Direct detection of light Zhengkang Kevin Zhang dark matter with - - PowerPoint PPT Presentation

Fermilab/KICP, Jun. 2019

Based on: Tanner Trickle, ZZ, Kathryn Zurek, arXiv: 1905.13744.

Direct detection of light dark matter with magnons

Zhengkang “Kevin” Zhang

UC Berkeley

Zhengkang “Kevin” Zhang (UC Berkeley) Fermilab/KICP, Jun. 2019

Roadmap

2

Kinematics

Kinematic matching in DM direct detection Collective excitations as a path forward for light DM

Dynamics

Phonons: detect spin-independent interactions Magnons: detect spin-dependent interactions

mχ = 100 keV eV keV MeV GeV meV eV keV MeV q

ΔE

n u c l e a r r e c

• i

l collective excitations: phonons, magnons electron excitations in semiconductors

Zhengkang “Kevin” Zhang (UC Berkeley) Fermilab/KICP, Jun. 2019

Kinematic matching

3

mχ = 100 GeV eV keV MeV GeV meV eV keV MeV q

ΔE

incoming DM velocity v~10-3 momentum transfer q energy transfer 𝛦E nuclear recoil ∆E = 1 2mχ

• (mχv)2 − (mχv − q)2

≤ vq − q2 2mχ

Zhengkang “Kevin” Zhang (UC Berkeley) Fermilab/KICP, Jun. 2019

Kinematic matching

4

mχ = 100 MeV eV keV MeV GeV meV eV keV MeV q

ΔE

nuclear recoil ∆E = 1 2mχ

• (mχv)2 − (mχv − q)2

≤ vq − q2 2mχ

Zhengkang “Kevin” Zhang (UC Berkeley) Fermilab/KICP, Jun. 2019

Kinematic matching

5

mχ = 100 MeV eV keV MeV GeV meV eV keV MeV q

ΔE

nuclear recoil electron excitations in semiconductors Band gap: O(eV). ∆E = 1 2mχ

• (mχv)2 − (mχv − q)2

≤ vq − q2 2mχ

Essig, Mardon, Volansky, 1108.5383. Graham, Kaplan, Rajendran, Walters, 1203.2531. Lee, Lisanti, Mishra-Sharma, Safdi, 1508.07361. Essig, Fernandez-Serra, Mardon, Soto, Volansky, Yu, 1509.01598. Derenzo, Essig, Massari, Soto, Yu, 1607.01009.

See talk by T. Yu.

Zhengkang “Kevin” Zhang (UC Berkeley) Fermilab/KICP, Jun. 2019

Kinematic matching

6

mχ = 100 keV eV keV MeV GeV meV eV keV MeV q

ΔE

nuclear recoil electron excitations in semiconductors ∆E = 1 2mχ

• (mχv)2 − (mχv − q)2

≤ vq − q2 2mχ

Zhengkang “Kevin” Zhang (UC Berkeley) Fermilab/KICP, Jun. 2019

Kinematic matching

7

mχ = 100 keV eV keV MeV GeV meV eV keV MeV q

ΔE

nuclear recoil collective excitations: phonons, magnons

10 20 30 40 50 60 70 80 90 100

Phonons/magnons in crystals with energies up to O(100meV). electron excitations in semiconductors ∆E = 1 2mχ

• (mχv)2 − (mχv − q)2

≤ vq − q2 2mχ

Knapen, Lin, Pyle, Zurek, 1712.06598. Griffin, Knapen, Lin, Zurek, 1807.10291. Trickle, ZZ, Zurek, 1905.13744. Griffin, Inzani, Trickle, ZZ, Zurek, to appear.

See talks by T. Lin, S. Griffin.

Zhengkang “Kevin” Zhang (UC Berkeley) Fermilab/KICP, Jun. 2019

Phonons in crystals: a brief recap

❖

Coupled quantum harmonic oscillators.

❖

Diagonalize the Hamiltonian => canonical modes — phonons (quanta

• f collective oscillation patterns).

8

phonon creation/annihilation operators phonon mode labels phonon polarization vectors atom displacements

See talks by T. Lin, S. Griffin.

Zhengkang “Kevin” Zhang (UC Berkeley) Fermilab/KICP, Jun. 2019

Phonons in crystals: a brief recap

❖

Single phonon excitation from DM scattering (dark photon mediator case):

9

Mν,k(q) = 1 NΩ egχ ✏∞ 1 q2 h⌫, k| X

l,j

Qjeiq·xlj|0i position operators create phonons phonon mode labels

Griffin, Knapen, Lin, Zurek, 1807.10291.

See talks by T. Lin, S. Griffin.

Zhengkang “Kevin” Zhang (UC Berkeley) Fermilab/KICP, Jun. 2019

Roadmap

10

Kinematics

Kinematic matching in DM direct detection Collective excitations as a path forward for light DM Phonons: detect spin-independent interactions

mχ = 100 keV eV keV MeV GeV meV eV keV MeV q

ΔE

n u c l e a r r e c

• i

l collective excitations: phonons, magnons electron excitations in semiconductors

Zhengkang “Kevin” Zhang (UC Berkeley) Fermilab/KICP, Jun. 2019

Roadmap

11

Kinematics

Kinematic matching in DM direct detection Collective excitations as a path forward for light DM Phonons: detect spin-independent interactions

mχ = 100 keV eV keV MeV GeV meV eV keV MeV q

ΔE

n u c l e a r r e c

• i

l collective excitations: phonons, magnons electron excitations in semiconductors

Dynamics

How does the DM couple to Standard Model particles?

Zhengkang “Kevin” Zhang (UC Berkeley) Fermilab/KICP, Jun. 2019

DM coupling to electron spin

❖

In the Standard Model, the neutron is electrically neutral. Its leading interaction with the photon is via a magnetic dipole moment.

❖

Something similar can happen in the dark sector. The DM may be neutral under the dark photon, but interacts via a multipole moment.

❖

In these scenarios, DM couples to the electron spin at low energy:

❖

Such couplings can also arise in scalar mediator models.

12

Zhengkang “Kevin” Zhang (UC Berkeley) Fermilab/KICP, Jun. 2019

Roadmap

13

Dynamics

Phonons: detect spin-independent interactions Magnons: detect spin-dependent interactions

Zhengkang “Kevin” Zhang (UC Berkeley) Fermilab/KICP, Jun. 2019

Magnons: what they are and how they couple to DM

❖

Crystal lattice sites occupied by effective spins (from electrons of magnetic ions.)

❖

Exchange couplings between neighboring spins => ordered ground state.

❖

Excitations about such a ground state are magnons.

14

Zhengkang “Kevin” Zhang (UC Berkeley) Fermilab/KICP, Jun. 2019

Magnons: what they are and how they couple to DM

❖

Technically, we need to expand the spins in terms of bosonic creation/annihilation

• perators via the Holstein-Primakoff transformation…

❖

… and then diagonalize the Hamiltonian via a Bogoliubov transformation…

15

where

global coordinates local coordinates (ground state spin points in +z direction) canonical magnon modes (quanta of collective precession patterns)

Zhengkang “Kevin” Zhang (UC Berkeley) Fermilab/KICP, Jun. 2019

Magnons: what they are and how they couple to DM

❖

Technically, we need to expand the spins in terms of bosonic creation/annihilation

• perators via the Holstein-Primakoff transformation…

❖

… and then diagonalize the Hamiltonian via a Bogoliubov transformation…

❖

DM-spin coupling => DM-magnon coupling.

16

where

global coordinates local coordinates (ground state spin points in +z direction) canonical magnon modes (quanta of collective precession patterns)

) Msisf

ν,k (q) =

1 NΩhsf| ˆ Oα

χ(q)|siihν, k|

X

lj

ˆ Sα

lj eiq·xlj|0i

spin operators create magnons (cf. position operators create phonons)

Zhengkang “Kevin” Zhang (UC Berkeley) Fermilab/KICP, Jun. 2019

Projected reach

❖

We consider a yttrium iron garnet (YIG, Y3Fe5O12) target.

17 Magnon dispersion calculated by including up to 3rd nearest neighbor exchange couplings taken from: Cherepanov, Kolokolov, L’vov, Physics Reports 229, 81 (1993).

10 20 30 40 50 60 70 80 90 100

❖

20 magnetic ions Fe3+ (spin 5/2) in the unit cell => 20 magnon branches.

❖

Anti-ferromagnetic exchange couplings. Ground state: 12 up, 8 down.

Zhengkang “Kevin” Zhang (UC Berkeley) Fermilab/KICP, Jun. 2019

Projected reach

❖

We consider a yttrium iron garnet (YIG, Y3Fe5O12) target.

18

gχgemχ/Λχ = 10-8 10-9 10-10 ωmin = 1 meV 10 meV 40 meV

10-2 10-1 1 10 10-45 10-44 10-43 10-42 10-41 10-40 10-39 10-38 10-37 10-36 10-35 10-34 10-33 mχ [MeV]

σe [cm2]

Magnetic dipole DM

gχ ge mχ

2/Λχ 2 = 10-5

1 0-6 1 0-7 ωmin = 1 meV 10 meV 40 meV

10-2 10-1 1 10 10-45 10-44 10-43 10-42 10-41 10-40 10-39 10-38 10-37 10-36 10-35 10-34 10-33 10-32 10-31 mχ [MeV]

σe [cm2]

Anapole DM

χ

π

χ

ω

χ

σ [ ]

Ωχ Ω

Projection assumes 3 signal events/kg/yr.

❖

Dark photon mediator (unconstrained by astro/cosmo):

Zhengkang “Kevin” Zhang (UC Berkeley) Fermilab/KICP, Jun. 2019

Projected reach

❖

We consider a yttrium iron garnet (YIG, Y3Fe5O12) target.

❖

Scalar mediator (impose white dwarf cooling constraint, consider SIDM subcomponent):

19

χ χ Λ χ

ω

χ

σ

χ χ Λχ

ω

10

χ

σ

gχ = 4π gχ = 1 ω

m i n

= 1 m e V 1 m e V 4 m e V

10-2 10-1 1 10 10-45 10-44 10-43 10-42 10-41 10-40 10-39 mχ [MeV]

σe [cm2]

Pseudo-mediated DM (Ωχ/ΩDM=0.05)

Zhengkang “Kevin” Zhang (UC Berkeley) Fermilab/KICP, Jun. 2019

Summary

❖

Collective excitations in condensed matter systems offer promising detection paths for light DM due to kinematic matching.

❖

There is also a dynamics aspect of direct detection. Different excitations can be sensitive to different DM interactions.

❖

Previously phonons have been demonstrated to have capability of probing interesting DM scenarios with spin-independent interactions.

❖

We have shown that magnons (collective spin excitations) can be used to probe spin-dependent DM interactions, complementary to phonons.

❖

Next steps:

❖

Detection schemes.

❖

DM absorption.

❖

Other types of target responses?

20

The End

21

Thank you for your attention!

Back-up slides

22

Zhengkang “Kevin” Zhang (UC Berkeley) Fermilab/KICP, Jun. 2019

Gapless vs. gapped magnons

❖

YIG has 1 gapless and 19 gapped magnon branches.

❖

They have different responses to DM scattering.

23

10 20 30 40 50 60 70 80 90 100

Gapless magnon branch: Goldstone mode of broken rotation symmetry.

Zhengkang “Kevin” Zhang (UC Berkeley) Fermilab/KICP, Jun. 2019

Gapless vs. gapped magnons

❖

Consider the limit q -> 0.

❖

The DM coupling acts like a uniform magnetic field.

❖

All the spins precess in phase => no change in energy.

❖

This corresponds to Goldstone mode excitation, i.e. only gapless magnons can be produced.

❖

Gapped magnon contributions become significant only for q beyond the first Brillouin zone.

24

Zhengkang “Kevin” Zhang (UC Berkeley) Fermilab/KICP, Jun. 2019

Effective theory of gapless magnons

❖

Integrate out short-distance degrees of freedom within the unit cell.

❖

The only low-energy d.o.f. is the spin density: (12-8)x5/2=10 per unit cell.

❖

Effective theory is a Heisenberg ferromagnet on a bcc lattice, which has

• nly 1 gapless magnon branch.

25

Zhengkang “Kevin” Zhang (UC Berkeley) Fermilab/KICP, Jun. 2019

Effective theory of gapless magnons

❖

Integrate out short-distance degrees of freedom within the unit cell.

❖

The only low-energy d.o.f. is the spin density: (12-8)x5/2=10 per unit cell.

❖

Effective theory is a Heisenberg ferromagnet on a bcc lattice, which has

• nly 1 gapless magnon branch.

26

✏ = p S/2 (1, i, 0) ✏ν,k,G =

n

X

j=1

r Sj 2

• Vjν,−kr∗

j + U∗ jν,krj

• eiG·xj

Msisf

ν,k (q) = q,k+G

1 p NΩ

3

X

α=1

hsf| ˆ Oα

χ(q)|sii ✏α ν,k,G

Zhengkang “Kevin” Zhang (UC Berkeley) Fermilab/KICP, Jun. 2019

Effective theory of gapless magnons

❖

Integrate out short-distance degrees of freedom within the unit cell.

❖

The only low-energy d.o.f. is the spin density: (12-8)x5/2=10 per unit cell.

❖

Effective theory is a Heisenberg ferromagnet on a bcc lattice, which has

• nly 1 gapless magnon branch.

❖

qmax = 2m𝜓v𝜓, qmin determined by detector threshold.

❖

Dependence on q follows from effective field theory expectations.

27

R ' 3 (kg·yr)−1 ✓ ns (4.6 ˚ A)−3 ◆✓4.95 g/cm3 ρT ◆✓0.1 MeV mχ ◆ Z d3vχ f(vχ) ✓10−3 vχ ◆✓ ˆ R 4 ⇥ 10−27 ◆ ˆ R =       

2g2

χg2 e(1+hc2i)

Λ2

χ

(q2

max q2 min)

(magnetic dipole) ,

g2

χg2 e(1+hc2i)

4Λ4

χ

(q4

max q4 min)

(anapole) , g2

χg2 ehs2i log(qmax/qmin)

(pseudo-mediated) .

Zhengkang “Kevin” Zhang (UC Berkeley) Fermilab/KICP, Jun. 2019

Effective theory vs. full theory

28

g

χ

g

e

m

χ

/ Λ

χ

= 1

• 8

1

• 9

1

• 1

ω

min

= 1 m e V 10 meV 40 meV

10-2 10-1 1 10 10-44 10-43 10-42 10-41 10-40 10-39 10-38 10-37 10-36 10-35 10-34 mχ [MeV] σe [cm2]

Magnetic dipole DM

g

χ

g

e

m

χ 2

/ Λ

χ 2

= 1

• 5

1

• 6

1

• 7

ω

min

= 1 m e V 10 meV 40 meV

10-2 10-1 1 10 10-45 10-44 10-43 10-42 10-41 10-40 10-39 10-38 10-37 10-36 10-35 10-34 10-33 10-32 mχ [MeV]

σe [cm2]

Anapole DM

χ

π

χ

ω

χ

σ [ ]

Ωχ Ω

Effective theory calculation (dashed) reproduced full results in the intermediate mass region.

Zhengkang “Kevin” Zhang (UC Berkeley) Fermilab/KICP, Jun. 2019

Effective theory vs. full theory

29

g

χ

g

e

m

χ

/ Λ

χ

= 1

• 8

1

• 9

1

• 1

ω

min

= 1 m e V 10 meV 40 meV

10-2 10-1 1 10 10-44 10-43 10-42 10-41 10-40 10-39 10-38 10-37 10-36 10-35 10-34 mχ [MeV] σe [cm2]

Magnetic dipole DM

g

χ

g

e

m

χ 2

/ Λ

χ 2

= 1

• 5

1

• 6

1

• 7

ω

min

= 1 m e V 10 meV 40 meV

10-2 10-1 1 10 10-45 10-44 10-43 10-42 10-41 10-40 10-39 10-38 10-37 10-36 10-35 10-34 10-33 10-32 mχ [MeV]

σe [cm2]

Anapole DM

χ

π

χ

ω

χ

σ [ ]

Ωχ Ω

Momentum transfer beyond the first Brillouin zone. Gapped magnons dominate. Momentum transfer too small. Only gapped magnons are kinematically accessible.