Signatures of Dark Matter Earth-Scattering: from sub-GeV particles to WIMPzillas Bradley J. Kavanagh LPTHE - Paris VI DM Signatures Workshop, Odense - 12th June 2017 bkavanagh@lpthe.jussieu.fr @BradleyKavanagh NewDark
Direct Detection Focus on DM-nucleus scattering for now DM flux: Detector χ Φ χ = ρ χ vf ( v ) m χ Convolve with DM-nucleus cross section to obtain nuclear recoil rate: � ∞ d R vf ( v ) d σ ∝ ρ χ d v d E R d E R m χ v min Bradley J Kavanagh (LPTHE, Paris) Earth-scattering of DM DM Signatures - 12th June 2017
Standard Halo Model 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 [But see e.g. 1705.05853] � f ( v ) = v 2 f ( v ) d Ω v Bradley J Kavanagh (LPTHE, Paris) Earth-scattering of DM DM Signatures - 12th June 2017
Annual Modulation (Earth’s Orbit) v Sun ≈ 230 km s − 1 v E ≈ 30 km s − 1 v Earth ( t ) = v Sun + v E ( t ) O(1-10%) annual modulation of DM flux Maximum in June, Minimum in December [1312.1355] Bradley J Kavanagh (LPTHE, Paris) Earth-scattering of DM DM Signatures - 12th June 2017
Daily Modulation (Earth’s Rotation) v Earth ( t ) = v Sun + v E ( t ) + v rot ( t ) v rot ≈ 0 . 5 km s − 1 222.6 SUPL ANDES 222.4 LNGS SUL SOUTH POLE 222.2 v lab [km/s] v lab 222.0 221.8 221.6 [1611.00802] 221.4 221.2 0 1 2 3 4 5 6 t [sidereal day] time [days] Produces a very small diurnal modulation (amplitude less than 0.1%) [1505.02615] Bradley J Kavanagh (LPTHE, Paris) Earth-scattering of DM DM Signatures - 12th June 2017
Gravitational Focusing (GF) Also modify DM velocities due to gravitational focusing from Sun and Earth Dec 1 GF due to Sun produces a %- DM Wind level annual modulation, with March 1 Sept 1 different phase compared to Sun Earth’s orbital speed Earth June 1 [astro-ph/0608390, 1308.1953, 1405.2340] Daily modulation amplitude Similar effect due to focusing from Earth, comparable to effects of Earth’s rotation. [1505.02615] Bradley J Kavanagh (LPTHE, Paris) Earth-scattering of DM DM Signatures - 12th June 2017
Gravitational Focusing (GF) Also modify DM velocities due to gravitational focusing from Sun and Earth Dec 1 GF due to Sun produces a %- DM Wind level annual modulation, with March 1 Sept 1 different phase compared to Sun Earth’s orbital speed Earth June 1 [astro-ph/0608390, 1308.1953, 1405.2340] Daily modulation amplitude Similar effect due to focusing from Earth, comparable to effects of Earth’s rotation. [1505.02615] Perturb the velocity distribution, perturb the rate! Bradley J Kavanagh (LPTHE, Paris) Earth-scattering of DM DM Signatures - 12th June 2017
Direct Detection Landscape 10 − 36 LUX (IDM-2016) 10 − 37 CDMSlite (2015) 10 − 38 CRESST-II (2015) Xenon1T (2017) 10 − 39 Xe Neutrino Floor (O’Hare 2016) 10 − 40 10 − 41 p [cm 2 ] 10 − 42 σ SI 10 − 43 10 − 44 8 B 10 − 45 10 − 46 10 − 47 10 − 48 10 − 1 10 0 10 1 10 2 10 3 10 4 m χ [GeV] Bradley J Kavanagh (LPTHE, Paris) Earth-scattering of DM DM Signatures - 12th June 2017
Direct Detection Landscape Sub-GeV DM 10 − 36 LUX (IDM-2016) 10 − 37 CDMSlite (2015) 10 − 38 CRESST-II (2015) Xenon1T (2017) 10 − 39 Xe Neutrino Floor (O’Hare 2016) 10 − 40 10 − 41 p [cm 2 ] 10 − 42 σ SI 10 − 43 10 − 44 8 B 10 − 45 10 − 46 10 − 47 10 − 48 10 − 1 10 0 10 1 10 2 10 3 10 4 m χ [GeV] Bradley J Kavanagh (LPTHE, Paris) Earth-scattering of DM DM Signatures - 12th June 2017
Direct Detection Landscape Sub-GeV DM 10 − 36 LUX (IDM-2016) 10 − 37 CDMSlite (2015) 10 − 38 CRESST-II (2015) Xenon1T (2017) 10 − 39 Xe Neutrino Floor (O’Hare 2016) 10 − 40 WIMPzillas 10 − 41 p [cm 2 ] 10 − 42 σ SI 10 − 43 10 − 44 8 B 10 − 45 10 − 46 10 − 47 10 − 48 10 − 1 10 0 10 1 10 2 10 3 10 4 m χ [GeV] Bradley J Kavanagh (LPTHE, Paris) Earth-scattering of DM DM Signatures - 12th June 2017
Earth-Scattering of sub-GeV DM BJK, Catena, Kouvaris [1611.05453] Emken, Kouvaris, Shoemaker [1702.07750] Emken & Kouvaris [1706.02249] Bradley J Kavanagh (LPTHE, Paris) Earth-scattering of DM DM Signatures - 12th June 2017
DD Landscape - Sub-GeV DM 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… Bradley J Kavanagh (LPTHE, Paris) Earth-scattering of DM DM Signatures - 12th June 2017
DD Landscape - Sub-GeV DM 10 − 34 Focus on this 10 − 35 region 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… Bradley J Kavanagh (LPTHE, Paris) Earth-scattering of DM DM Signatures - 12th June 2017
Direct Detection of DM (in space?) Detector χ Unscattered (free) DM: f 0 ( v ) Bradley J Kavanagh (LPTHE, Paris) Earth-scattering of DM DM Signatures - 12th June 2017
Direct Detection of DM on Earth Detector χ Bradley J Kavanagh (LPTHE, Paris) Earth-scattering of DM DM Signatures - 12th June 2017
Earth-Scattering - Stopping Previous calculations usually only consider DM stopping: Detector Zaharijas & Farrar [astro-ph/0406531] Kouvaris & Shoemaker [1405.1729,1509.08720] DAMA [1505.05336] χ Slowing/stopping of DM, without changing direction v i → v f < v i Bradley J Kavanagh (LPTHE, Paris) Earth-scattering of DM DM Signatures - 12th June 2017
Deflection of Dark Matter How good is the ‘stopping’ approximation? Nucleus χ α Need to calculate the distribution of the deflection angle : α P (cos α ) = 1 d σ d E R d E R d cos α σ d σ ∝ const. For standard SI, we have at low mass d E R But let’s be more general… Bradley J Kavanagh (LPTHE, Paris) Earth-scattering of DM DM Signatures - 12th June 2017
Non-relativistic effective field theory (NREFT) 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] O 1 = 1 SI O 4 = ~ S χ · ~ S N SD [1008.1591, 1203.3542, 1308.6288, 1505.03117] See also Riccardo Catena’s talk for more details… Bradley J Kavanagh (LPTHE, Paris) Earth-scattering of DM DM Signatures - 12th June 2017
Non-relativistic effective field theory (NREFT) 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] O 12 = ~ S χ · ( ~ O 1 = 1 v ⊥ ) S N × ~ SI O 3 = i ~ v ⊥ ) /m N O 13 = i ( ~ v ⊥ )( ~ S N · ( ~ q × ~ S χ · ~ S N · ~ q ) /m N O 4 = ~ S χ · ~ O 14 = i ( ~ q )( ~ v ⊥ ) /m N S N S χ · ~ S N · ~ O 5 = i ~ v ⊥ ) /m N SD O 15 = − ( ~ q )(( ~ S χ · ( ~ q × ~ v ⊥ ) · ~ q/m 2 S χ · ~ S N × ~ N O 6 = ( ~ q )( ~ q ) /m 2 S χ · ~ S N · ~ N . . O 7 = ~ . v ⊥ S N · ~ O 8 = ~ v ⊥ S χ · ~ O 9 = i ~ S χ · ( ~ S N × ~ q ) /m N � Recoil q � � v ⊥ = � v + O 10 = i ~ q S N · ~ q/m N momentum 2 µ χ N O 11 = i ~ S χ · ~ q/m N [1008.1591, 1203.3542, 1308.6288, 1505.03117] See also Riccardo Catena’s talk for more details… Bradley J Kavanagh (LPTHE, Paris) Earth-scattering of DM DM Signatures - 12th June 2017
Energy spectra m χ = 100 GeV Standard SI/SD int. d σ ∼ 1 /v 2 d E R Bradley J Kavanagh (LPTHE, Paris) Earth-scattering of DM DM Signatures - 12th June 2017
Energy spectra m χ = 100 GeV d σ ∼ v 2 ⊥ /v 2 d E R d σ ∼ q 2 /v 2 d E R Bradley J Kavanagh (LPTHE, Paris) Earth-scattering of DM DM Signatures - 12th June 2017
DM deflection distribution P (cos α ) = 1 d σ d E R Standard SI interaction d E R d cos α σ ���������� ���� �� - � χ = ��� ��� ���������� ���� �� - � χ = �� ��� � ��� � � � � � � � � � � � �� � � � �� � ��� � � � �� � � � �� ��� � ( ��� α ) � ( ��� α ) � � ��� ��� � � - � - ��� � ��� � - � - ��� � ��� � �� ���������� ������ ��� α �� ���������� ������ ��� α Backward Forward Bradley J Kavanagh (LPTHE, Paris) Earth-scattering of DM DM Signatures - 12th June 2017
Earth-Scattering - Attenuation Forget slowing and think Detector instead about attenuation: χ f ( v ) → f 0 ( v ) − f A ( v ) Attenuation of DM flux: Bradley J Kavanagh (LPTHE, Paris) Earth-scattering of DM DM Signatures - 12th June 2017
Earth-Scattering - Deflection Detector χ Bradley J Kavanagh (LPTHE, Paris) Earth-scattering of DM DM Signatures - 12th June 2017
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