Earth-Shadowing effects in Dark Matter direct detection Bradley J. Kavanagh LPTHE (Paris) with Riccardo Catena (Chalmers) and Chris Kouvaris (CP 3 -Origins) 6th Amsterdam-Paris-Stockholm Meeting 31st August 2016 bradley.kavanagh@lpthe.jussieu.fr @BradleyKavanagh NewDark
Earth Shadowing f ( v ) DM velocity distribution is affected by DM interactions in the Earth Detector Size of effect depends on Mean Free Path : λ = ( σ n ) − 1 χ Variation with detector position and time gives characteristic signatures altered flux, daily modulation, directionality… Bradley J Kavanagh (LPTHE - Paris) Earth-Shadowing effects APS VI - 31st August 2016
Direct detection DM N N v ∼ 10 − 3 χ χ � ∞ d R vf ( v ) d σ ρ χ d 3 v = Differential recoil rate: d E R d E R m χ m N v min Include all DM particles with � m N E R enough speed to induce a v min = 2 µ 2 recoil of energy : E R χ N Bradley J Kavanagh (LPTHE - Paris) Earth-Shadowing effects APS VI - 31st August 2016
Speed distribution Standard Halo Model (SHM) Speed distribution: � F ( v ) = v 2 f ( v ) d Ω v Minimum speed req. to excite recoil of energy : E R � m N E R v min = 2 µ 2 χ N Values of for v min m χ = 50 GeV m χ = 1 GeV scattering on Oxygen E th = 2 keV E th = 0 . 3 keV nuclei for… Bradley J Kavanagh (LPTHE - Paris) Earth-Shadowing effects APS VI - 31st August 2016
Current cross section limits Stringent limits on DM-nucleon SI scattering cross section 10 − 35 10 − 36 10 − 37 CRESST-II 10 − 38 10 − 39 p [cm 2 ] 10 − 40 CDMSlite ρ 0 . 3 σ SI 10 − 41 10 − 42 10 − 43 10 − 44 LUX 10 − 45 10 − 46 CRESST-II [1509.01515] 0 . 1 1 10 100 300 m χ [GeV] LUX [1512.03506] CDMSlite [1509.02448] Bradley J Kavanagh (LPTHE - Paris) Earth-Shadowing effects APS VI - 31st August 2016
Current cross section limits Stringent limits on DM-nucleon SI scattering cross section 10 − 35 10 − 36 Probability of DM 10 − 37 CRESST-II scattering in the p = 50% 10 − 38 Earth p = 10% 10 − 39 p [cm 2 ] p = 1% 10 − 40 CDMSlite ρ 0 . 3 σ SI 10 − 41 10 − 42 10 − 43 10 − 44 LUX 10 − 45 10 − 46 0 . 1 1 10 100 300 CRESST-II [1509.01515] m χ [GeV] LUX [1512.03506] CDMSlite [1509.02448] Bradley J Kavanagh (LPTHE - Paris) Earth-Shadowing effects APS VI - 31st August 2016
Current cross section limits Low mass DM may still have large Earth scattering probability 10 − 35 10 − 36 Probability of DM scattering in the 10 − 37 Earth CRESST-II p [cm 2 ] p = 50% 10 − 38 p = 10% ρ 0 . 3 σ SI 10 − 39 p = 1% CDMSlite 10 − 40 10 − 41 LUX 10 − 42 0 . 1 1 10 100 300 CRESST-II [1509.01515] m χ [GeV] LUX [1512.03506] CDMSlite [1509.02448] Bradley J Kavanagh (LPTHE - Paris) Earth-Shadowing effects APS VI - 31st August 2016
Current cross section limits Subdominant DM component may still have large cross section 10 − 35 10 − 36 LUX 10 − 37 Probability of DM CRESST-II p [cm 2 ] scattering in the 10 − 38 Earth ρ 0 . 3 σ SI 10 − 39 ρ χ → 1% ρ χ p = 50% CDMSlite 10 − 40 p = 10% 10 − 41 p = 1% 10 − 42 0 . 1 1 10 100 300 CRESST-II [1509.01515] m χ [GeV] LUX [1512.03506] CDMSlite [1509.02448] Bradley J Kavanagh (LPTHE - Paris) Earth-Shadowing effects APS VI - 31st August 2016
Current cross section limits Non-standard DM-nucleon interactions: σ 8 p ∼ v 2 σ 12 p ∼ q 2 10 − 28 10 − 27 10 − 28 10 − 29 10 − 29 10 − 30 10 − 30 CRESST-II p [cm 2 ] p [cm 2 ] 10 − 31 10 − 31 p = 50% CRESST-II ρ 0 . 3 σ 12 ρ 0 . 3 σ 8 10 − 32 p = 10% 10 − 32 = p 10 − 33 5 0 % p = 1% 10 − 33 = p 1 0 % 10 − 34 = p 10 − 34 1 % 10 − 35 LUX LUX 10 − 35 10 − 36 0 . 1 1 10 100 300 0 . 1 1 10 100 300 m χ [GeV] m χ [GeV] 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 Detector χ Unscattered (free) DM: f 0 ( v ) Bradley J Kavanagh (LPTHE - Paris) Earth-Shadowing effects APS VI - 31st August 2016
Earth Shadowing Detector Assuming DM mean free path λ � R E 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-Shadowing effects APS VI - 31st August 2016
Earth Shadowing Detector Assuming DM mean free path λ � R E χ Bradley J Kavanagh (LPTHE - Paris) Earth-Shadowing effects APS VI - 31st August 2016
Earth Shadowing Detector Assuming DM mean free path λ � R E Considered in early Monte Carlo simulations Collar & Avignone [PLB 275, 1992 and others] χ Enhancement of DM flux: f ( v ) → f 0 ( v ) + f D ( v ) Bradley J Kavanagh (LPTHE - Paris) Earth-Shadowing effects APS VI - 31st August 2016
Earth Shadowing 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-Shadowing effects APS VI - 31st August 2016
Earth scattering calculation Total DM velocity distribution: f ( v ) = f 0 ( v ) − f A ( v ) + f D ( v ) • Calculate perturbed DM velocity distribution analytically to first order R E / λ 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) n i ( r ) • 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 Bradley J Kavanagh (LPTHE - Paris) Earth-Shadowing effects APS VI - 31st August 2016
Earth scattering calculation Total DM velocity distribution: f ( v ) = f 0 ( v ) − f A ( v ) + f D ( v ) • Calculate perturbed DM velocity distribution analytically to first order R E / λ 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) n i ( r ) • 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 A sketch of the calculation… Bradley J Kavanagh (LPTHE - Paris) Earth-Shadowing effects APS VI - 31st August 2016
DM attenuation v � = ( v � , cos θ � , φ � ) ¯ n ) − 1 λ = ( σ ¯ d e ff (cos θ � ) θ � v � Sum over χ Earth nuclei � − d e ff (cos θ � ) � f 0 ( v � ) − f A ( v � ) = f 0 ( v � ) exp ¯ λ ( v � ) Bradley J Kavanagh (LPTHE - Paris) Earth-Shadowing effects APS VI - 31st August 2016
DM deflection v � = ( v � , cos θ � , φ � ) ¯ n ) − 1 λ = ( σ ¯ v = ( v, cos θ , φ ) v � θ � α v κ = v/v � fixed by kinematics χ � 1 � 2 π ( κ ) 4 d φ d e ff (cos θ � ) f D ( v � ) = 2 π P (cos α ) f ( κ v � , cos θ , φ ) d cos θ ¯ λ ( κ v � ) � 1 0 Bradley J Kavanagh (LPTHE - Paris) Earth-Shadowing effects APS VI - 31st August 2016
DM deflection v � = ( v � , cos θ � , φ � ) ¯ n ) − 1 λ = ( σ ¯ v = ( v, cos θ , φ ) v � θ � α v κ = v/v � fixed by kinematics χ � 1 � 2 π ( κ ) 4 d φ d e ff (cos θ � ) f D ( v � ) = 2 π P (cos α ) f ( κ v � , cos θ , φ ) d cos θ ¯ λ ( κ v � ) � 1 0 Bradley J Kavanagh (LPTHE - Paris) Earth-Shadowing effects APS VI - 31st August 2016
DM-nucleon operators In order to obtain , we need to know . P (cos α ) d σ / d E R Consider different possible operators in a non-relativistic EFT (NREFT) framework : Fitzpatrick et al. [1203.3542] Construct interactions from relevant NR degrees of freedom: ~ ~ q q ~ ~ , , , ~ v ⊥ = ~ S χ v + S N 2 µ χ N m N Standard spin-independent operator: O 1 = 1 O 4 = ~ S χ · ~ Standard spin-dependent operator: S N 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
DM deflection � χ = ��� ��� � ������ ������� � χ = �� ��� � ������ ������� ��� ��� � � � � � � � � � � � �� � � � �� ��� ��� � � � �� � � � �� ��� ��� � ( ��� α ) � ( ��� α ) ��� ��� ��� ��� ��� ��� - ��� - ��� ��� ��� ��� - ��� - ��� ��� ��� ��� �� ���������� ������ ��� α �� ���������� ������ ��� α Backward Forward Bradley J Kavanagh (LPTHE - Paris) Earth-Shadowing effects APS VI - 31st August 2016
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