novel techniques for detecting sub-gev dark...

Novel Techniques for Detecting sub-GeV

Dark MatterTien-Tien Yu

YITP - Stony Brookwith Rouven Essig, Marivi Fernandez Serra, Jeremy Mardon,

Adrián Soto, Tomer Volansky 1504.XXXXX

April 29, 2015 UC Irvine Theory Seminar

candidates for DM

candidates for DM

WIMPs theoretically motivated

WIMP miracle gives detectable signatures

current state of affairs

1310.8327

current state of affairs

1310.8327??

ER =q2

2mN⇠

m2�v

2

mN

nucleus

DM

*not to scale

e-

DM

ER =q2

2mN⇠

m2�v

2

mN

*not to scale

e-

nucleus

DMsignal: heat

phonons scintillation photons ionization electrons

ER =q2

2mN⇠

m2�v

2

mN

*not to scale

e-

nucleus

DM

ER =q2

2mN⇠

m2�v

2

mN

m� = 100 GeV, ER ⇠ 1 MeV

*not to scale

e-

nucleus

DM

m� = 100 MeV, ER ⇠ 1 eV

ER =q2

2mN⇠

m2�v

2

mN

*not to scale

e-

nucleus

candidates for DM

sub-GeV DM is theoretically motivated

Hidden Photon Mediator

MDM/EDM

DM DM

SM SM

dipole moment

Hall et al [0911.1120] Essig et al [1108.5383] Lin et al [1111.0293] Chu et al [1112.0493]

Sigurdson et al, Phys. Rev. D70 (2004) 083501 + Erratum-ibid.

Banks et al [1007.5515] Graham et al [1203.2531]

Kadota and Silk [1402.7295]

DM DM

SM SM

A’

Akinetic mixing

Strongly Interacting

Boddy et al [1408.6532] Hochberg et al [1402.5143,1411.3727]

DM

nucleus

*not to scale

�Ee = ~q · ~v � q2

2µ�N

⇠ 1

2eV ⇥

⇣ m�

MeV

⌘

e-

DM

e-

*not to scale

signal: a few ionized

electrons

m� = 100 MeV, ER ⇠ 50 eV

�Ee = ~q · ~v � q2

2µ�N

⇠ 1

2eV ⇥

⇣ m�

MeV

⌘

nucleus

DM

e-

*not to scale

signal: a few ionized

electrons

m� = 100 MeV, ER ⇠ 50 eV

�Ee = ~q · ~v � q2

2µ�N

⇠ 1

2eV ⇥

⇣ m�

MeV

⌘

nucleus

*sensitive to precise form of electron energy levels and wave functions in

target

electron scatteringXENON10 limits

R. Essig, A. Manalaysay, J. Mardon, P. Sorenson, T. Volansky 1206.2644

electron energy

• noble gases: ~10 eV

• semiconductors: ~1 eV

Calculation Ingredients

ingredients

dh�vid lnER

=�e

8µ2�e


⌘(vmin) =

Z

vmin

d3v

vfMB(~v)

astrophysics

vmin =ER + EB

q+

q

2m�

ingredients

dh�vid lnER

=�e

8µ2�e


��fi!i

0(~q,~k)��2=

V

(2⇡)3

Z

BZd3k0

��Z

d3x ⇤i

0,

~

k

0(~x) i,

~

k

(~x)ei~q·~x��2

solid state physics

probability of going from state i to i’

ingredients

dh�vid lnER

=�e

8µ2�e


number of target nuclei per unit mass

local DM density

R = NT⇢�m�

Z

ER,cut

d lnERdh�vid lnER

energy threshold

ingredients

dh�vid lnER

=�e

8µ2�e


��fi!i

0(~q,~k)��2=

V

(2⇡)3

Z

BZd3k0

��Z

d3x ⇤i

0,

~

k

0(~x) i,

~

k

(~x)ei~q·~x��2

computationally difficult!

solid state physics

analytic numerical

valence bands

conduction bands

band gap

e-

1

detector2

light heat electric charge

e-e-

e-

1


electrons in a solid are part of a complicated, many-body system

gas solid

analytic approximations• semi-classical

approach

• initial wave functions are spherical

• plane wave final states with altered mass

• no interference

• good for high q

1203.2531

Single-electron detection

1108.5383

Single-electron detection

1108.5383

*assumed single-electron detection

Recoil energy spectrum

� � ��

��

��

�� [��]

��

[��/��

/��]

��

�� (�) = �--- �� (�) = ��/�----- �� (�) = (��/�)�

��

�� = � �� = ��

valence bands

conduction bands

band gap

e-

e-

1

detector2


What happens in step 2?

Energy to create an electron-hole pair

previously, we thought of the experimental parameter as recoil energy thresholds.

!Instead, experimentalists measure

actual number of electrons.

Can use the following conversion: Ge: 2.9 eV/electron Si: 3.6 eV/electron

Recoil energy spectrum

� � ��

��

��

�� [��]

��

[��/��

/��]

��

�� (�) = �--- �� (�) = ��/�----- �� (�) = (��/�)�

��

�� = � �� = ��

interlude

semiconductors

valence

conduction

band gap ~0.67 eV for Ge ~1.11 eV for Si

Band structure

k-points

valence!bands

conduction!bands

semiconductors

• electron wave functions inside a crystal are complicated, but there are methods to approximate them

• we assume a wavefunction of the form:

i,

~

k

(~x) =1pV

X

G

i

(~k + ~

G)ei(~

k+~

G)~x

lives in Brillouin Zone

reciprocal lattice vector

ingredients

dh�vid lnER

=�e

8µ2�e


��fi!i

0(~q,~k)��2=

V

(2⇡)3

Z

BZd3k0

��Z

d3x ⇤i

0,

~

k

0(~x) i,

~

k

(~x)ei~q·~x��2

probability of exciting an electron from valence band i to conduction band i’

solid state physics

ingredients

dh�vid lnER

=�e

8µ2�e


��fi!i

0(~q,~k)��2=

V

(2⇡)3

Z

BZd3k0

��Z

d3x ⇤i

0,

~

k

0(~x) i,

~

k

(~x)ei~q·~x��2

probability of exciting an electron from valence band i to conduction band i’

solid state physics

valence

conduction

band gap

ingredients

dh�vid lnER

=�e

8µ2�e


��fi!i0(~q,~k)��2=

��X

G

⇤i0(~k + ~G+ ~q) i(~k + ~G)

��

2

��fi!i

0(~q,~k)��2=

V

(2⇡)3

Z

BZd3k0

��Z

d3x ⇤i

0,

~

k

0(~x) i,

~

k

(~x)ei~q·~x��2

mild directional dependence we ignore for now

solid state physics

• open source code that calculates electronic structure within density functional theory (DFT) using plane waves and pseudopotentials

• use a mesh of 64 k-vectors, 100 bands, and a regular grid of G-vectors ��~k + ~G

��2

2me< Ec

http://www.quantum-espresso.org/

cut-off energy ~70 Ry

http://http://www.quantum-espresso.org/

� ��

��

��

��

��

��

��

��

[�� ]

� ��[�]

��=� � ��=�� =��

��

��

��

��

choosing parameters

� � ��

��

��

��

��

��

��

��

��

�� [� ]

(��/��

�(��))/(��/��

�(��))

��

��=� ��

��

��

��

vmin > vesc + vE

end of interlude

Cross-section reach vs. detector threshold

1 10 100 100010-4410-4310-4210-4110-4010-3910-3810-3710-3610-3510-3410-33

m� [MeV]

�e[cm2]

FDM(q)=1

1e

5e

10e

15e--- GeSi XENON10

1 10 100 100010-4410-4310-4210-4110-4010-3910-3810-3710-3610-3510-3410-33

m� [MeV]�e[cm2]

FDM(q)=(�me /q)2

1e

5e

10e 15e

--- GeSi

XENON10

Freeze-In

smaller atomic mass = more electrons per target mass

Si wins at high masses and low thresholds

1 kg-year, zero background *preliminary

Cross-section reach vs. detector threshold

smaller bandgap = higher rate

Ge wins at low masses and high thresholds

1 10 100 100010-4410-4310-4210-4110-4010-3910-3810-3710-3610-3510-3410-33

m� [MeV]

�e[cm2]

FDM(q)=1

1e

5e

10e

15e--- GeSi XENON10

1 10 100 100010-4410-4310-4210-4110-4010-3910-3810-3710-3610-3510-3410-33

m� [MeV]�e[cm2]

FDM(q)=(�me /q)2

1e

5e

10e 15e

--- GeSi

XENON10

Freeze-In

1 kg-year, zero background *preliminary

� �� -��-��-��-��-��-��-��-��-��-��-��

�� [��]

��[�� ]

��(�)=�

��

��

--- ��

��

��

��

��-��

� �� -��-��-��-��-��-��-��-��-��-��-��

�� [��]

��[�� ]

��(�)=�

��

��

--- ��

��

�

��

��

��

��/��

��

Heavy A’

MDM

Light A’

EDM

� �� -��-��-��-��-��-��-��-��-��-��-��-��-��-��-��-��

�� [��]

��[�� ]

��(�)=��/�

��

��

--- ��

�

��

��

��

��

� �� -��-��-��-��-��-��-��-��-��-��-��-��

�� [��]

��[�� ]

��(�)=(��/�)�

��

��

��

--- ��

��

��-��

��

��

��

��

1 10 100 100010-4510-4410-4310-4210-4110-4010-3910-3810-3710-3610-3510-3410-3310-3210-3110-3010-29

m� [MeV]

�e[cm2]

FDM(q)=1

XENON10

SuperCDMS

DAMIC

Experimental projections

• DAMIC: 1. 1 kg-day, 4e, 0.008=3.6 events 2. 1 kg-day, 3e, 0.025=3.6 events 3. 50 kg-days, 4e, 0.4=3.8 events 4. 50 kg-days, 3e, 1.2=4.3 events • SuperCDMS 1. 20 kg-years, Ge, 4e, 3.6 events (eff=0.7) 2. 20 kg-years, Ge, 1e, 3.6 events (eff=0.7) 3. 10 kg-years, Si, 4e, 3.6 events (eff=0.7) 4. 10 kg-years, Si, 1e, 3.6 events (eff=0.7)

current DAMIC limit: 107 g-days, 11e

1 10 100 100010-4510-4410-4310-4210-4110-4010-3910-3810-3710-3610-3510-3410-3310-3210-3110-3010-2910-28

m� [MeV]

�e[cm2]

FDM(q)=(�me /q)2

XENON10

SuperCDMS

DAMIC

*preliminary

annual modulation

Sun

Earth June

Earth Dec

DM halo

DM “wind”

annual modulation

� ��

��

��

��

��

�� [��]

� ��

�� (�) = �--- �� (�) = (��/�)�

��

��

� � ��

��

��

��

��

��

��

��

��

��

��

��

�� [��]

� ��

�� (�) = �--- �� (�) = (��/�)�

��=��

��=� ��

��

fmod

=R

max

�Rmin

2Rmean

sits on tail of velocity distribution

could also consider gravitational focusing, c.f. 1308.1953

*preliminary

annual modulation

� �� -��-��-��-��-��-��-��-��-��-��-��-��-��-��-��-��-��

�� [��]

��[�� ]

��(�)=�

��

��

��

��

� �� -��-��-��-��-��-��-��-��-��-��-��-��-��-��-��-��-��-��

�� [��]

��[�� ]

��(�)=(��/�)�

��

��

��

��

*preliminary

conclusions• sub-GeV dark matter is theoretically motivated

• but this mass range is currently unexplored by direct detection experiments, which rely on nuclear recoil.

• exchanging nuclear recoil for electron recoil is a possible resolution

• The best projections so far are theory predictions for noble gases

• semiconductor experiments have the potential to have a further reach due to the small band gap

• ongoing discussions with CDMS and DAMIC

novel techniques for detecting sub-gev dark...

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