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Novel Approaches in Probing Low-Mass Bosonic Dark Matter

This project explores new methods to detect low-mass bosonic dark matter and neutrino-mediated forces, challenging traditional WIMP searches. By focusing on coherent effects of a low-mass dark matter field, it aims to find signals that are first-power in the interaction constant κ.

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Novel Approaches in Probing Low-Mass Bosonic Dark Matter

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  1. Yevgeny Stadnik New Probes for Low-Mass Bosonic Dark Matter and Neutrino-Mediated Forces Humboldt Fellow Johannes Gutenberg University, Mainz, Germany Collaborators (Theory): Victor Flambaum Collaborators (Experiment): nEDM collaboration at PSI and Sussex 53rd Rencontres de Moriond EW, La Thuile, March 2018

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

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

  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. Challenge:Observable is fourth powerin a small interaction constant (eי << 1)!

  6. 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 powerin the interaction constant?

  7. 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)

  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) • Coherently oscillating field, since cold (Eφ≈mφc2)

  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) • Classical field for mφ ≤ 0.1 eV, sincenφ(λdB,φ/2π)3 >> 1

  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 • Coherent + classical DM field = “Cosmic laser field”

  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 field” • 10-22eV ≤ mφ ≤ 0.1 eV <=> 10-8 Hz ≤ f ≤ 1013 Hz λdB,φ≤ Ldwarf galaxy~ 1 kpc Classical field

  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 field” • 10-22eV ≤ mφ ≤ 0.1 eV <=> 10-8 Hz ≤ f ≤ 1013 Hz • mφ ~ 10-22eV <=> T ~ 1 year 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)

  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) • 10-22eV ≤ mφ ≤ 0.1 eV inaccessible to traditional “scattering-off-nuclei” searches, since |pφ| ~ 10-3mφ is extremely small => recoil effects of individual particles suppressed

  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) • 10-22eV ≤ mφ ≤ 0.1 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 fieldin low-energy atomic and astrophysical phenomena that are first power in the interaction constant κ:

  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 of individual particles suppressed • BUT can look for coherent effects of a low-mass DM fieldin 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(!)

  17. 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 1015-fold improvement 1000-fold improvement See 2017 Moriond Gravitation talk

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

  19. Oscillating Electric Dipole Moments Nucleons: [Graham, Rajendran, PRD84, 055013 (2011)] Atoms and molecules: [Stadnik, Flambaum, PRD89, 043522 (2014)] Electric Dipole Moment (EDM) = parity (P) and time-reversal-invariance (T) violating electric moment

  20. Searching for Spin-Dependent Effects Proposals:[Flambaum, talk at Patras Workshop, 2013; Stadnik, Flambaum, PRD89, 043522 (2014); arXiv:1511.04098; Stadnik, PhD Thesis (2017)] Use spin-polarised sources: Atomic magnetometers, ultracold neutrons, torsion pendula

  21. Searching for Spin-Dependent Effects Proposals:[Flambaum, talk at Patras Workshop, 2013; Stadnik, Flambaum, PRD89, 043522 (2014); arXiv:1511.04098; Stadnik, PhD Thesis (2017)] Use spin-polarised sources: Atomic magnetometers, ultracold neutrons, torsion pendula Experiment (n/Hg):[nEDM collaboration, PRX7, 041034 (2017) + Nick Ayres’ talk] B-field effect Axion DM effect

  22. Searching for Spin-Dependent Effects Proposals:[Flambaum, talk at Patras Workshop, 2013; Stadnik, Flambaum, PRD89, 043522 (2014); arXiv:1511.04098; Stadnik, PhD Thesis (2017)] Use spin-polarised sources: Atomic magnetometers, ultracold neutrons, torsion pendula Experiment (n/Hg):[nEDM collaboration, PRX7, 041034 (2017) + Nick Ayres’ talk] B-field effect Axion DM effect

  23. Searching for Spin-Dependent Effects Proposals:[Flambaum, talk at Patras Workshop, 2013; Stadnik, Flambaum, PRD89, 043522 (2014); arXiv:1511.04098; Stadnik, PhD Thesis (2017)] Use spin-polarised sources: Atomic magnetometers, ultracold neutrons, torsion pendula Experiment (n/Hg):[nEDM collaboration, PRX7, 041034 (2017) + Nick Ayres’ talk] E σ B

  24. Searching for Spin-Dependent Effects Proposals:[Flambaum, talk at Patras Workshop, 2013; Stadnik, Flambaum, PRD89, 043522 (2014); arXiv:1511.04098; Stadnik, PhD Thesis (2017)] Use spin-polarised sources: Atomic magnetometers, ultracold neutrons, torsion pendula Experiment (n/Hg):[nEDM collaboration, PRX7, 041034 (2017) + Nick Ayres’ talk] E σ B Earth’s rotation

  25. Constraints on Interaction of Axion Dark Matter with Gluons nEDM constraints: [nEDM collaboration, PRX7, 041034 (2017)] 3 orders of magnitude improvement!

  26. Constraints on Interaction of Axion Dark Matter with Nucleons νn/νHg constraints: [nEDM collaboration, PRX7, 041034 (2017)] 40-fold improvement (laboratory bounds)!

  27. Constraints on Interaction of Axion Dark Matter with Nucleons νn/νHg constraints: [nEDM collaboration, PRX7, 041034 (2017)] 40-fold improvement (laboratory bounds)! Expected sensitivity (atomic co-magnetometry)

  28. “Long-Range” Neutrino-Mediated Forces

  29. Probing “Long-Range” Neutrino-Mediated Forces [Stadnik, arXiv:1711.03700]

  30. Probing “Long-Range” Neutrino-Mediated Forces [Stadnik, arXiv:1711.03700] Enormous enhancement of energy shift in s-wave atomic states (l = 0, no centrifugal barrier)!

  31. Probing “Long-Range” Neutrino-Mediated Forces [Stadnik, arXiv:1711.03700] Enormous enhancement of energy shift in s-wave atomic states (l = 0, no centrifugal barrier)! rc = cutoff radius Finite-sized nucleus: (aB/rc)2 ≈ (aB/Rnucl)2 ~ 109 Point-like nucleus: (aB/rc)2 ≈ (aB/λZ,W)2 ~ 1015

  32. Probing “Long-Range” Neutrino-Mediated Forces [Stadnik, arXiv:1711.03700] • Spectroscopy measurements of and calculations in: • Simple atoms (H, D) • Exotic atoms (e-e+, e-μ+) • Simple nuclei (np) • Heavy atoms (Ca+)

  33. Probing “Long-Range” Neutrino-Mediated Forces [Stadnik, arXiv:1711.03700] • Spectroscopy measurements of and calculations in: • Simple atoms (H, D) • Exotic atoms (e-e+, e-μ+) • Simple nuclei (np) • Heavy atoms (Ca+) Muonium ground-state hyperfine interval: νexp = 4463302776(51) Hz νtheor = 4463302868(271) Hz Δνneutrinos ≈ 2 Hz

  34. Constraints on “Long-Range” Neutrino-Mediated Forces [Stadnik, arXiv:1711.03700] 18 orders of magnitude improvement!

  35. Summary • New classes of dark matter effects that are first power in the underlying interaction constant => Up to 15 orders of magnitude improvement • Improved limits on dark bosons from atomic experiments (independent of ρDM) • 18 orders of magnitude improvement on “long-range” neutrino-mediated forces from atomic spectroscopy (close to testing the SM prediction!) • More details in full slides (also on ResearchGate)

  36. Low-mass Spin-0 Dark Matter Dark Matter Pseudoscalars (Axions): φ→ -φ P → Time-varying spin-dependent effects 1000-fold improvement

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

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

  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!

  40. 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.

  41. 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; up to extra 1000-fold enhancement in deformed nuclei) [O. Sushkov, Flambaum, Khriplovich, JETP60, 873 (1984)], [Stadnik, Flambaum, PRD89, 043522 (2014)] (1) (2)

  42. 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)]

  43. Low-mass Spin-0 Dark Matter Dark Matter Scalars (Dilatons): φ→ +φ P → Time-varying fundamental constants 1015-fold improvement

  44. 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 <φ2> = φ02/2 ∝ρφ Slow rolling (t~ tUniverse) Rapid oscillations (t<< tUniverse)

  45. Dark Matter-Induced Cosmological Evolution of the Fundamental Constants [Stadnik, Flambaum, PRL114, 161301 (2015);PRL115, 201301 (2015)] Consider quadratic couplings of an oscillating classical scalar field, φ(t) = φ0 cos(mφt), with SM fields. ‘Slow’ drifts[Astrophysics (high ρDM): BBN, CMB] Oscillating variations[Laboratory (high precision)]

  46. Dark Matter-Induced Cosmological Evolution of the Fundamental Constants [Stadnik, Flambaum, PRL114, 161301 (2015);PRL115, 201301 (2015)] Fermions: Photon: W and Z Bosons:

  47. BBN Constraints on ‘Slow’ Drifts in Fundamental Constants due to Dark Matter [Stadnik, Flambaum, PRL115, 201301 (2015)] • Largest effects of DM in early Universe (highest ρDM) • Big Bang nucleosynthesis (tweak ≈ 1s – tBBN ≈ 3 min) • Primordial 4He abundance sensitive to n/p ratio (almost all neutrons bound in 4He after BBN)

  48. Atomic Spectroscopy Searches for Oscillating Variations in Fundamental Constants due to Dark Matter [Arvanitaki, Huang, Van Tilburg, PRD91, 015015 (2015)],[Stadnik, Flambaum, PRL114, 161301 (2015)] ω = mφ (linear coupling) or ω = 2mφ (quadratic coupling) • Precision of optical clocks approaching ~10-18 fractional level • Sensitivity coefficients KX calculated extensively by Flambaum group and co-workers (1998 – present) Dy/Cs:[Van Tilburg et al., PRL115, 011802 (2015)],[Stadnik, Flambaum, PRL115, 201301 (2015)] Rb/Cs:[Hees et al., PRL117, 061301 (2016)],[Stadnik, Flambaum, PRA94, 022111 (2016)]

  49. Effects of Varying Fundamental Constants on Atomic Transitions [Dzuba, Flambaum, Webb, PRL82, 888 (1999); PRA59, 230 (1999); Dzuba, Flambaum, Marchenko, PRA68, 022506 (2003); Angstmann, Dzuba, Flambaum, PRA70, 014102 (2004); Dzuba, Flambaum, PRA77, 012515 (2008)] • Atomic optical transitions: Non-relativistic atomic unit of frequency Relativistic factor

  50. Effects of Varying Fundamental Constants on Atomic Transitions [Dzuba, Flambaum, Webb, PRL82, 888 (1999); PRA59, 230 (1999); Dzuba, Flambaum, Marchenko, PRA68, 022506 (2003); Angstmann, Dzuba, Flambaum, PRA70, 014102 (2004); Dzuba, Flambaum, PRA77, 012515 (2008)] • Atomic optical transitions:

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