼ 1 v2 O8 = Sχ · v⊥ ⇒ d dER ∼ (1 − mN ER 2µ2

χN v2 )

α

(α) χ=

Forward Backward

Standard SI

λ = (σn)−1

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Bradley J Kavanagh (LPTHE & IPhT) DM in the Earth’s Shadow IDM - Sheffield - 19th July 2016

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

ρ0.3 σSI

p [cm2]

LUX CDMSlite CRESST-II p = 50% p = 10% p = 1%

Current cross section limits

Stringent limits on DM-nucleon SI scattering cross section Probability of DM scattering in the Earth

CRESST-II [1509.01515] LUX [1512.03506] CDMSlite [1509.02448]

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Bradley J Kavanagh (LPTHE & IPhT) DM in the Earth’s Shadow IDM - Sheffield - 19th July 2016

Low mass DM may still have large Earth scattering probability

0.1 1 10 100 300

mχ [GeV]

10−42 10−41 10−40 10−39 10−38 10−37 10−36 10−35

ρ0.3 σSI

p [cm2]

LUX CDMSlite CRESST-II p = 50% p = 10% p = 1%

Current cross section limits

Probability of DM scattering in the Earth

CRESST-II [1509.01515] LUX [1512.03506] CDMSlite [1509.02448]

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Bradley J Kavanagh (LPTHE & IPhT) DM in the Earth’s Shadow IDM - Sheffield - 19th July 2016

0.1 1 10 100 300

mχ [GeV]

10−42 10−41 10−40 10−39 10−38 10−37 10−36 10−35

ρ0.3 σSI

p [cm2]

LUX CDMSlite CRESST-II p = 50% p = 10% p = 1%

Subdominant DM component may still have large cross section

Current cross section limits

Probability of DM scattering in the Earth

ρχ → 1% ρχ

CRESST-II [1509.01515] LUX [1512.03506] CDMSlite [1509.02448]

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Bradley J Kavanagh (LPTHE & IPhT) DM in the Earth’s Shadow IDM - Sheffield - 19th July 2016

Non-standard DM-nucleon interactions:

Current cross section limits

0.1 1 10 100 300

mχ [GeV]

10−35 10−34 10−33 10−32 10−31 10−30 10−29 10−28

ρ0.3 σ8

p [cm2]

LUX CRESST-II p = 50% p = 10% p = 1%

σ8

p ∼ v2

σ12

p ∼ q2

0.1 1 10 100 300

mχ [GeV]

10−36 10−35 10−34 10−33 10−32 10−31 10−30 10−29 10−28 10−27

ρ0.3 σ12

p [cm2]

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

SuperCDMS [1503.03379] LUX [1504.06554] CRESST-II [1601.04447] See talk by Riccardo Catena

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Bradley J Kavanagh (LPTHE & IPhT) DM in the Earth’s Shadow IDM - Sheffield - 19th July 2016

Preliminary Results

Focus on low mass DM (for now):
Fix cross section such that average probability of DM scatter in the

Earth is 10% (well below current limits for all operators considered)

Look at DM speed distribution…
… and differential event rate (in CRESST-II)
For different DM-nucleon operators and different incoming DM

velocities (equivalent to different detector positions…)

mχ = 0.5 GeV F(v) =

v2f(v) dΩv

dR dER ∝

dσ

dER vF(v) dv

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Bradley J Kavanagh (LPTHE & IPhT) DM in the Earth’s Shadow IDM - Sheffield - 19th July 2016 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 F(v) [10−3 km/s]

mχ = 0.5 GeV; O1; pscat = 10%

Free γ = 0 γ = π/2 γ = π

100 200 300 400 500 600 700 800 v [km/s] 0.80 0.85 0.90 0.95 1.00 1.05 1.10 1.15 1.20 Fpert(v)/Ffree(v)

Operator 1 - attenuation only

O1 = 1

Isotropic deflection vχγ=0 vχγ=π/2 vχγ=π

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Bradley J Kavanagh (LPTHE & IPhT) DM in the Earth’s Shadow IDM - Sheffield - 19th July 2016 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 F(v) [10−3 km/s]

mχ = 0.5 GeV; O1; pscat = 10%

Free γ = 0 γ = π/2 γ = π

100 200 300 400 500 600 700 800 v [km/s] 0.80 0.85 0.90 0.95 1.00 1.05 1.10 1.15 1.20 Fpert(v)/Ffree(v)

Operator 1 - attenuation + deflection

O1 = 1

Isotropic deflection vχγ=0 vχγ=π/2 vχγ=π

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Bradley J Kavanagh (LPTHE & IPhT) DM in the Earth’s Shadow IDM - Sheffield - 19th July 2016 10−2 10−1 1 Differential Rate [arb. units]

mχ = 0.5 GeV; O1; pscat = 10%

Free γ = 0 γ = π/2 γ = π

200 250 300 400 500 ER [eV] 0.80 0.85 0.90 0.95 1.00 1.05 Ratepert/Ratefree 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 F(v) [10−3 km/s]

mχ = 0.5 GeV; O1; pscat = 10%

Free γ = 0 γ = π/2 γ = π

100 200 300 400 500 600 700 800 v [km/s] 0.80 0.85 0.90 0.95 1.00 1.05 1.10 1.15 1.20 Fpert(v)/Ffree(v)

Operator 1 - attenuation + deflection

O1 = 1

Isotropic deflection

Eth

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Bradley J Kavanagh (LPTHE & IPhT) DM in the Earth’s Shadow IDM - Sheffield - 19th July 2016 10−2 10−1 1 Differential Rate [arb. units]

mχ = 0.5 GeV; O8; pscat = 10%

Free γ = 0 γ = π/2 γ = π

200 250 300 400 500 ER [eV] 0.70 0.75 0.80 0.85 0.90 0.95 1.00 1.05 1.10 Ratepert/Ratefree 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 F(v) [10−3 km/s]

mχ = 0.5 GeV; O8; pscat = 10%

Free γ = 0 γ = π/2 γ = π

100 200 300 400 500 600 700 800 v [km/s] 0.80 0.85 0.90 0.95 1.00 1.05 1.10 1.15 1.20 Fpert(v)/Ffree(v)

Operator 8 - attenuation + deflection

O8 = Sχ · v⊥

Mostly forward deflection

Eth

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Bradley J Kavanagh (LPTHE & IPhT) DM in the Earth’s Shadow IDM - Sheffield - 19th July 2016 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 F(v) [10−3 km/s]

mχ = 0.5 GeV; O12; pscat = 10%

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 1.2 1.3 Fpert(v)/Ffree(v) 10−2 10−1 1 Differential Rate [arb. units]

mχ = 0.5 GeV; O12; pscat = 10%

Free γ = 0 γ = π/2 γ = π

200 250 300 400 500 ER [eV] 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 Ratepert/Ratefree

Operator 12 - attenuation + deflection

Mostly backward deflection O12 = Sχ · ( SN × v⊥)

Eth

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Bradley J Kavanagh (LPTHE & IPhT) DM in the Earth’s Shadow IDM - Sheffield - 19th July 2016

π 4 π 2 3π 4

π Average DM direction, γ 0.70 0.75 0.80 0.85 0.90 0.95 1.00 1.05 1.10 Npert/Nfree

O1 (attenuation only) O8 (attenuation only) O1 O8

Modulation signal

Number of signal events vχγ=0 vχγ=π/2 vχγ=π Modulation due to time-variation of Different phase for different interactions!

γ

mχ = 0.5 GeV

pscat = 10%

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Bradley J Kavanagh (LPTHE & IPhT) DM in the Earth’s Shadow IDM - Sheffield - 19th July 2016

Signatures

Overall change in the DM flux (depending on detector location)
Daily modulation signal as DM direction (in the detector frame)

varies with Earth’s rotation

Annual modulation signal as DM direction varies with the Earth’s
rbit
Effects are latitude-dependent - could cross check with detectors in

different locations

Look at directional rate - expect up-going flux to be decreased

(increased) when the detector is maximally (minimally) shielded

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Bradley J Kavanagh (LPTHE & IPhT) DM in the Earth’s Shadow IDM - Sheffield - 19th July 2016

Conclusions

Significant Earth-scattering is still allowed and detectable given

current constraints

Need to include both attenuation and deflection of DM - which may

enhance the flux

Careful calculation including multiple elements, correct density

profiles and different interactions

Attenuation only dominates if DM particles must cross the Earth

before reaching the detector

The average incoming DM direction varies with time - interesting

daily and annual modulation signals

Different interactions may lead to modulations with different phases -

and may therefore be distinguishable

Need to carefully calculate modulation, location dependence,

directionality… and effects on current limits

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Bradley J Kavanagh (LPTHE & IPhT) DM in the Earth’s Shadow IDM - Sheffield - 19th July 2016

Conclusions

Significant Earth-scattering is still allowed and detectable given

current constraints

Need to include both attenuation and deflection of DM - which may

enhance the flux

Careful calculation including multiple elements, correct density

profiles and different interactions

Attenuation only dominates if DM particles must cross the Earth

before reaching the detector

The average incoming DM direction varies with time - interesting

daily and annual modulation signals

Different interactions may lead to modulations with different phases -

and may therefore be distinguishable

Need to carefully calculate modulation, location dependence,

directionality… and effects on current limits

Thank you!

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Bradley J Kavanagh (LPTHE & IPhT) DM in the Earth’s Shadow IDM - Sheffield - 19th July 2016

Backup Slides

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Bradley J Kavanagh (LPTHE & IPhT) DM in the Earth’s Shadow IDM - Sheffield - 19th July 2016

Heavier DM

α

(α) χ=

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Bradley J Kavanagh (LPTHE & IPhT) DM in the Earth’s Shadow IDM - Sheffield - 19th July 2016

α

(α) χ=

Heavier DM

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Bradley J Kavanagh (LPTHE & IPhT) DM in the Earth’s Shadow IDM - Sheffield - 19th July 2016

Maximum cross section

0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 F(v) [10−3 km/s]

mχ = 0.5 GeV; O1; pscat = 35%

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 1.2 1.3 Fpert(v)/Ffree(v) 10−2 10−1 1 Differential Rate [arb. units]

mχ = 0.5 GeV; O1; pscat = 35%

Free γ = 0 γ = π/2 γ = π

200 250 300 400 500 ER [eV] 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 Ratepert/Ratefree