Earth-Scattering of Dark Matter: when Dark Matter particle physics - - PowerPoint PPT Presentation

▶
earth scattering of dark matter
SMART_READER_LITE
LIVE PREVIEW

Earth-Scattering of Dark Matter: when Dark Matter particle physics - - PowerPoint PPT Presentation

Sep 12, 2023 100 likes •833 views

Earth-Scattering of Dark Matter: when Dark Matter particle physics and astrophysics collide Bradley J. Kavanagh LPTHE - Paris VI Based on arXiv:1611.05453 with Riccardo Catena and Chris Kouvaris MIAPP, Munich - 21st March 2017

slide-1
SLIDE 1

NewDark

@BradleyKavanagh bkavanagh@lpthe.jussieu.fr

Bradley J. Kavanagh LPTHE - Paris VI MIAPP, Munich - 21st March 2017

Earth-Scattering of Dark Matter:

when Dark Matter particle physics and astrophysics collide

Based on arXiv:1611.05453 with Riccardo Catena and Chris Kouvaris

slide-2
SLIDE 2

Local DM density: ρχ ∼ 0.3 GeV/cm3

Dark Matter is heavier in Munich

slide-3
SLIDE 3

Local DM density: ρχ ∼ 0.3 GeV/cm3

Dark Matter is heavier in Munich

In the UK, for mχ ∼ 150 GeV you get about 1 DM particle per glass…

slide-4
SLIDE 4

Local DM density: ρχ ∼ 0.3 GeV/cm3

Dark Matter is heavier in Munich

In the UK, for mχ ∼ 150 GeV you get about 1 DM particle per glass… In Munich, you need mχ ∼ 300 GeV to get 1 DM particle per glass…

slide-5
SLIDE 5

NewDark

@BradleyKavanagh bkavanagh@lpthe.jussieu.fr

Bradley J. Kavanagh LPTHE - Paris VI MIAPP, Munich - 21st March 2017

Earth-Scattering of Dark Matter:

when Dark Matter particle physics and astrophysics collide

Based on arXiv:1611.05453 with Riccardo Catena and Chris Kouvaris

slide-6
SLIDE 6

Astrophysics Particle physics

slide-7
SLIDE 7

Astrophysics Particle physics Nuclear Physics

slide-8
SLIDE 8

Astrophysics Particle physics

slide-9
SLIDE 9

‘Standard’ SI/SD WIMPs with SHM distribution

slide-10
SLIDE 10

Astrophysics

Reconstructing DM parameters without astro assumptions

1303.6868, 1312.1852, 1410.8051, 1609.08630 and others

slide-11
SLIDE 11

Astrophysics

Reconstructing DM parameters without astro assumptions

1303.6868, 1312.1852, 1410.8051, 1609.08630 and others

Particle physics

Discriminating DM

  • perators

1505.07406

DM-SM operator running and mixing

1605.04917, 1702.00016

slide-12
SLIDE 12

Astrophysics

Reconstructing DM parameters without astro assumptions

1303.6868, 1312.1852, 1410.8051, 1609.08630 and others

Particle physics

Discriminating DM

  • perators

1505.07406

DM-SM operator running and mixing

1605.04917, 1702.00016

Earth-Scattering of DM?

slide-13
SLIDE 13

Bradley J Kavanagh (LPTHE, Paris) MIAPP, Munich - 21st Mar. 2017 Earth-scattering of DM

Direct Detection of DM (in space?)

χ

Detector Unscattered (free) DM: f0(v)

slide-14
SLIDE 14

Bradley J Kavanagh (LPTHE, Paris) MIAPP, Munich - 21st Mar. 2017 Earth-scattering of DM

Direct Detection of DM on Earth

χ

Detector Unscattered (free) DM: f0(v)

slide-15
SLIDE 15

Bradley J Kavanagh (LPTHE, Paris) MIAPP, Munich - 21st Mar. 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:

slide-16
SLIDE 16

Bradley J Kavanagh (LPTHE, Paris) MIAPP, Munich - 21st Mar. 2017 Earth-scattering of DM

Earth-Scattering - Deflection

χ

Detector

slide-17
SLIDE 17

Bradley J Kavanagh (LPTHE, Paris) MIAPP, Munich - 21st Mar. 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…

slide-18
SLIDE 18

Bradley J Kavanagh (LPTHE, Paris) MIAPP, Munich - 21st Mar. 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)

slide-19
SLIDE 19

Bradley J Kavanagh (LPTHE, Paris) MIAPP, Munich - 21st Mar. 2017 Earth-scattering of DM

The current landscape

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

How big is the probability of scattering in the Earth?

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

slide-20
SLIDE 20

Bradley J Kavanagh (LPTHE, Paris) MIAPP, Munich - 21st Mar. 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%

The current landscape

What effect can DM scattering in the Earth have?

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

slide-21
SLIDE 21

Bradley J Kavanagh (LPTHE, Paris) MIAPP, Munich - 21st Mar. 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%

The current landscape

What effect can DM scattering in the Earth have?

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

Focus on this region

slide-22
SLIDE 22

Bradley J Kavanagh (LPTHE, Paris) MIAPP, Munich - 21st Mar. 2017 Earth-scattering of DM

Earth-Scattering Calculation

Detector Total DM velocity distribution:

χ

λ RE

Assuming DM mean free path

˜ f(v) = f0(v) − fA(v) + fD(v)

slide-23
SLIDE 23

Bradley J Kavanagh (LPTHE, Paris) MIAPP, Munich - 21st Mar. 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)

[See Nassim Bozorgnia’s talk 06/03]

f(v) = v2

  • f(v) dΩv

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

slide-24
SLIDE 24

Bradley J Kavanagh (LPTHE, Paris) MIAPP, Munich - 21st Mar. 2017 Earth-scattering of DM

Attenuation

Detector

A B

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

  • −d(cos θ)

λ(v)

  • λ(v)−1 = n σ(v)
slide-25
SLIDE 25

Bradley J Kavanagh (LPTHE, Paris) MIAPP, Munich - 21st Mar. 2017 Earth-scattering of DM

deff = 1 ¯ n

  • AB

n(r)dl ¯ λ(v)−1 = ¯ n σ(v) f0(v) − fA(v) = f0(v) exp

  • −deff(cos θ)

¯ λ(v)

  • Attenuation

Detector

A B

v = (v, cos θ, φ)

slide-26
SLIDE 26

Bradley J Kavanagh (LPTHE, Paris) MIAPP, Munich - 21st Mar. 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
slide-27
SLIDE 27

Bradley J Kavanagh (LPTHE, Paris) MIAPP, Munich - 21st Mar. 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

slide-28
SLIDE 28

Bradley J Kavanagh (LPTHE, Paris) MIAPP, Munich - 21st Mar. 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)

slide-29
SLIDE 29

Bradley J Kavanagh (LPTHE, Paris) MIAPP, Munich - 21st Mar. 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]

slide-30
SLIDE 30

Bradley J Kavanagh (LPTHE, Paris) MIAPP, Munich - 21st Mar. 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

slide-31
SLIDE 31

Bradley J Kavanagh (LPTHE, Paris) MIAPP, Munich - 21st Mar. 2017 Earth-scattering of DM

NREFT operator basis SI SD

O1 = 1 O4 = ~ Sχ · ~ SN

[1008.1591, 1203.3542, 1308.6288, 1505.03117]

Write down all possible non-relativistic (NR) WIMP-nucleon operators which can mediate the elastic scattering.

[Fan et al - 1008.1591, Fitzpatrick et al. - 1203.3542]

slide-32
SLIDE 32

Bradley J Kavanagh (LPTHE, Paris) MIAPP, Munich - 21st Mar. 2017 Earth-scattering of DM

NREFT operator basis

O1 = 1 O3 = i~ SN · (~ q × ~ v⊥)/mN O4 = ~ Sχ · ~ SN O5 = i~ Sχ · (~ q × ~ v⊥)/mN O6 = (~ Sχ · ~ q)(~ SN · ~ q)/m2

N

O7 = ~ SN · ~ v⊥ O8 = ~ Sχ · ~ v⊥ O9 = i~ Sχ · (~ SN × ~ q)/mN O10 = i~ SN · ~ q/mN O11 = i~ Sχ · ~ q/mN

SI SD

[1008.1591, 1203.3542, 1308.6288, 1505.03117]

O12 = ~ Sχ · (~ SN × ~ v⊥) O13 = i(~ Sχ · ~ v⊥)(~ SN · ~ q)/mN O14 = i(~ Sχ · ~ q)(~ SN · ~ v⊥)/mN O15 = −(~ Sχ · ~ q)((~ SN × ~ v⊥) · ~ q/m2

N

. . . NB: two sets of operators, one for protons and one for neutrons… Write down all possible non-relativistic (NR) WIMP-nucleon operators which can mediate the elastic scattering.

[Fan et al - 1008.1591, Fitzpatrick et al. - 1203.3542]

  • v⊥ =

v +

  • q

2µχN

slide-33
SLIDE 33

Bradley J Kavanagh (LPTHE, Paris) MIAPP, Munich - 21st Mar. 2017 Earth-scattering of DM

Energy spectra

Standard SI/SD int.

mχ = 100 GeV

dσ dER ∼ 1/v2

slide-34
SLIDE 34

Bradley J Kavanagh (LPTHE, Paris) MIAPP, Munich - 21st Mar. 2017 Earth-scattering of DM

Energy spectra mχ = 100 GeV

dσ dER ∼ v2

⊥/v2

dσ dER ∼ q2/v2

slide-35
SLIDE 35

Bradley J Kavanagh (LPTHE, Paris) MIAPP, Munich - 21st Mar. 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

slide-36
SLIDE 36

Bradley J Kavanagh (LPTHE, Paris) MIAPP, Munich - 21st Mar. 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 )

Standard SI

Forward Backward

slide-37
SLIDE 37

Bradley J Kavanagh (LPTHE, Paris) MIAPP, Munich - 21st Mar. 2017 Earth-scattering of DM

Constraints on NREFT operators

0.1 1 10 100 300

mχ [GeV]

10−40 10−39 10−38 10−37 10−36 10−35 10−34 10−33 10−32 10−31 10−30 10−29 10−28

ρ0.3 ˜ σp

8 [cm2]

LUX C R E S S T

  • I

I p = 50% p = 1 % p = 1%

Operator ˆ O8 0.1 1 10 100 300

mχ [GeV]

10−42 10−40 10−38 10−36 10−34 10−32 10−30 10−28 10−26

ρ0.3 ˜ σp

12 [cm2]

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

Operator ˆ O12

Focus on low mass DM: mχ = 0.5 GeV Fix couplings to give 10% probability of scattering Focus on SI operator (O1), as well as O8 and O12:

slide-38
SLIDE 38

Bradley J Kavanagh (LPTHE, Paris) MIAPP, Munich - 21st Mar. 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!

slide-39
SLIDE 39

Bradley J Kavanagh (LPTHE, Paris) MIAPP, Munich - 21st Mar. 2017 Earth-scattering of DM

EARTHSHADOW Code

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

slide-40
SLIDE 40

Bradley J Kavanagh (LPTHE, Paris) MIAPP, Munich - 21st Mar. 2017 Earth-scattering of DM

Results

slide-41
SLIDE 41

Bradley J Kavanagh (LPTHE, Paris) MIAPP, Munich - 21st Mar. 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)

slide-42
SLIDE 42

Bradley J Kavanagh (LPTHE, Paris) MIAPP, Munich - 21st Mar. 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)

slide-43
SLIDE 43

Bradley J Kavanagh (LPTHE, Paris) MIAPP, Munich - 21st Mar. 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

slide-44
SLIDE 44

Bradley J Kavanagh (LPTHE, Paris) MIAPP, Munich - 21st Mar. 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%

slide-45
SLIDE 45

Bradley J Kavanagh (LPTHE, Paris) MIAPP, Munich - 21st Mar. 2017 Earth-scattering of DM

Low mass vs High mass

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%

Higher mass DM

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 % 5 % 10 % 2 5 % 50 %

Operator O1 mχ = 50 GeV

  • 30%
  • 20%
  • 10%

0% 10% 20% 30%

slide-46
SLIDE 46

Bradley J Kavanagh (LPTHE, Paris) MIAPP, Munich - 21st Mar. 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

slide-47
SLIDE 47

Bradley J Kavanagh (LPTHE, Paris) MIAPP, Munich - 21st Mar. 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

slide-48
SLIDE 48

Bradley J Kavanagh (LPTHE, Paris) MIAPP, Munich - 21st Mar. 2017 Earth-scattering of DM

Mapping the CRESST-II Rate

slide-49
SLIDE 49

Bradley J Kavanagh (LPTHE, Paris) MIAPP, Munich - 21st Mar. 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

slide-50
SLIDE 50

Bradley J Kavanagh (LPTHE, Paris) MIAPP, Munich - 21st Mar. 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

slide-51
SLIDE 51

Bradley J Kavanagh (LPTHE, Paris) MIAPP, Munich - 21st Mar. 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

slide-52
SLIDE 52

Bradley J Kavanagh (LPTHE, Paris) MIAPP, Munich - 21st Mar. 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

slide-53
SLIDE 53

Bradley J Kavanagh (LPTHE, Paris) MIAPP, Munich - 21st Mar. 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

slide-54
SLIDE 54

Bradley J Kavanagh (LPTHE, Paris) MIAPP, Munich - 21st Mar. 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

slide-55
SLIDE 55

Bradley J Kavanagh (LPTHE, Paris) MIAPP, Munich - 21st Mar. 2017 Earth-scattering of DM

Ideas for the future

slide-56
SLIDE 56

Bradley J Kavanagh (LPTHE, Paris) MIAPP, Munich - 21st Mar. 2017 Earth-scattering of DM

Mapping out the parameter space

Continue mapping out parameter space and explore impact on upper limits for a range of interactions… (mχ, σp)

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 = 1 % p = 1%

0.1 1 10 100 300

mχ [GeV]

10−42 10−40 10−38 10−36 10−34 10−32 10−30 10−28 10−26

ρ0.3 ˜ σp

12 [cm2]

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

Operator ˆ O12

…and encourage experimental collaborations to explore full NREFT parameter space.

slide-57
SLIDE 57

Bradley J Kavanagh (LPTHE, Paris) MIAPP, Munich - 21st Mar. 2017 Earth-scattering of DM

Directionality

Distortion of should also lead to a directional signature

f(v)

Studied previously for very efficiency stopping

[1509.08720]

In our case, Earth-Scattering should give an excess of particles

  • riginating from the ‘downward’

direction (depending on time of day) Detector

χ

Recent proposal for directional sensitivity to low mass DM using semiconductor detectors

[1703.05371]

slide-58
SLIDE 58

Bradley J Kavanagh (LPTHE, Paris) MIAPP, Munich - 21st Mar. 2017 Earth-scattering of DM

Astrophysical Uncertainties

How robust are these results against changes to the (free) velocity distribution?

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

Doesn’t depend on spectral information, only timing information. Also, what about degeneracy between cross section and DM density…?

slide-59
SLIDE 59

Bradley J Kavanagh (LPTHE, Paris) MIAPP, Munich - 21st Mar. 2017 Earth-scattering of DM

Low mass Dark Matter

The ‘many-scatter’ regime for low mass DM? Low mass DM loses almost no energy on scattering

  • α

(α)

  • χ =

Forward Backward

For standard SI interactions the scattering is isotropic Should be able to model as a random walk/diffusion process

slide-60
SLIDE 60

Bradley J Kavanagh (LPTHE, Paris) MIAPP, Munich - 21st Mar. 2017 Earth-scattering of DM

High mass Dark Matter

What about very heavy DM?

[1608.07648]

slide-61
SLIDE 61

Bradley J Kavanagh (LPTHE, Paris) MIAPP, Munich - 21st Mar. 2017 Earth-scattering of DM

High mass Dark Matter

What about very heavy DM?

[1608.07648]

WIMPzillas!

[hep-ph/9810361, 1606.00923]

mχ ∼ 107 GeV pscat ∼ 1

for

slide-62
SLIDE 62

Bradley J Kavanagh (LPTHE, Paris) MIAPP, Munich - 21st Mar. 2017 Earth-scattering of DM

High mass Dark Matter

What about very heavy DM? In the limit, DM is not deflected and loses no energy when scattering with Earth nuclei

mχ → ∞

But for finite , get a small deflection and energy loss.

mχ

Heavy DM effectively follows smooth, curved trajectories through the Earth

slide-63
SLIDE 63

Bradley J Kavanagh (LPTHE, Paris) MIAPP, Munich - 21st Mar. 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!

slide-64
SLIDE 64

Bradley J Kavanagh (LPTHE, Paris) MIAPP, Munich - 21st Mar. 2017 Earth-scattering of DM

Future ideas

  • Mapping out the parameter space - What are the signatures of

different DM-nucleon (DM-e? Long-range?) interactions?

  • Directional signatures of Earth-Scattering - Does directional

sensitivity enhance these effects?

  • The impact of astrophysical uncertainties - Would diurnal

modulation be a ‘clean’ signature? What about ?

  • Low mass DM - Can we make progress in the diffusion regime?
  • High mass DM - WIMPzilla trajectories should be simpler. What are

the signatures for heavy SIMP DM?

  • Monte Carlo simulations - Can we tackle Earth-Scattering for an

arbitrary point in parameter space? How can we test/calibrate these simulations?

ρχ

slide-65
SLIDE 65

Bradley J Kavanagh (LPTHE, Paris) MIAPP, Munich - 21st Mar. 2017 Earth-scattering of DM

Backup Slides

slide-66
SLIDE 66

Bradley J Kavanagh (LPTHE, Paris) MIAPP, Munich - 21st Mar. 2017 Earth-scattering of DM

INO - Operator 8

Operator O8

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

slide-67
SLIDE 67

Bradley J Kavanagh (LPTHE, Paris) MIAPP, Munich - 21st Mar. 2017 Earth-scattering of DM

Mapping the CRESST-II Rate

slide-68
SLIDE 68

Bradley J Kavanagh (LPTHE, Paris) MIAPP, Munich - 21st Mar. 2017 Earth-scattering of DM

Mapping the CRESST-II Rate

slide-69
SLIDE 69

Bradley J Kavanagh (LPTHE, Paris) MIAPP, Munich - 21st Mar. 2017 Earth-scattering of DM

Mapping the CRESST-II Rate

slide-70
SLIDE 70

Bradley J Kavanagh (LPTHE, Paris) MIAPP, Munich - 21st Mar. 2017 Earth-scattering of DM

fD(v) = dl λi(r, v) v v f0(v)P(v → v) d3v

Deflection α v v

C dl Rate of particles entering the region: dS nχ f0(v) v cos α dS d3v Probability of scattering in the region: dl λi(r, v) cos α P(v → v) d3v Rate of particles leaving the region: nχfD(v) v dS d3v Deflected velocity distribution:

slide-71
SLIDE 71

Bradley J Kavanagh (LPTHE, Paris) MIAPP, Munich - 21st Mar. 2017 Earth-scattering of DM

Probability of scattering from one velocity to another can be written:

Deflection

Deflected velocity distribution (from a single point): fixed by kinematics (for a given ) α Need to integrate over all incoming velocities and over all points C: P(v → v) = 1 2π 1 v2 δ(v − v/κi) P(cos α) = 1 2π v v3 δ(v − κiv) P(cos α) fD(v) = 1 2π

  • AB

dl λi(r, v)

  • d3v v2

v4 δ(v − κiv)f0(v, ˆ v)Pi(cos α) Collect everything together, and sum over Earth species… fD(v) = dl λi(r, v) v v f0(v)P(v → v) d3v v/v ≡ κi

slide-72
SLIDE 72

Bradley J Kavanagh (LPTHE, Paris) MIAPP, Munich - 21st Mar. 2017 Earth-scattering of DM

Deflection

fixed by kinematics (for a given ) α Then integrate over all incoming velocities and over all points C: Collect everything together, and sum over Earth species… v/v ≡ κi

α v v

C dl dS Equate rate of particles entering and leaving region, having scattered… fD(v) = 1 2π

  • AB

dl λi(r, v)

  • d3v v2

v4 f0(v, ˆ v)Pi(cos α)

[Detailed calculation in the paper]