Signatures of Earth-Scattering in the Direct Detection of Dark Matter Bradley J. Kavanagh LPTHE - Paris VI Based on arXiv:1611.05453 with Riccardo Catena and Chris Kouvaris MPIK, Heidelberg - 9th January 2017 bkavanagh@lpthe.jussieu.fr @BradleyKavanagh NewDark
Dark Matter Planck [1502.01589] Hradecky et al. [astro-ph/0006397] Rubin, Ford & Thonnard (1980) Bradley J Kavanagh (LPTHE, Paris) Earth-scattering of DM MPIK, Heidelberg - 9th Jan. 2017
Dark Matter at the Sun’s Radius Global Local Model total mass distribution in Estimate local DM density from Milky Way and extract DM kinematics of local stars density at Solar Radius (~8 kpc) (assuming local disk equilibrium) E.g. Iocco et al. [1502.03821] E.g. Garbari et al. [1206.0015] Values in the range: ρ χ ∼ 0 . 2–0 . 8 GeV cm − 3 But not zero! c.f. Garbari et al. [1204.3924] Read [1404.1938] Bradley J Kavanagh (LPTHE, Paris) Earth-scattering of DM MPIK, Heidelberg - 9th Jan. 2017
Direct Detection of DM on Earth Detector χ Bradley J Kavanagh (LPTHE, Paris) Earth-scattering of DM MPIK, Heidelberg - 9th Jan. 2017
Direct Detection of DM on Earth Detector χ Unscattered (free) DM: f 0 ( v ) Bradley J Kavanagh (LPTHE, Paris) Earth-scattering of DM MPIK, Heidelberg - 9th Jan. 2017
Earth-Scattering - Attenuation Detector Previous calculations usually only consider DM attenuation Zaharijas & Farrar [astro-ph/0406531] Kouvaris & Shoemaker [1405.1729,1509.08720] DAMA [1505.05336] χ f ( v ) → f 0 ( v ) − f A ( v ) Attenuation of DM flux: Bradley J Kavanagh (LPTHE, Paris) Earth-scattering of DM MPIK, Heidelberg - 9th Jan. 2017
Earth-Scattering - Deflection Detector χ Bradley J Kavanagh (LPTHE, Paris) Earth-scattering of DM MPIK, Heidelberg - 9th Jan. 2017
Earth-Scattering - Deflection Detector Assuming DM mean free path λ � R E Considered in early Monte Carlo simulations Collar & Avignone [PLB 275, 1992 and others] χ We’ll use the ‘single scatter’ approximation… Bradley J Kavanagh (LPTHE, Paris) Earth-scattering of DM MPIK, Heidelberg - 9th Jan. 2017
Earth-Scattering Detector Assuming DM mean free path λ � R E χ ˜ f ( v ) = f 0 ( v ) − f A ( v ) + f D ( v ) Total DM velocity distribution: altered flux, daily modulation, directionality… Bradley J Kavanagh (LPTHE, Paris) Earth-scattering of DM MPIK, Heidelberg - 9th Jan. 2017
Outline Direct Detection (a more detailed look) Calculating the Earth-Scattering effect Non-relativistic Effective Field Theory of DM Impact on the DM velocity distribution and modulation signatures Future work Bradley J Kavanagh (LPTHE, Paris) Earth-scattering of DM MPIK, Heidelberg - 9th Jan. 2017
Direct detection Detector Target nucleus m χ & 1 GeV v ∼ 10 − 3 χ Bradley J Kavanagh (LPTHE, Paris) Earth-scattering of DM MPIK, Heidelberg - 9th Jan. 2017
Direct detection Detector m χ & 1 GeV v ∼ 10 − 3 Bradley J Kavanagh (LPTHE, Paris) Earth-scattering of DM MPIK, Heidelberg - 9th Jan. 2017
Direct detection Detector Light (scintillation) m χ & 1 GeV v ∼ 10 − 3 Charge Heat (phonons) (ionisation) Bradley J Kavanagh (LPTHE, Paris) Earth-scattering of DM MPIK, Heidelberg - 9th Jan. 2017
Direct detection Detector Light (scintillation) m χ & 1 GeV v ∼ 10 − 3 Charge Heat (phonons) (ionisation) Include all particles with enough � ∞ d R vf ( v ) d σ ρ χ d 3 v speed to excite recoil of energy : = E R d E R d E R m χ m A v min � m N E R v min = 2 µ 2 χ N Bradley J Kavanagh (LPTHE, Paris) Earth-scattering of DM MPIK, Heidelberg - 9th Jan. 2017
Direct detection Detector Light (scintillation) m χ & 1 GeV v ∼ 10 − 3 Charge Heat (phonons) (ionisation) Include all particles with enough � ∞ d R vf ( v ) d σ ρ χ d 3 v speed to excite recoil of energy : = E R d E R d E R m χ m A v min � m N E R v min = 2 µ 2 χ N Particle and Astrophysics nuclear physics Bradley J Kavanagh (LPTHE, Paris) Earth-scattering of DM MPIK, Heidelberg - 9th Jan. 2017
Direct detection Detector Light (scintillation) m χ & 1 GeV v ∼ 10 − 3 Charge Heat (phonons) (ionisation) Include all particles with enough � ∞ d R vf ( v ) d σ ρ χ d 3 v speed to excite recoil of energy : = E R d E R d E R m χ m A v min � m N E R v min = 2 µ 2 χ N Particle and Astrophysics nuclear physics But plenty of alternative ideas: DM-electron recoils [1108.5383] Superconducting detectors [1504.07237] Axion DM searches [1404.1455] Bradley J Kavanagh (LPTHE, Paris) Earth-scattering of DM MPIK, Heidelberg - 9th Jan. 2017
Particle Physics of DM (the simple picture) Typically assume contact interactions (heavy mediators). In the non-relativistic limit, obtain two main contributions. σ p Write in terms of DM-proton cross section : d σ A σ p χ p v 2 C A F 2 ( E R ) Form factor accounts for ∝ d E R µ 2 loss of coherence at high energy Enhancement factor different for: C SI A ∼ A 2 spin-independent (SI) interactions - C SD ∼ ( J + 1) /J spin-dependent (SD) interactions - A Interactions which are higher order in v are possible - see later… Bradley J Kavanagh (LPTHE, Paris) Earth-scattering of DM MPIK, Heidelberg - 9th Jan. 2017
Astrophysics of DM (the simple picture) Standard Halo Model (SHM) is typically assumed: isotropic, ρ ( r ) ∝ r − 2 spherically symmetric distribution of particles with . Leads to a Maxwell-Boltzmann (MB) distribution (in the lab frame): − ( v − v e ) 2 � � v ) − 3 / 2 exp f Lab ( v ) = (2 πσ 2 Θ ( | v − v e | − v esc ) 2 σ 2 v which is well matched in some hydro simulations. [1601.04707, 1601.04725, 1601.05402] � v e - Earth’s Velocity f ( v ) = v 2 f ( v ) d Ω v v e ∼ 220 − 250 km s − 1 σ v ∼ 155 − 175 km s − 1 Feast et al. [astro-ph/9706293], Bovy et al. [1209.0759] − 41 km s − 1 v esc = 533 +54 Piffl et al. (RAVE) [1309.4293] Bradley J Kavanagh (LPTHE, Paris) Earth-scattering of DM MPIK, Heidelberg - 9th Jan. 2017
The final event rate SI interactions, SHM distribution Bradley J Kavanagh (LPTHE, Paris) Earth-scattering of DM MPIK, Heidelberg - 9th Jan. 2017
The current landscape 10 − 34 10 − 35 10 − 36 10 − 37 10 − 38 CRESST-II SI [cm 2 ] 10 − 39 10 − 40 ρ 0 . 3 σ p 10 − 41 10 − 42 10 − 43 10 − 44 10 − 45 LUX 10 − 46 0 . 1 1 10 100 300 m χ [GeV] CRESST-II [1509.01515] LUX [1608.07648] + many others… How big is the probability of scattering in the Earth? Bradley J Kavanagh (LPTHE, Paris) Earth-scattering of DM MPIK, Heidelberg - 9th Jan. 2017
The current landscape 10 − 34 10 − 35 10 − 36 10 − 37 = p 5 0 % 10 − 38 CRESST-II p = 10% SI [cm 2 ] 10 − 39 p = 1% 10 − 40 ρ 0 . 3 σ p 10 − 41 10 − 42 10 − 43 10 − 44 10 − 45 LUX 10 − 46 0 . 1 1 10 100 300 m χ [GeV] CRESST-II [1509.01515] LUX [1608.07648] + many others… What effect can DM scattering in the Earth have? Bradley J Kavanagh (LPTHE, Paris) Earth-scattering of DM MPIK, Heidelberg - 9th Jan. 2017
Earth-Scattering Bradley J Kavanagh (LPTHE, Paris) Earth-scattering of DM MPIK, Heidelberg - 9th Jan. 2017
Earth-Scattering Calculation Detector Assuming DM mean free path λ � R E χ ˜ f ( v ) = f 0 ( v ) − f A ( v ) + f D ( v ) Total DM velocity distribution: Bradley J Kavanagh (LPTHE, Paris) Earth-scattering of DM MPIK, Heidelberg - 9th Jan. 2017
Attenuation λ ( v ) − 1 = n σ ( v ) v = ( v, cos θ , φ ) B Detector A � − d (cos θ ) � f 0 ( v ) − f A ( v ) = f 0 ( v ) exp λ ( v ) Bradley J Kavanagh (LPTHE, Paris) Earth-scattering of DM MPIK, Heidelberg - 9th Jan. 2017
Attenuation λ ( v ) − 1 = ¯ ¯ v = ( v, cos θ , φ ) n σ ( v ) B Detector d e ff = 1 � n ( r )d l ¯ n AB A � � − d e ff (cos θ ) f 0 ( v ) − f A ( v ) = f 0 ( v ) exp ¯ λ ( v ) Bradley J Kavanagh (LPTHE, Paris) Earth-scattering of DM MPIK, Heidelberg - 9th Jan. 2017
Attenuation λ i ( v ) − 1 = ¯ ¯ v = ( v, cos θ , φ ) n i σ ( v ) B Detector d e ff ,i = 1 � n i ( r )d l ¯ n i AB A � species � d e ff ,i (cos θ ) � f 0 ( v ) − f A ( v ) = f 0 ( v ) exp − ¯ λ i ( v ) i Sum over 8 most abundant elements in the Earth: O, Si, Mg, Fe, Ca, Na, S, Al Bradley J Kavanagh (LPTHE, Paris) Earth-scattering of DM MPIK, Heidelberg - 9th Jan. 2017
Effective Earth-crossing distance Most scattering comes from Oxygen (in the mantle) and Iron (in the core) × 10 23 × 10 32 2 . 0 1 . 2 Oxygen Oxygen Iron Iron 1 . 0 1 . 5 0 . 8 n d e ff ( θ ) [ cm − 2 ] n ( r ) [ cm − 3 ] 1 . 0 0 . 6 0 . 4 ¯ 0 . 5 0 . 2 0 . 0 0 . 0 0 . 0 0 . 2 0 . 4 0 . 6 0 . 8 1 . 0 0 π / 4 π / 2 r/R E θ NB: little Earth-scattering for spin-dependent interactions Bradley J Kavanagh (LPTHE, Paris) Earth-scattering of DM MPIK, Heidelberg - 9th Jan. 2017
Deflection v � = ( v � , cos θ � , φ � ) λ i ( v ) − 1 = ¯ ¯ n i σ ( v ) B v = ( v, cos θ , φ ) Detector C A Bradley J Kavanagh (LPTHE, Paris) Earth-scattering of DM MPIK, Heidelberg - 9th Jan. 2017
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