Novel Techniques for Detecting sub-GeV Dark...
Transcript of 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
Zq dq|f(k, q)|2|FDM (q)|2⌘(vmin)
�e =µ2�e
16⇡m2�m
2e
|M�e(q)|2
q2=↵2m2e
�(q) = �e ⇥ |FDM (q)|2
particle physics
ingredients
dh�vid lnER
=�e
8µ2�e
Zq dq|f(k, q)|2|FDM (q)|2⌘(vmin)
⌘(vmin) =
Z
vmin
d3v
vfMB(~v)
astrophysics
vmin =ER + EB
q+
q
2m�
ingredients
dh�vid lnER
=�e
8µ2�e
Zq dq|f(k, q)|2|FDM (q)|2⌘(vmin)
���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
Zq dq|f(k, q)|2|FDM (q)|2⌘(vmin)
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
Zq dq|f(k, q)|2|FDM (q)|2⌘(vmin)
���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
light heat electric charge
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
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valence bands
conduction bands
band gap
e-
e-
1
detector2
light heat electric charge
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
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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
Zq dq|f(k, q)|2|FDM (q)|2⌘(vmin)
���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
Zq dq|f(k, q)|2|FDM (q)|2⌘(vmin)
���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
Zq dq|f(k, q)|2|FDM (q)|2⌘(vmin)
���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
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choosing parameters
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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
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Heavy A’
MDM
Light A’
EDM
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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
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fmod
=R
max
�Rmin
2Rmean
sits on tail of velocity distribution
could also consider gravitational focusing, c.f. 1308.1953
*preliminary
annual modulation
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*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