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Electron Recoil & Dark Matter Direct Detection Qing Wang Tsinghua Univ. Beijing

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2 Background and Status of ER Our present understanding

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3 Cosmology, Astrophysics Search DM particle physics

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4 Cosmology & Astrophysics Found Cosmology & Astrophysics Found

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5 Particle Physics Not Found Particle Physics Not Found Direct Detection ndirect Detection ndirect Detection Collider Experiment No unambiguous evidence has been obtained to date

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6 Nuclear Recoil lectron Recoil

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7 lectron Recoil not considered at very beginning ! lectron Recoil not considered at very beginning !

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Target recoil v target initial v 0 DM initial v 0 DM final v For M>>m rest nucleon E R ~ 2v 0 2 m 2 /M ~ 2keV × ( m/ 10GeV ) 2 × 100GeV /M v 0 ~10 -3 for electron m>>M E R ~2v 0 2 M~1eV Chemistry & Biology Estimation of Recoil Energy M, v v 0 ˊ m v 0, v ˊ Angle between incident particle & target CM frame m reduce from 10GeV to 1GeV NR reduce from 2keV to 20eV ER keep 1eV Theory & Exp not prefer electron recoil traditional threshold Lower detection bound Too small for electron recoil energy

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9 1 st rise up 1 st rise up ER energy~keV ER energy~keV

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10 Bounded electron of NaI(Tl) has probability v 2 >1/2 p>0.5MeV Bounded electron of NaI(Tl) has probability v 2 >1/2 p>0.5MeV Sodiumiodide

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11 DAMA signal was explained as ER avoid contradiction with other exps Assume DM only interact with leptons leptophilic But Leptons loop induce enough NR And electron cannot seen as free particle While CDMS analysis on ER spectrum gives no signal Phys.Rev. D81 (2010) Phys.Rev. D80 (2009) with some velocity distribution Theory & Exp not prefer ER again !

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12 2 nd rise up 2 nd rise up A new gauge boson X, couples to SM particles and the WIMP through kinetic vector boson mixing with properties: 2m e m X m χ β m χ α DM Typical values m X = 0.1–1 GeV, m χ = 0.1–1 TeV α DM = α em pick back small recoil energy 10eV pick back small recoil energy 10eV m χ = 10 GeV m χ = 100GeV m χ = 1000 GeV hydrogenic atom massless mediator

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14 Recoil energy 10eV Recoil energy 10eV Free electron with momentum distribution change to bound state wave function effect of large momentum tail change to larger contribution from initial larger momentum state phase space smaller contribution due to overcome ionization energy

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17 Recoil energy: keV region: NR dominant eV region: ER dominant ! 10~several hundred eV region: ? Thats CDEX most interested region !

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18 ER spectrum Phase B > NR spectrum Static target Static target If R Universal Needs initial momentum distribution and bounded states effects Needs initial momentum distribution and bounded states effects Event rate Recoil energy Incident kinetic energy Incident particle mass Static free electron Static free electron NR spectrum Phase A > ER spectrum

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19 Impact of electron Initial velocity Free electron with some momentum distribution Free electron with some momentum distribution

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20 Effect of initial velocity Energy< Energy< Too big energy Too big energy Phase Phase Free electron with some momentum distribution

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21 Free electron with some momentum distribution

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22 Free electron with some momentum distribution

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24 More steep Reduce little bit increase When dark matter mass become small

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25 At 10~several hundred eV region: Competation result of ER and NR is still not clear May or may not produce measurable event rate More nuclear & atomic calculation is needed !

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