(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