Electron Recoil &

Dark Matter Direct Detection

Qing Wang Tsinghua Univ. Beijing

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Background and Status of ER

Our present understanding

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Cosmology, Astrophysics

Search DM

particle physics

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Cosmology & Astrophysics ： Found ！

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Particle Physics ： Not Found ！

Direct D

etection

Indirect Detection

Collider Experiment

No unambiguous evidence has been obtained to date

6Nuclear Recoil & Electron Recoil

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Electron Recoil not considered at very beginning !

Target recoil v target initial v0’ DM initial v0 DM final v’

For M>>m rest nucleon ER~2v02m2/M~ 2keV ×(m/10GeV)2×100GeV/M

v0~10-3 ； for electron m>>M ER~2v02M~1eV Chemistry & Biology

Estimation of Recoil Energy M, v ， v0ˊ

m ， v0, vˊ

Angle between incident particle & target CM frame

m reduce from 10GeVto 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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1st rise up ER energy~keV

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Bounded electron of NaI(Tl) has 10-4 probability v2>1/2 （ p>0.5MeV ）

Sodiumiodide

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DAMA signal was explained as ERavoid contradiction with other exps

Assume DM only interact with leptons leptophilic

But Leptons loop induce enough NR

And electroncannot seen as free particle

While CDMS analysis on ER spectrum gives no signal

Phys.Rev. D81 (2010) 042002

Phys.Rev. D80 (2009) 083502

with some velocity distribution

Theory & Exp not prefer ER again !

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2nd rise up

A new gauge boson X, couples to SM particles and the WIMP through kinetic vector boson mixing with properties: 2me ≤ mX ≤ mχ β ≤ mχ αDM

Typical values ： mX = 0.1–1 GeV, mχ = 0.1–1 TeV ， αDM = αem

pick back small recoil energy~10eV

mχ = 10 GeV mχ = 100GeV

mχ = 1000 GeV

hydrogenic atom ； massless mediator

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Recoil energy~1-10eV

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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Recoil energy:

keV region: NR dominant ！

eV region: ER dominant !

10~several hundred eV region: ?

That’s CDEX most interested region !

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ER spectrum

Phase B ： >

NR spectrum

Static target ：

If R0 Universal

Needs initial momentum distribution and bounded states effects!

0.245, 0.433,0.571

Event rate

Recoil energy Incident kinetic energy

Incident particle mass

Static free electron

NR spectrum

Phase A ： >

ER spectrum

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Impact of electron

Initial velocity

Free electron with some momentum

distribution

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Effect of initial velocity

Energy<0

Too big energy ？

Phase A

Phase B

Phase B

Free electron with some momentum

distribution

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4.7, 5×10-8

4.3, 7×10-7

Free electron with some momentum

distribution

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4.3, 7×10-7

2.8, 3×10-5

0.37, 0.33

Free electron with some momentum

distribution

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More steep

Red

uce little b

it

increase

When dark matter mass become small

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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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