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

Looking for Dark Matter in the Earth's Shadow Bradley J. Kavanagh LPTHE (Paris) & IPhT (CEA/Saclay) with Riccardo Catena (Chalmers) and Chris Kouvaris (CP 3 -Origins) IDM - Sheffield - 19th July 2016 bradley.kavanagh@lpthe.jussieu.fr @BradleyKavanagh NewDark

Earth Shadowing Detector χ Unscattered (free) DM: f 0 ( v ) Bradley J Kavanagh (LPTHE & IPhT) DM in the Earth’s Shadow IDM - Sheffield - 19th July 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 & IPhT) DM in the Earth’s Shadow IDM - Sheffield - 19th July 2016

Earth Shadowing Detector Assuming DM mean free path λ � R E χ Bradley J Kavanagh (LPTHE & IPhT) DM in the Earth’s Shadow IDM - Sheffield - 19th July 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 & IPhT) DM in the Earth’s Shadow IDM - Sheffield - 19th July 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 & IPhT) DM in the Earth’s Shadow IDM - Sheffield - 19th July 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) Bradley J Kavanagh (LPTHE & IPhT) DM in the Earth’s Shadow IDM - Sheffield - 19th July 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 � )(1 − d e ff (cos θ � ) f 0 ( v � ) − f A ( v � ) = f 0 ( v � ) exp ) ¯ ¯ λ ( v � ) λ ( v � ) Bradley J Kavanagh (LPTHE & IPhT) DM in the Earth’s Shadow IDM - Sheffield - 19th July 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 & IPhT) DM in the Earth’s Shadow IDM - Sheffield - 19th July 2016

DM deflection � χ = ��� ��� � ������ ������� � χ = �� ��� � ������ ������� ��� ��� � � � � � � � � � � � �� � � � �� ��� ��� � � � �� � � � �� ��� ��� � ( ��� α ) � ( ��� α ) ��� ��� ��� ��� ��� ��� - ��� - ��� ��� ��� ��� - ��� - ��� ��� ��� ��� �� ���������� ������ ��� α �� ���������� ������ ��� α Backward Forward Bradley J Kavanagh (LPTHE & IPhT) DM in the Earth’s Shadow IDM - Sheffield - 19th July 2016

DM deflection Standard SI � χ = ��� ��� � ������ ������� ��� � � � � O 1 = 1 ⇒ d σ ∼ 1 � � � �� ��� v 2 d E R � � � �� ��� v ⊥ ⇒ d � ∼ (1 − m N E R � ( ��� α ) O 8 = � χ N v 2 ) S χ · � 2 µ 2 d E R ��� v ⊥ ) ⇒ d � ∼ E R O 12 = � S χ · ( � S N × � ��� d E R v 2 ��� - ��� - ��� ��� ��� ��� �� ���������� ������ ��� α Backward Forward Bradley J Kavanagh (LPTHE & IPhT) DM in the Earth’s Shadow IDM - Sheffield - 19th July 2016

DM deflection Standard SI � χ = ��� ��� � ������ ������� ��� � � � � O 1 = 1 ⇒ d σ ∼ 1 � � � �� ��� v 2 d E R � � � �� ��� v ⊥ ⇒ d � ∼ (1 − m N E R � ( ��� α ) O 8 = � χ N v 2 ) S χ · � 2 µ 2 d E R ��� v ⊥ ) ⇒ d � ∼ E R O 12 = � S χ · ( � S N × � ��� d E R v 2 ��� - ��� - ��� ��� ��� ��� Size of effect depends �� ���������� ������ ��� α on m ean free path : Backward Forward λ = ( σ n ) − 1 Bradley J Kavanagh (LPTHE & IPhT) DM in the Earth’s Shadow IDM - Sheffield - 19th July 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 & IPhT) DM in the Earth’s Shadow IDM - Sheffield - 19th July 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 & IPhT) DM in the Earth’s Shadow IDM - Sheffield - 19th July 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 & IPhT) DM in the Earth’s Shadow IDM - Sheffield - 19th July 2016

Current cross section limits Non-standard DM-nucleon interactions: See talk by Riccardo Catena 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 & IPhT) DM in the Earth’s Shadow IDM - Sheffield - 19th July 2016

Preliminary Results • Focus on low mass DM (for now): m χ = 0 . 5 GeV • 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… � v 2 f ( v ) d Ω v F ( v ) = • … and differential event rate (in CRESST-II) d R d σ � vF ( v ) d v ∝ d E R d E R • For different DM-nucleon operators and different incoming DM velocities (equivalent to different detector positions…) Bradley J Kavanagh (LPTHE & IPhT) DM in the Earth’s Shadow IDM - Sheffield - 19th July 2016

Operator 1 - attenuation only O 1 = 1 Isotropic deflection m χ = 0 . 5 GeV; O 1 ; p scat = 10% 4 . 0 Free 3 . 5 γ = 0 � v χ � γ = π 3 . 0 γ = π / 2 F ( v ) [10 − 3 km / s] γ = π 2 . 5 2 . 0 � v χ � γ = π / 2 1 . 5 1 . 0 0 . 5 1 . 20 F pert ( v ) /F free ( v ) 1 . 15 1 . 10 1 . 05 � v χ � γ =0 1 . 00 0 . 95 0 . 90 0 . 85 0 . 80 0 100 200 300 400 500 600 700 800 v [km / s] Bradley J Kavanagh (LPTHE & IPhT) DM in the Earth’s Shadow IDM - Sheffield - 19th July 2016

Operator 1 - attenuation + deflection O 1 = 1 Isotropic deflection m χ = 0 . 5 GeV; O 1 ; p scat = 10% 4 . 0 Free 3 . 5 γ = 0 � v χ � γ = π 3 . 0 γ = π / 2 F ( v ) [10 − 3 km / s] γ = π 2 . 5 2 . 0 � v χ � γ = π / 2 1 . 5 1 . 0 0 . 5 1 . 20 F pert ( v ) /F free ( v ) 1 . 15 1 . 10 1 . 05 � v χ � γ =0 1 . 00 0 . 95 0 . 90 0 . 85 0 . 80 0 100 200 300 400 500 600 700 800 v [km / s] Bradley J Kavanagh (LPTHE & IPhT) DM in the Earth’s Shadow IDM - Sheffield - 19th July 2016