Earth-Shadowing effects in Dark Matter direct detection Bradley J. - - PowerPoint PPT Presentation

Earth-Shadowing effects in Dark Matter direct detection

Bradley J. Kavanagh LPTHE (Paris)

NewDark

6th Amsterdam-Paris-Stockholm Meeting 31st August 2016

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

Bradley J Kavanagh (LPTHE - Paris) Earth-Shadowing effects APS VI - 31st August 2016

Variation with detector position and time gives characteristic signatures Size of effect depends on Mean Free Path: altered flux, daily modulation, directionality…

Earth Shadowing

χ

Detector DM velocity distribution is affected by DM interactions in the Earth

f(v) λ = (σn)−1

Bradley J Kavanagh (LPTHE - Paris) Earth-Shadowing effects APS VI - 31st August 2016

dR dER = ρχ mχmN ∞

vmin

vf(v) dσ dER d3v

Direct detection

χ N χ N v ∼ 10−3

DM

vmin =

• mN ER

2µ2

χN

Differential recoil rate: Include all DM particles with enough speed to induce a recoil of energy :

ER

Bradley J Kavanagh (LPTHE - Paris) Earth-Shadowing effects APS VI - 31st August 2016

F(v) = v2

• f(v) dΩv

Speed distribution

vmin =

• mN ER

2µ2

χN

mχ = 1 GeV Eth = 0.3 keV mχ = 50 GeV Eth = 2 keV

Standard Halo Model (SHM) Values of for scattering on Oxygen nuclei for… Minimum speed req. to excite recoil of energy :

vmin ER

Speed distribution:

Bradley J Kavanagh (LPTHE - Paris) Earth-Shadowing effects APS VI - 31st August 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

Current cross section limits

Stringent limits on DM-nucleon SI scattering cross section

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

Bradley J Kavanagh (LPTHE - Paris) Earth-Shadowing effects APS VI - 31st August 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]

Bradley J Kavanagh (LPTHE - Paris) Earth-Shadowing effects APS VI - 31st August 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]

Bradley J Kavanagh (LPTHE - Paris) Earth-Shadowing effects APS VI - 31st August 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]

Bradley J Kavanagh (LPTHE - Paris) Earth-Shadowing effects APS VI - 31st August 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]

Bradley J Kavanagh (LPTHE - Paris) Earth-Shadowing effects APS VI - 31st August 2016

Earth Shadowing

χ

Detector Unscattered (free) DM: f0(v)

Bradley J Kavanagh (LPTHE - Paris) Earth-Shadowing effects APS VI - 31st August 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

Bradley J Kavanagh (LPTHE - Paris) Earth-Shadowing effects APS VI - 31st August 2016

Earth Shadowing

χ

Detector

λ RE

Assuming DM mean free path

Bradley J Kavanagh (LPTHE - Paris) Earth-Shadowing effects APS VI - 31st August 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

Bradley J Kavanagh (LPTHE - Paris) Earth-Shadowing effects APS VI - 31st August 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

Bradley J Kavanagh (LPTHE - Paris) Earth-Shadowing effects APS VI - 31st August 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)
• Public code to be released

RE/λ ni(r)

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

Bradley J Kavanagh (LPTHE - Paris) Earth-Shadowing effects APS VI - 31st August 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)
• Public code to be released

RE/λ ni(r)

Total DM velocity distribution: f(v) = f0(v) − fA(v) + fD(v) A sketch of the calculation…

Bradley J Kavanagh (LPTHE - Paris) Earth-Shadowing effects APS VI - 31st August 2016

¯ λ = (σ¯ n)−1

DM attenuation

χ

θ v = (v, cos θ, φ)

deff(cos θ)

v

Sum over Earth nuclei

f0(v) − fA(v) = f0(v) exp

• −deff(cos θ)

¯ λ(v)

Bradley J Kavanagh (LPTHE - Paris) Earth-Shadowing effects APS VI - 31st August 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

Bradley J Kavanagh (LPTHE - Paris) Earth-Shadowing effects APS VI - 31st August 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

Bradley J Kavanagh (LPTHE - Paris) Earth-Shadowing effects APS VI - 31st August 2016

DM-nucleon operators

In order to obtain , we need to know . dσ/dER P(cos α) Consider different possible operators in a non-relativistic EFT (NREFT) framework :

Fitzpatrick et al. [1203.3542]

Construct interactions from relevant NR degrees of freedom:

, , ,

~ Sχ ~ SN ~ q mN ~ v⊥ = ~ v + ~ q 2µχN

O1 = 1 O4 = ~ Sχ · ~ SN Standard spin-independent operator: Standard spin-dependent operator: But we can construct operators higher-order in and …

• v
• q

[1008.1591, 1203.3542, 1308.6288, 1505.03117]

Bradley J Kavanagh (LPTHE - Paris) Earth-Shadowing effects APS VI - 31st August 2016

• α

(α) χ=

DM deflection

• α

(α) χ=

Forward Backward

Bradley J Kavanagh (LPTHE - Paris) Earth-Shadowing effects APS VI - 31st August 2016

• α

(α) χ=

DM deflection

• α

(α) χ=

Forward Backward

Bradley J Kavanagh (LPTHE - Paris) Earth-Shadowing effects APS VI - 31st August 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

Bradley J Kavanagh (LPTHE - Paris) Earth-Shadowing effects APS VI - 31st August 2016

F(v) = v2

• f(v) dΩv

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 average incoming

DM directions (denoted by the angle ) corresponding to different detector positions and times

mχ = 0.5 GeV γ dR dER ∝ ∞

vmin

vF(v) dσ dER dv

[1601.04447]

Bradley J Kavanagh (LPTHE - Paris) Earth-Shadowing effects APS VI - 31st August 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

Bradley J Kavanagh (LPTHE - Paris) Earth-Shadowing effects APS VI - 31st August 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

Bradley J Kavanagh (LPTHE - Paris) Earth-Shadowing effects APS VI - 31st August 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

Bradley J Kavanagh (LPTHE - Paris) Earth-Shadowing effects APS VI - 31st August 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; 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 vχγ=0 vχγ=π/2 vχγ=π

Bradley J Kavanagh (LPTHE - Paris) Earth-Shadowing effects APS VI - 31st August 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)

Operator 12 - attenuation + deflection

Mostly backward deflection O12 = Sχ · ( SN × v⊥) vχγ=0 vχγ=π/2 vχγ=π

Bradley J Kavanagh (LPTHE - Paris) Earth-Shadowing effects APS VI - 31st August 2016

π 4 π 2 3π 4

π Average DM direction, γ 0.6 0.7 0.8 0.9 1.0 1.1 1.2 Npert/Nfree

O1 O8 O12

• Atten. only

Atten.+Defl.

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%

Bradley J Kavanagh (LPTHE - Paris) Earth-Shadowing effects APS VI - 31st August 2016

Modulation signal

Number of signal events

5 10 15 20 time [hours] 0.90 0.95 1.00 1.05 1.10 1.15 1.20 Npert/Nfree LNGS (43.0 N)

O1 O8 O12

5 10 15 20 time [hours] 0.90 0.95 1.00 1.05 1.10 1.15 1.20 Npert/Nfree CJPL (28.0 N)

O1 O8 O12

Attenuation + Deflection Attenuation only

mχ = 0.5 GeV

pscat = 10%

Gran Sasso, Italy Jinping, China

Need to calculate as a function of time and location:

γ

Bradley J Kavanagh (LPTHE - Paris) Earth-Shadowing effects APS VI - 31st August 2016

5 10 15 20 time [hours] 0.6 0.7 0.8 0.9 1.0 1.1 Npert/Nfree SUPL (37.0 S)

O1 O8 O12

Modulation signal

Number of signal events

5 10 15 20 time [hours] 0.90 0.95 1.00 1.05 1.10 1.15 1.20 Npert/Nfree LNGS (43.0 N)

O1 O8 O12

mχ = 0.5 GeV

pscat = 10%

Gran Sasso, Italy Victoria, Australia

Attenuation + Deflection Attenuation only

Bradley J Kavanagh (LPTHE - Paris) Earth-Shadowing effects APS VI - 31st August 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 [not shown here…]
• 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

Bradley J Kavanagh (LPTHE - Paris) Earth-Shadowing effects APS VI - 31st August 2016

Single-scatter Approximation

The Single-scatter approximation is important to capture the effects of deflection. The limits don’t always allow very strongly interacting DM, but…

• Calculations in the many-scatter/‘diffusion’ regime
• Dedicated simulations to test the single-scatter regime

and connect to very high cross sections

• For interactions which give DM deflection peaked in a

particular direction, additional scatters will effectively broaden this distribution (may be able to account for this?) …the single-scatter approximation will obviously break down as the interaction cross section increases. What then?

[With thanks to Pat Scott]

Bradley J Kavanagh (LPTHE - Paris) Earth-Shadowing effects APS VI - 31st August 2016

Summary

• Significant Earth-scattering is still allowed

and detectable by current experiments

• Need to include both attenuation and

deflection of DM

• Careful calculation including multiple

elements, correct density profiles and different interactions

• 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

5 10 15 20 time [hours] 0.90 0.95 1.00 1.05 1.10 1.15 1.20 Npert/Nfree LNGS (43.0 N)

O1 O8 O12

Gran Sasso, Italy

Attenuation + Deflection Attenuation only

Bradley J Kavanagh (LPTHE - Paris) Earth-Shadowing effects APS VI - 31st August 2016

Summary

• Significant Earth-scattering is still allowed

and detectable by current experiments

• Need to include both attenuation and

deflection of DM

• Careful calculation including multiple

elements, correct density profiles and different interactions

• 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

5 10 15 20 time [hours] 0.90 0.95 1.00 1.05 1.10 1.15 1.20 Npert/Nfree LNGS (43.0 N)

O1 O8 O12

Gran Sasso, Italy

Attenuation + Deflection Attenuation only

Thank you!

Bradley J Kavanagh (LPTHE - Paris) Earth-Shadowing effects APS VI - 31st August 2016

Backup Slides

Bradley J Kavanagh (LPTHE - Paris) Earth-Shadowing effects APS VI - 31st August 2016

Heavier DM

• α

(α) χ=

Bradley J Kavanagh (LPTHE - Paris) Earth-Shadowing effects APS VI - 31st August 2016

• α

(α) χ=

Heavier DM

Bradley J Kavanagh (LPTHE - Paris) Earth-Shadowing effects APS VI - 31st August 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

Bradley J Kavanagh (LPTHE - Paris) Earth-Shadowing effects APS VI - 31st August 2016

CRESST-II rate at the Equator

5 10 15 20 time [hours] 0.80 0.85 0.90 0.95 1.00 1.05 1.10 1.15 1.20 Npert/Nfree EQUATOR (0.0 N)

O1 O8 O12