Probing Low-Energy Exotic Bosons for Dark Matter

1. Yevgeny Stadnik, Victor Flambaum New Low-Energy Atomic and Astrophysical Probes for Dark Matter and Exotic Bosons Johannes Gutenberg University, Mainz, Germany University of New South Wales, Sydney, Australia In collaboration with the nEDM collaboration at PSI and Sussex: Nicholas Ayres*, Phillip Harris*, Klaus Kirch†, Michal Rawlik‡ * University of Sussex, United Kingdom † Paul Scherrer Institute, Switzerland ‡ ETH Zurich, Switzerland Probing the dark sector and general relativity at all scales, CERN, August 2017

2. Motivation Overwhelming astrophysical evidence for existence of dark matter (~5 times more dark matter than ordinary matter).

3. Motivation Overwhelming astrophysical evidence for existence of dark matter (~5 times more dark matter than ordinary matter). – “What is dark matter and how does it interact with ordinary matter non-gravitationally?”

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

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

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

7. Motivation Traditional “scattering-off-nuclei” searches for heavy WIMP dark matter particles (mχ ~ GeV) have not yet produced a strong positive result. Problem:Observable is quarticin the interaction constant eי, which is extremely small (eי << 1)!

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

9. Low-mass Spin-0 Dark Matter • Low-mass spin-0 particles form a coherently oscillating classicalfield 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)

10. Low-mass Spin-0 Dark Matter • Low-mass spin-0 particles form a coherently oscillating classicalfield 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 ≤ 0.1 eV, sincenφ(λdB,φ/2π)3 >> 1

11. Low-mass Spin-0 Dark Matter • Low-mass spin-0 particles form a coherently oscillating classicalfield 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 ≤ 0.1 eV, sincenφ(λdB,φ/2π)3 >> 1 • Coherent + classical DM field = “Cosmic laser”

12. Low-mass Spin-0 Dark Matter • Low-mass spin-0 particles form a coherently oscillating classicalfield 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 ≤ 0.1 eV, sincenφ(λdB,φ/2π)3 >> 1 • Coherent + classical DM field = “Cosmic laser” • 10-22eV ≤ mφ ≤ 0.1 eV <=> 10-8 Hz ≤ f ≤ 1013 Hz λdB,φ≤ Ldwarf galaxy~ 1 kpc Classical field

13. Low-mass Spin-0 Dark Matter • Low-mass spin-0 particles form a coherently oscillating classicalfield 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 ≤ 0.1 eV, sincenφ(λdB,φ/2π)3 >> 1 • Coherent + classical DM field = “Cosmic laser” • 10-22eV ≤ mφ ≤ 0.1 eV <=> 10-8 Hz ≤ f ≤ 1013 Hz • mφ ~ 10-22eV DM can resolve several long-standing “small-scale crises” of the cold DM model

14. Low-mass Spin-0 Dark Matter • Low-mass spin-0 particles form a coherently oscillating classicalfield 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 ≤ 0.1 eV, sincenφ(λdB,φ/2π)3 >> 1 • Coherent + classical DM field = “Cosmic laser” • 10-22eV ≤ mφ ≤ 0.1 eV <=> 10-8 Hz ≤ f ≤ 1013 Hz • mφ ~ 10-22eV DM can resolve several long-standing “small-scale crises” of the cold DM model • f ~ 10-8 Hz (mφ ~ 10-22eV) <=> T ~ 1 year

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

16. Low-mass Spin-0 Dark Matter • Low-mass spin-0 particles form a coherently oscillating classicalfield φ(t) = φ0 cos(mφc2t/ℏ), with energy density <ρφ>≈ mφ2φ02/2 (ρDM,local≈ 0.4 GeV/cm3) • 10-22eV ≤ mφ ≤ 0.1 eV inaccessible to traditional “scattering-off-nuclei” searches, since |pφ| ~ 10-3mφ is extremely small => recoil effects suppressed

17. Low-mass Spin-0 Dark Matter • Low-mass spin-0 particles form a coherently oscillating classicalfield φ(t) = φ0 cos(mφc2t/ℏ), with energy density <ρφ>≈ mφ2φ02/2 (ρDM,local≈ 0.4 GeV/cm3) • 10-22eV ≤ mφ ≤ 0.1 eV inaccessible to traditional “scattering-off-nuclei” searches, since |pφ| ~ 10-3mφ is extremely small => recoil effects suppressed • BUT can look for novel effects of low-mass DM in low-energy atomic and astrophysical phenomena that are linear in the interaction constant κ:

18. Low-mass Spin-0 Dark Matter • Low-mass spin-0 particles form a coherently oscillating classicalfield φ(t) = φ0 cos(mφc2t/ℏ), with energy density <ρφ>≈ mφ2φ02/2 (ρDM,local≈ 0.4 GeV/cm3) • 10-22eV ≤ mφ ≤ 0.1 eV inaccessible to traditional “scattering-off-nuclei” searches, since |pφ| ~ 10-3mφ is extremely small => recoil effects suppressed • BUT can look for novel effects of low-mass DM in low-energy atomic and astrophysical phenomena that are linear in the interaction constant κ: • Consideration of linear effects => Improved sensitivity to certain DM interactions by up to 15 orders of magnitude(!)

19. Low-mass Spin-0 Dark Matter Dark Matter

20. Low-mass Spin-0 Dark Matter Dark Matter Scalars (Dilatons): φ→ +φ P

21. Low-mass Spin-0 Dark Matter Dark Matter Scalars (Dilatons): φ→ +φ Pseudoscalars (Axions): φ→ -φ P P

22. Low-mass Spin-0 Dark Matter Dark Matter Scalars (Dilatons): φ→ +φ Pseudoscalars (Axions): φ→ -φ P P → Time-varying fundamental constants

23. Low-mass Spin-0 Dark Matter Dark Matter Scalars (Dilatons): φ→ +φ Pseudoscalars (Axions): φ→ -φ P P → Time-varying fundamental constants → Time-varying spin-dependent effects

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

25. “Axion Wind” Spin-Precession Effect [Flambaum, talk at Patras Workshop, 2013], [Graham, Rajendran, PRD88, 035023 (2013)], [Stadnik, Flambaum, PRD89, 043522 (2014)] Pseudo-magnetic field

26. Axion-Induced Oscillating Spin-Gravity Coupling [Stadnik, Flambaum, PRD89, 043522 (2014)] Distortion of DM field by massive body

27. Oscillating Electric Dipole Moments Electric Dipole Moment (EDM) = parity (P) and time-reversal-invariance (T) violating electric moment

28. Axion-Induced Oscillating Neutron EDM [Crewther, Di Vecchia, Veneziano, Witten, PLB88, 123 (1979)], [Pospelov, Ritz, PRL83, 2526 (1999)], [Graham, Rajendran, PRD84, 055013 (2011)]

29. 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.”

30. 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!

31. 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!

32. 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!

33. Lifting of Schiff’s Theorem [Sandars, PRL19, 1396 (1967)], [O. Sushkov, Flambaum, Khriplovich, JETP60, 873 (1984)] In real (heavy) atoms:Incomplete screening of external electric field due to finite nuclear size, parametrised by nuclear Schiff moment.

34. Axion-Induced Oscillating Atomic and Molecular EDMs Induced through hadronic mechanisms: Oscillating nuclear Schiff moments (I ≥ 1/2 => J ≥ 0) [O. Sushkov, Flambaum, Khriplovich, JETP60, 873 (1984)], [Stadnik, Flambaum, PRD89, 043522 (2014)]

35. Axion-Induced Oscillating Atomic and Molecular EDMs 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) [O. Sushkov, Flambaum, Khriplovich, JETP60, 873 (1984)], [Stadnik, Flambaum, PRD89, 043522 (2014)]

36. Axion-Induced Oscillating Atomic and Molecular EDMs 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) [O. Sushkov, Flambaum, Khriplovich, JETP60, 873 (1984)], [Stadnik, Flambaum, PRD89, 043522 (2014)] (1)

37. Axion-Induced Oscillating Atomic and Molecular EDMs 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) Oscillating P,T-violating intranuclear forces (tree level => larger by ~4π2≈ 40; additional enhancement in deformed nuclei) [O. Sushkov, Flambaum, Khriplovich, JETP60, 873 (1984)], [Stadnik, Flambaum, PRD89, 043522 (2014)] (1) (2)

38. Axion-Induced Oscillating Atomic and Molecular EDMs Also induced through non-hadronic mechanisms for J ≥ 1/2 atoms, via mixing of opposite-parity atomic states. [Stadnik, Flambaum, PRD89, 043522 (2014)], [Roberts, Stadnik, Dzuba, Flambaum, Leefer, Budker, PRL113, 081601 (2014); PRD90, 096005 (2014)]

39. Searching for Spin-Dependent Effects Need spin-polarised sources!

40. Searching for Spin-Dependent Effects Need spin-polarised sources! n/Hg:[nEDM collaboration (Ayres, Harris, Kirch, Rawlik et al.), Flambaum, Stadnik, In preparation]

41. Searching for Spin-Dependent Effects Need spin-polarised sources! n/Hg:[nEDM collaboration (Ayres, Harris, Kirch, Rawlik et al.), Flambaum, Stadnik, In preparation] Earth’s rotation

42. Constraints on Interaction of Axion Dark Matter with Gluons (Preliminary) nEDM constraints: [nEDM collaboration, In preparation] 3 orders of magnitude improvement!

43. Constraints on Interaction of Axion Dark Matter with Nucleons (Preliminary) νn/νHg constraints: [nEDM collaboration, In preparation] 40-fold improvement!

44. Low-mass Spin-0 Dark Matter Dark Matter Scalars (Dilatons): φ→ +φ P → Time-varying fundamental constants

45. Cosmological Evolution of the Fundamental ‘Constants’ • Dirac’s large numbers hypothesis: G ∝1/t

46. Cosmological Evolution of the Fundamental ‘Constants’ • Dirac’s large numbers hypothesis: G ∝1/t • Fundamental constants not predicted from theory, but determined from measurements (local – not universal)

47. Cosmological Evolution of the Fundamental ‘Constants’ • Dirac’s large numbers hypothesis: G ∝1/t • Fundamental constants not predicted from theory, but determined from measurements (local – not universal) • Possible models for cosmological evolution of fundamental constants?

48. Cosmological Evolution of the Fundamental ‘Constants’ • Dirac’s large numbers hypothesis: G ∝1/t • Fundamental constants not predicted from theory, but determined from measurements (local – not universal) • Possible models for cosmological evolution of fundamental constants? Dark energy (mφ ≈ 0) Slow rolling (t~ tUniverse)

49. Cosmological Evolution of the Fundamental ‘Constants’ • Dirac’s large numbers hypothesis: G ∝1/t • Fundamental constants not predicted from theory, but determined from measurements (local – not universal) • Possible models for cosmological evolution of fundamental constants? Dark energy (mφ ≈ 0) Dark matter? φ(t) = φ0 cos(mφt) Slow rolling (t~ tUniverse) Rapid oscillations (t<< tUniverse)

50. Cosmological Evolution of the Fundamental ‘Constants’ • Dirac’s large numbers hypothesis: G ∝1/t • Fundamental constants not predicted from theory, but determined from measurements (local – not universal) • Possible models for cosmological evolution of fundamental constants? Dark energy (mφ ≈ 0) Dark matter? φ(t) = φ0 cos(mφt) <φ> = 0 Slow rolling (t~ tUniverse) Rapid oscillations (t<< tUniverse)