(The “soft” frontier in dark matter direct detection)
1
Detecting light dark matter with athermal phonons
@ KITP04/10/2018
Simon KnapenLBNL & UC Berkeley
Work with Tongyan Lin, Kathryn Zurek, Sinead Griffin and Matt Pyle
Freeze-out, Freeze-in, Asymmetric, SIMP, …
meV eV keV MeV GeV 109 GeVTeV10-22 eV
Models of Dark Matter2
Light bosonic Dark Matter WIMP Composite
Dark Matter
! !
SM SM
meV eV keV MeV GeV
dark photon
Freeze-in
Freeze-outStellar cooling limits BBN limit
Freeze-out: Freeze-in:
Dark Matter drops out of equilibrium with Standard Model (e.g. WIMP’s)Dark Matter is never in equilibrium; Standard Model “leaks” into the dark sector
Dark matter direct detectionCosmic visions report 2017: 1707.04591
Lower thresholds
Larger volume
Theory:1. The mediator is important,
independent set of constraints (effective theory breaks down, similar to LHC constraints on Dark Matter)
2. Beyond “billiard ball” scattering: structure effects are critical!
Experiment:1. Low target mass materials:
2. Ultra-sensitive calorimeters with low dark counts
What do we need?
q < 2m�v�, v� ⇡ 10�3
ER =q2
2mN< 10�6 ⇥
m2�
mN
3
Y. Hochberg et. al.: 1512.04533 D. Green, S. Rajendran: 1701.08750 SK, T. Lin, K. Zurek: 1709.07882…
This talk
Structure effects
m! > 1 MeV: Recoil of nuclei/electrons
Scatter of collective excitations(e.g. phonons)
m! < 1 MeV: q ≈ m! v! < keV ~ nm-1
Transition to different effective theory
Low threshold detectors5
5mm x 5mm x5 mm Polar Crystal
TES and QP collection antennas (W)
Athermal Phonon Collection Fins (Al)
Superfluid helium detector Polar material detector
SK, T. Lin, M. Pyle, K. Zurek: 1712.06598See also: Y. Hochberg, M. Pyle, Y. Zhao, K. Zurek: 1512.04533
!
Talk by D. McKinsey(afternoon)
W. Guo, D. McKinsey: 1302.0534
Talk by M. Pyle(tomorrow)
0 1 2 3 4 5 6
q [keV]
0
1
2
3
4
5
✏[m
eV]
phon
on roton
Bijl-Feynman
Measured
Quadratic
0.5 1.0 1.5 2.0 2.5 3.0q [1/A]
0
10
20
30
40
50
✏[K
]
Issue: speed of Dark Matter >> speed of sound
Cannot scatter against single, on shell excitation
Phonons & rotons in superfluid He
K. Schultz, K. Zurek: 1604.08206 SK, T. Lin, K. Zurek: 1611.06228
6
He
pi pf
(k2,!2)
(k1,!1)
(q,!)
Final state: two hard, back-to-back phonons
Calculate the 3-excitation matrix elementR. Feynman, 1954H. W. Jackson, E. Feenberg, 1962E. Feenberg, 1969M. J. Stephen, 1969
Calculation7
Step 1:
Step 2:
Step 3:
Define orthogonal basis of states (ansatz + data input needed)
Specify Hamiltonian description (Quantum hydrodynamics or microscopic formalism)
Calculate the matrix element
Matrix element
hq� k,k|H � E0|qi =q · (q� k)S(k) + q · kS(q� k)� q2S(k)S(q� k)
2mHe
pNp
S(q� k)S(k)S(q)
Static structure function (fixed from data)
Expanding the rate in small q
Power law reproduced in state-of-the-art simulation data
✏0(ki) = !/2
SK, T. Lin, K. Zurek: 1611.06228
Campbell, Krotscheck and Lichtenegger (2015)
Combination of standard perturbation theory & dynamical multiparticle fluctuations theory
• More sophisticated ansatz for the potential
• Resummed self-energies
8
A Modern Simulation
0.5 1.0 1.5 2.0 2.5 3.0 3.5
q [keV]
1
2
3
4
5
6
7
8
![m
eV]
log10(S(q, !) ⇥ eV)
�4
�3
�2
�1
0
1
2
3
4
phonons
rotons
No resolution for low momentum transfer
Use our analytic expressions to extrapolate
vs
He?
9
Comparison with simulation
10�3 10�2 10�1 100
q [keV]
10�10
10�8
10�6
10�4
10�2
100
102
S(q
,!)
[1/e
V]
! = 3 meV
CKL15
q4 extrapolation
Leading order
q4 scaling is reproduced in the simulation data
10�3 10�2 10�1 1 10 102
mX [MeV]
10�44
10�43
10�42
10�41
10�40
10�39
10�38
10�37
10�36
10�35
�p
[cm
2 ]
Nuclear recoil
↵X = 10�11 (mX/MeV)3/2, gn = 10�11
↵X = 10�11 (mX/MeV)3/2, gn = 10�10
Massless mediator
Leading order
CKL15
kg x year exposure1 meV threshold
Reach agrees within a factor of ~ 2
SK, T. Lin, K. Zurek: 1611.06228
10
Reach
Superfluid helium is sensitive down to m! ~ 10 keV
Cosmic visions report 2017: 1707.04591
Polar materials11
At least two different atoms in the unit cell
GaAs Al2O3 (Sapphire)
2 atoms in primitive cell 10 atoms in primitive cell
Primary crystal axis
Why polar materials?12
3. Semi-conductors or insulators: screening is small
4. Crystal axis allows for directional detection (daily modulation!)
5. Readily available now
1. Optical phonons for kinematic matching
� X W � L0
5
10
15
20
25
30
35
40
!(m
eV)
LO
TO
TA
LA
GaAs
2. Natural dipole in unit cell (dark photon mediator sources tiny electric field)
E
Ga As
Optical phonon
SK, T. Lin, M. Pyle, K. Zurek: 1712.06598
Frölich Hamiltonian13
S. Griffin, SK, T. Lin, M. Pyle, K. Zurek: in preparation
Electric dipole interacting with test charge:
VASP phonopyCrystal structure
Phonon energies & eigenvectors
DFT calculation diagonalize force matrix
Force constantsBorn effective charges
Calculation overview:
Sum over:atoms in unit cellphonon modes1st Brioullin zoneReciprocal lattice
phonon energy
Born effective charge tensor for each atom
phonon eigenvectors(atomic displacements)
high frequency dielectric tensor
H. Frölich, 1954C. Verdi, F. Giustino, Phys. Rev. Lett. 115, 176401 (2015)
Reach14
SK, T. Lin, M. Pyle, K. Zurek: 1712.06598S. Griffin, SK, T. Lin, M. Pyle, K. Zurek: in preparation
Both GaAs and Sapphire probe Dark Matter masses as low as 10 keV(Reach comparable to Dirac materials)
Probe the Freeze-in prediction with gram month exposure
10�3 10�2 10�1 100 101 102 103
m� [MeV]
10�4510�4410�4310�4210�4110�4010�3910�3810�3710�3610�3510�3410�3310�32
�e
[cm
2 ]
BBNStellar bounds
Freeze-in
SuperCDMS G2DAMIC-1K
LBECA
SENSEI-100g
ZrTe5
Al SC
Xenon10
Dark photon mediatormA0 ⌧ keV
LOph
onon
scintillat
or
GaAs
10�3 10�2 10�1 100 101 102 103
m� [MeV]
10�4510�4410�4310�4210�4110�4010�3910�3810�3710�3610�3510�3410�3310�32
�e
[cm
2 ]
BBNStellar bounds
Freeze-in
SuperCDMS G2DAMIC-1K
LBECA
SENSEI-100g
ZrTe5
Al SC
Xenon10
Dark photon mediatormA0 ⌧ keV1 meV
25meV
Al2O3
Preliminary
Daily modulation15
S. Griffin, SK, T. Lin, M. Pyle, K. Zurek: in preparation
Sapphire band structure depends on direction
For Freeze-in dark matter 103 - 104 events with 1 kg year exposure
� Z A �0
20
40
60
80
100
120
!(m
eV)
Al2O3
0.0 0.2 0.4 0.6 0.8 1.0
t/day
0.8
0.9
1.0
1.1
1.2
1.3
R/h
Ri
m� =50 keVAl2O3, ! > 1 meV
Al2O3, ! > 25 meV
Al2O3, ! > 50 meV
GaAs
0.0 0.2 0.4 0.6 0.8 1.0
t/day
0.85
0.90
0.95
1.00
1.05
1.10
1.15
1.20
R/h
Ri
m� =100 keVAl2O3, ! > 1 meV
Al2O3, ! > 25 meV
Al2O3, ! > 50 meV
GaAs
Preliminary
Preliminary
Daily modulation16
S. Griffin, SK, T. Lin, M. Pyle, K. Zurek: in preparation
Sapphire band structure depends on direction
For Freeze-in dark matter 103 - 104 events with 1 kg year exposure
� Z A �0
20
40
60
80
100
120
!(m
eV)
Al2O3
Modes with large oscillating dipole dominate
Scalar mediator17
SK, T. Lin, M. Pyle, K. Zurek: 1712.06598
101 102 103
mX [keV]
10�44
10�43
10�42
10�41
10�40
10�39
10�38
10�37
10�36
10�35
�n
[cm
2 ]
DM-nucleon couplingMassless mediator limit
He multiphonon
GaAs, ! =!LO
GaAs, ! > meV
Destructive interference for the optical phonon mode
Expected to work better for crystals with larger mass hierarchies
phonon form factor:
daily modulation!
Dark photon absorption18
SK, T. Lin, M. Pyle, K. Zurek: 1712.06598
10�3 10�2 10�1 100 101 102
mA0 [eV]
10�18
10�16
10�14
10�12
10�10
Stellarconstraints
Al SC
e�
excitation
Ge
phononexcitation
Si
Dirac material
Molecu
les
Direct detectionconstraints
1 kg-yr, GaAs
Dark photon dark matter:
Absorption rate
SM photon absorption rate
in medium kinetic mixing parameter
Extract from the complex index of refraction
(Sapphire still in progress)
Looking ahead19
Theory:• Complete the daily modulation analysis• Absorption rate for sapphire• Calculate neutrino and coherent photon backgrounds (expected to be small)• Reach for other dark matter models A. Cosuner, D. Grabowska, SK, K. Zurek: ongoing
Experiment:• See talks by Daniel & Matt today and tomorrow
Summary20
Freeze-inmeV eV keV MeV GeV
dark photon Freeze-out
5mm x 5mm x5 mm Polar Crystal
TES and QP collection antennas (W)
Athermal Phonon Collection Fins (Al)
Polar materials
dark photon mediator & scalar mediator
dark photon absorption
!Superfluid Helium
scalar mediator
Low threshold detectors can access a wide range of models and dark matter masses
has daily modulation