1. 23rd International Spin Symposium, Ferrara, September 2018
Searches for Dark Matter and New Particles with EDM and Spin-Precession Measurements
Yevgeny Stadnik
Humboldt Fellow
Johannes Gutenberg University, Mainz, Germany
Collaborators (Theory):
Victor Flambaum (UNSW)
Collaborators (Experiment):
nEDM collaboration at PSI and Sussex
BASE collaboration at CERN and RIKEN
CASPEr collaboration at Mainz
23rd International Spin Symposium, Ferrara, September 2018 1

2. Basics of Atomic EDMs
Electric Dipole Moment (EDM) = parity (P) and time-reversal-invariance (T) violating electric moment 2

3. Basics of Atomic EDMs
Electric Dipole Moment (EDM) = parity (P) and time-reversal-invariance (T) violating electric moment 3

4. Basics of Atomic EDMs
Electric Dipole Moment (EDM) = parity (P) and time-reversal-invariance (T) violating electric moment 4

5. Sensitivity of EDM Experiments
|d Hg| limit ≈ 7*10-30 e cm 5

6. Sensitivity of EDM Experiments
|d Hg| limit ≈ 7*10-30 e cm
+δQ
(dHg)classical = δQ·LHg
LHg ≈ 3*10-8 cm
-δQ 6

7. Sensitivity of EDM Experiments
|d Hg| limit ≈ 7*10-30 e cm
+δQ
(dHg)classical = δQ·LHg
LHg ≈ 3*10-8 cm
-δQ
δQ sensitivity ~ e (!) 7

8. Mechanisms for EDM Generation
Atomic/molecular level
Nuclear level
Nucleon level
Quark/lepton level
Particle level, CP phases
(ēγ5e)(ēe)
Higgs, axion
(ēγ5e)(N̄N)
(ēγ5e)(q̄q)
EDM (paramagnetic system)
(N̄γ5N)(ēe)
(q̄γ5q)(ēe) de
SUSY dq
MQM
d̃q
EDM (diamagnetic system)
(N̄γ5N)(N̄N)
Schiff moment dN
(q̄γ5q)(q̄q)
Strong CP phase
GG̃
Neutron EDM, proton EDM 8

9. Manifestations of Dark Bosons
Stellar emission
New forces
Interconversion with ordinary particles
Dark matter 9

10. Manifestations of Dark Bosons
Stellar emission
New forces
Non-cosmological phenomena provide important constraints on exotic bosons -> help us identify regions of physical parameter space that are feasible and interesting to search for.
Stellar “cooling” (which is actually heating, since this is not the convection mechanism) arises due to Primakoff process (normally for the production of neutral pseudoscalar mesons by high-energy photons interacting with an atomic nucleus): since all SM charged particles in stellar interior are non-relativistic, only the Coulomb electric fields of these charged particles are important (and not the magnetic fields).
The energy drain by axions and other low-mass feebly-interacting novel particles is equivalent to a local energy sink, i.e., at a given density and temperature, the effective energy generation rate is decreased in the presence of axions; however, this is fixed by equilibrium stellar structure (observed) and so the inclusion of axion losses must lead to an increase in the true nuclear burning rate -> a higher temperature (so this is not true “axion cooling”).
Interconversion with ordinary particles
Dark matter 10

11. Manifestations of Dark Bosons
Stellar emission
New forces
Non-cosmological phenomena provide important constraints on exotic bosons -> help us identify regions of physical parameter space that are feasible and interesting to search for.
Stellar “cooling” (which is actually heating, since this is not the convection mechanism) arises due to Primakoff process (normally for the production of neutral pseudoscalar mesons by high-energy photons interacting with an atomic nucleus): since all SM charged particles in stellar interior are non-relativistic, only the Coulomb electric fields of these charged particles are important (and not the magnetic fields).
The energy drain by axions and other low-mass feebly-interacting novel particles is equivalent to a local energy sink, i.e., at a given density and temperature, the effective energy generation rate is decreased in the presence of axions; however, this is fixed by equilibrium stellar structure (observed) and so the inclusion of axion losses must lead to an increase in the true nuclear burning rate -> a higher temperature (so this is not true “axion cooling”).
Interconversion with ordinary particles
Dark matter 11

12. Non-Cosmological Sources of Dark Bosons
[Stadnik, Dzuba, Flambaum, PRL 120, (2018)],
[Dzuba, Flambaum, Samsonov, Stadnik, PRD 98, (2018)] 49

13. Non-Cosmological Sources of Dark Bosons
[Stadnik, Dzuba, Flambaum, PRL 120, (2018)],
[Dzuba, Flambaum, Samsonov, Stadnik, PRD 98, (2018)]
P,T-violating forces => Atomic and Molecular EDMs 50

14. Non-Cosmological Sources of Dark Bosons
[Stadnik, Dzuba, Flambaum, PRL 120, (2018)],
[Dzuba, Flambaum, Samsonov, Stadnik, PRD 98, (2018)]
P,T-violating forces => Atomic and Molecular EDMs
Atomic EDM experiments: Cs, Tl, Xe, Hg, Ra
Molecular EDM experiments: YbF, HfF+, ThO 51

15. Constraints on Scalar-Pseudoscalar Electron-Electron Interaction
EDM constraints: [Stadnik, Dzuba, Flambaum, PRL 120, (2018)]
Many orders of magnitude improvement! 55

16. Manifestations of Dark Bosons
Stellar emission
New forces
Non-cosmological phenomena provide important constraints on exotic bosons -> help us identify regions of physical parameter space that are feasible and interesting to search for.
Stellar “cooling” (which is actually heating, since this is not the convection mechanism) arises due to Primakoff process (normally for the production of neutral pseudoscalar mesons by high-energy photons interacting with an atomic nucleus): since all SM charged particles in stellar interior are non-relativistic, only the Coulomb electric fields of these charged particles are important (and not the magnetic fields).
The energy drain by axions and other low-mass feebly-interacting novel particles is equivalent to a local energy sink, i.e., at a given density and temperature, the effective energy generation rate is decreased in the presence of axions; however, this is fixed by equilibrium stellar structure (observed) and so the inclusion of axion losses must lead to an increase in the true nuclear burning rate -> a higher temperature (so this is not true “axion cooling”).
Interconversion with ordinary particles
Dark matter 56

17. Motivation
Overwhelming astrophysical evidence for existence of dark matter (~5 times more dark matter than ordinary matter).
ρDM ≈ 0.4 GeV/cm3
vDM ~ 300 km/s 59

18. Motivation
Traditional “scattering-off-nuclei” searches for heavy WIMP dark matter particles (mχ ~ GeV) have not yet produced a strong positive result. 61

19. Motivation
Traditional “scattering-off-nuclei” searches for heavy WIMP dark matter particles (mχ ~ GeV) have not yet produced a strong positive result. 62

20. Motivation
Traditional “scattering-off-nuclei” searches for heavy WIMP dark matter particles (mχ ~ GeV) have not yet produced a strong positive result. 63

21. Motivation
Traditional “scattering-off-nuclei” searches for heavy WIMP dark matter particles (mχ ~ GeV) have not yet produced a strong positive result.
Challenge: Observable is fourth power in a small interaction constant (eי << 1)! 64

22. Motivation
Traditional “scattering-off-nuclei” searches for heavy WIMP dark matter particles (mχ ~ GeV) have not yet produced a strong positive result.
Question: Can we instead look for effects of dark matter that are first power in the interaction constant? 65

23. Low-mass Spin-0 Dark Matter
Low-mass spin-0 particles form a coherently oscillating classical field φ(t) = φ0 cos(mφc2t/ℏ), with energy density <ρφ> ≈ mφ2φ02/2 (ρDM,local ≈ 0.4 GeV/cm3) 66

24. Low-mass Spin-0 Dark Matter
Low-mass spin-0 particles form a coherently oscillating classical field φ(t) = φ0 cos(mφc2t/ℏ), with energy density <ρφ> ≈ mφ2φ02/2 (ρDM,local ≈ 0.4 GeV/cm3)
Coherently oscillating field, since cold (Eφ ≈ mφc2) 70

25. Low-mass Spin-0 Dark Matter
Low-mass spin-0 particles form a coherently oscillating classical field φ(t) = φ0 cos(mφc2t/ℏ), with energy density <ρφ> ≈ mφ2φ02/2 (ρDM,local ≈ 0.4 GeV/cm3)
Coherently oscillating field, since cold (Eφ ≈ mφc2)
Classical field for mφ << 1 eV, since nφ(λdB,φ /2π)3 >> 1 71

26. Low-mass Spin-0 Dark Matter
Low-mass spin-0 particles form a coherently oscillating classical field φ(t) = φ0 cos(mφc2t/ℏ), with energy density <ρφ> ≈ mφ2φ02/2 (ρDM,local ≈ 0.4 GeV/cm3)
Coherently oscillating field, since cold (Eφ ≈ mφc2)
Classical field for mφ << 1 eV, since nφ(λdB,φ /2π)3 >> 1
Coherent + classical DM field = “Cosmic laser field” 72

27. Low-mass Spin-0 Dark Matter
Low-mass spin-0 particles form a coherently oscillating classical field φ(t) = φ0 cos(mφc2t/ℏ), with energy density <ρφ> ≈ mφ2φ02/2 (ρDM,local ≈ 0.4 GeV/cm3)
Coherently oscillating field, since cold (Eφ ≈ mφc2)
Classical field for mφ << 1 eV, since nφ(λdB,φ /2π)3 >> 1
Coherent + classical DM field = “Cosmic laser field”
10-22 eV ≲ mφ << 1 eV <=> 10-8 Hz ≲ f << 1014 Hz
Physical range of frequencies!
1 parsec = 3.26 light years; R_{dwarf galaxy} ~ 1 kpc.
Energy scales: Hubble scale ~ 10^{-33} eV; Planck scale ~ 10^{28} eV. i.e. ~ 61 orders of magnitude in range.
λdB,φ ≤ L dwarf galaxy ~ 1 kpc
Classical field 73

28. Low-mass Spin-0 Dark Matter
Low-mass spin-0 particles form a coherently oscillating classical field φ(t) = φ0 cos(mφc2t/ℏ), with energy density <ρφ> ≈ mφ2φ02/2 (ρDM,local ≈ 0.4 GeV/cm3)
Coherently oscillating field, since cold (Eφ ≈ mφc2)
Classical field for mφ << 1 eV, since nφ(λdB,φ /2π)3 >> 1
Coherent + classical DM field = “Cosmic laser field”
10-22 eV ≲ mφ << 1 eV <=> 10-8 Hz ≲ f << 1014 Hz
mφ ~ eV <=> T ~ 1 year
1 parsec = 3.26 light years; R_{dwarf galaxy} ~ 1 kpc.
Energy scales: Hubble scale ~ 10^{-33} eV; Planck scale ~ 10^{28} eV. i.e. ~ 61 orders of magnitude in range.
λdB,φ ≤ L dwarf galaxy ~ 1 kpc
Classical field 74

29. Low-mass Spin-0 Dark Matter
Low-mass spin-0 particles form a coherently oscillating classical field φ(t) = φ0 cos(mφc2t/ℏ), with energy density <ρφ> ≈ mφ2φ02/2 (ρDM,local ≈ 0.4 GeV/cm3) 75

30. Low-mass Spin-0 Dark Matter
Low-mass spin-0 particles form a coherently oscillating classical field φ(t) = φ0 cos(mφc2t/ℏ), with energy density <ρφ> ≈ mφ2φ02/2 (ρDM,local ≈ 0.4 GeV/cm3)
10-22 eV ≲ mφ << 1 eV inaccessible to traditional “scattering-off-nuclei” searches, since |pφ| ~ 10-3mφ is extremely small => recoil effects of individual particles suppressed 76

31. Low-mass Spin-0 Dark Matter
Low-mass spin-0 particles form a coherently oscillating classical field φ(t) = φ0 cos(mφc2t/ℏ), with energy density <ρφ> ≈ mφ2φ02/2 (ρDM,local ≈ 0.4 GeV/cm3)
10-22 eV ≲ mφ << 1 eV inaccessible to traditional “scattering-off-nuclei” searches, since |pφ| ~ 10-3mφ is extremely small => recoil effects of individual particles suppressed
BUT can look for coherent effects of a low-mass DM field in low-energy atomic and astrophysical phenomena that are first power in the interaction constant κ : 77

32. Low-mass Spin-0 Dark Matter
Low-mass spin-0 particles form a coherently oscillating classical field φ(t) = φ0 cos(mφc2t/ℏ), with energy density <ρφ> ≈ mφ2φ02/2 (ρDM,local ≈ 0.4 GeV/cm3)
10-22 eV ≲ mφ << 1 eV inaccessible to traditional “scattering-off-nuclei” searches, since |pφ| ~ 10-3mφ is extremely small => recoil effects of individual particles suppressed
BUT can look for coherent effects of a low-mass DM field in low-energy atomic and astrophysical phenomena that are first power in the interaction constant κ :
First-power effects => Improved sensitivity to certain DM interactions by up to 15 orders of magnitude (!) 78

33. Low-mass Spin-0 Dark Matter
Pseudoscalars
(Axions):
φ → -φ
QCD axion resolves strong CP problem P
→ Time-varying spin-dependent effects
1000-fold improvement 87

34. “Axion Wind” Spin-Precession Effect
[Flambaum, talk at Patras Workshop, 2013], [Graham, Rajendran, PRD 88, (2013)], [Stadnik, Flambaum, PRD 89, (2014)]
Pseudo-magnetic field *
* Compare with usual magnetic field: H = -μf ·B 88

35. Oscillating Electric Dipole Moments
Nucleons: [Graham, Rajendran, PRD 84, (2011)]
Atoms and molecules: [Stadnik, Flambaum, PRD 89, (2014)]
Electric Dipole Moment (EDM) = parity (P) and time-reversal-invariance (T) violating electric moment 90

36. Axion-Induced Oscillating Neutron EDM
[Crewther, Di Vecchia, Veneziano, Witten, PLB 88, 123 (1979)], [Pospelov, Ritz, PRL 83, 2526 (1999)], [Graham, Rajendran, PRD 84, (2011)]
Chiral-log enhancement in soft pion limit. 91

37. Schiff’s Theorem
[Schiff, Phys. Rev. 132, 2194 (1963)]
Schiff’s Theorem: “In a neutral atom made up of point-like non-relativistic charged particles (interacting only electrostatically), the constituent EDMs are screened from an external electric field.” 92

38. Schiff’s Theorem
[Schiff, Phys. Rev. 132, 2194 (1963)]
Schiff’s Theorem: “In a neutral atom made up of point-like non-relativistic charged particles (interacting only electrostatically), the constituent EDMs are screened from an external electric field.”
Classical explanation for nuclear EDM: A neutral atom does not accelerate in an external electric field! 93

39. Schiff’s Theorem
[Schiff, Phys. Rev. 132, 2194 (1963)]
Schiff’s Theorem: “In a neutral atom made up of point-like non-relativistic charged particles (interacting only electrostatically), the constituent EDMs are screened from an external electric field.”
Classical explanation for nuclear EDM: A neutral atom does not accelerate in an external electric field! 94

40. Schiff’s Theorem
[Schiff, Phys. Rev. 132, 2194 (1963)]
Schiff’s Theorem: “In a neutral atom made up of point-like non-relativistic charged particles (interacting only electrostatically), the constituent EDMs are screened from an external electric field.”
Classical explanation for nuclear EDM: A neutral atom does not accelerate in an external electric field! 95

41. Lifting of Schiff’s Theorem
[Sandars, PRL 19, 1396 (1967)], [O. Sushkov, Flambaum, Khriplovich, JETP 60, 873 (1984)]
In real (heavy) atoms: Incomplete screening of external electric field due to finite nuclear size, parametrised by nuclear Schiff moment. 96

42. Axion-Induced Oscillating Atomic and Molecular EDMs
[O. Sushkov, Flambaum, Khriplovich, JETP 60, 873 (1984)], [Stadnik, Flambaum, PRD 89, (2014)]
Induced through hadronic mechanisms:
Oscillating nuclear Schiff moments (I ≥ 1/2 => J ≥ 0) 97

43. Axion-Induced Oscillating Atomic and Molecular EDMs
[O. Sushkov, Flambaum, Khriplovich, JETP 60, 873 (1984)], [Stadnik, Flambaum, PRD 89, (2014)]
Induced through hadronic mechanisms:
Oscillating nuclear Schiff moments (I ≥ 1/2 => J ≥ 0)
Oscillating nuclear magnetic quadrupole moments (I ≥ 1 => J ≥ 1/2; magnetic => no Schiff screening) 98

44. Axion-Induced Oscillating Atomic and Molecular EDMs
[O. Sushkov, Flambaum, Khriplovich, JETP 60, 873 (1984)], [Stadnik, Flambaum, PRD 89, (2014)]
Induced through hadronic mechanisms:
Oscillating nuclear Schiff moments (I ≥ 1/2 => J ≥ 0)
Oscillating nuclear magnetic quadrupole moments (I ≥ 1 => J ≥ 1/2; magnetic => no Schiff screening)
Underlying mechanisms:
Intrinsic oscillating nucleon EDMs (1-loop level, 1/(8π2) loop factor)
Closely-spaced energy spacing enhancement and collective enhancement are possible in deformed nuclei  (Is the latter only for P,T-odd nuclear forces? The former definitely works only for P,T-odd nuclear forces!)
(1) 99

45. Axion-Induced Oscillating Atomic and Molecular EDMs
[O. Sushkov, Flambaum, Khriplovich, JETP 60, 873 (1984)], [Stadnik, Flambaum, PRD 89, (2014)]
Induced through hadronic mechanisms:
Oscillating nuclear Schiff moments (I ≥ 1/2 => J ≥ 0)
Oscillating nuclear magnetic quadrupole moments (I ≥ 1 => J ≥ 1/2; magnetic => no Schiff screening)
Underlying mechanisms:
Intrinsic oscillating nucleon EDMs (1-loop level, 1/(8π2) loop factor)
Oscillating P,T-violating intranuclear forces (tree level ; up to extra 1000-fold enhancement in deformed nuclei)
Closely-spaced energy spacing enhancement and collective enhancement are possible in deformed nuclei  (Is the latter only for P,T-odd nuclear forces? The former definitely works only for P,T-odd nuclear forces!)
(1)
(2)
100

46. Axion-Induced Oscillating Atomic and Molecular EDMs
[O. Sushkov, Flambaum, Khriplovich, JETP 60, 873 (1984)], [Stadnik, Flambaum, PRD 89, (2014)]
Induced through hadronic mechanisms:
Oscillating nuclear Schiff moments (I ≥ 1/2 => J ≥ 0)
Oscillating nuclear magnetic quadrupole moments (I ≥ 1 => J ≥ 1/2; magnetic => no Schiff screening)
Underlying mechanisms:
Intrinsic oscillating nucleon EDMs (1-loop level, 1/(8π2) loop factor)
Oscillating P,T-violating intranuclear forces (tree level ; up to extra 1000-fold enhancement in deformed nuclei)
Closely-spaced energy spacing enhancement and collective enhancement are possible in deformed nuclei  (Is the latter only for P,T-odd nuclear forces? The former definitely works only for P,T-odd nuclear forces!)
(1)
(2)
101

47. Searching for Spin-Dependent Effects
Proposals: [Flambaum, talk at Patras Workshop, 2013; Stadnik, Flambaum, PRD 89, (2014); arXiv: ; Stadnik, PhD Thesis (2017)]
Use spin-polarised sources: Atomic magnetometers, ultracold neutrons, torsion pendula
The UNCs are colder than 199Hg atoms (vapour), so their centre of mass is displaced downwards relatively by ~0.3 – 0.5cm -> B-field gradients are an issue, but can be dealt with. 199Hg atoms are needed to deal with the larger effect of B-field fluctuations. There also exist many possible false-EDM systematic effects.
104

48. Searching for Spin-Dependent Effects
Proposals: [Flambaum, talk at Patras Workshop, 2013; Stadnik, Flambaum, PRD 89, (2014); arXiv: ; Stadnik, PhD Thesis (2017)]
Use spin-polarised sources: Atomic magnetometers, ultracold neutrons, torsion pendula
Experiment (n/Hg): [nEDM collaboration (Klaus Kirch talk), PRX 7, (2017)]
The UNCs are colder than 199Hg atoms (vapour), so their centre of mass is displaced downwards relatively by ~0.3 – 0.5cm -> B-field gradients are an issue, but can be dealt with. 199Hg atoms are needed to deal with the larger effect of B-field fluctuations. There also exist many possible false-EDM systematic effects.
B-field effect
Axion DM effect
105

49. Searching for Spin-Dependent Effects
Proposals: [Flambaum, talk at Patras Workshop, 2013; Stadnik, Flambaum, PRD 89, (2014); arXiv: ; Stadnik, PhD Thesis (2017)]
Use spin-polarised sources: Atomic magnetometers, ultracold neutrons, torsion pendula
Experiment (n/Hg): [nEDM collaboration (Klaus Kirch talk), PRX 7, (2017)]
The UNCs are colder than 199Hg atoms (vapour), so their centre of mass is displaced downwards relatively by ~0.3 – 0.5cm -> B-field gradients are an issue, but can be dealt with. 199Hg atoms are needed to deal with the larger effect of B-field fluctuations. There also exist many possible false-EDM systematic effects.
B-field effect
Axion DM effect
106

50. Searching for Spin-Dependent Effects
Proposals: [Flambaum, talk at Patras Workshop, 2013; Stadnik, Flambaum, PRD 89, (2014); arXiv: ; Stadnik, PhD Thesis (2017)]
Use spin-polarised sources: Atomic magnetometers, ultracold neutrons, torsion pendula
Experiment (n/Hg): [nEDM collaboration (Klaus Kirch talk), PRX 7, (2017)]
The UNCs are colder than 199Hg atoms (vapour), so their centre of mass is displaced downwards relatively by ~0.3 – 0.5cm -> B-field gradients are an issue, but can be dealt with. 199Hg atoms are needed to deal with the larger effect of B-field fluctuations. There also exist many possible false-EDM systematic effects. E σ B
107

51. Searching for Spin-Dependent Effects
Proposals: [Flambaum, talk at Patras Workshop, 2013; Stadnik, Flambaum, PRD 89, (2014); arXiv: ; Stadnik, PhD Thesis (2017)]
Use spin-polarised sources: Atomic magnetometers, ultracold neutrons, torsion pendula
Experiment (n/Hg): [nEDM collaboration (Klaus Kirch talk), PRX 7, (2017)]
The UNCs are colder than 199Hg atoms (vapour), so their centre of mass is displaced downwards relatively by ~0.3 – 0.5cm -> B-field gradients are an issue, but can be dealt with. 199Hg atoms are needed to deal with the larger effect of B-field fluctuations. There also exist many possible false-EDM systematic effects. E σ B
Beff
Earth’s rotation
108

52. Constraints on Interaction of Axion Dark Matter with Gluons
nEDM constraints: [nEDM collaboration, PRX 7, (2017)]
3 orders of magnitude improvement!
Point out the Planck scale for comparison
117

53. Constraints on Interaction of Axion Dark Matter with Nucleons
νn/νHg constraints: [nEDM collaboration, PRX 7, (2017)]
40-fold improvement (laboratory bounds)!
118

54. Expected sensitivity (atomic co-magnetometry)
Constraints on Interaction of Axion Dark Matter with Nucleons
νn/νHg constraints: [nEDM collaboration, PRX 7, (2017)]
40-fold improvement (laboratory bounds)!
First-power vs second-power effects
Expected sensitivity (atomic co-magnetometry)
119

55. Summary
Improved limits on low-mass dark bosons from atomic and molecular EDM experiments (new forces, independent of ρDM)
New classes of dark matter effects that are first power in the underlying interaction constant => Up to 1000-fold improvement with experiments searching for oscillating EDMs and anomalous spin-precession effects
189