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Yevgeny Stadnik, Victor Flambaum
Novel searches for dark matter and fifth-
forces with atomic clock spectroscopy,
laser interferometry and pulsar timing
Helmholtz Institute Mainz, Germany
University of New South Wales, Sydney, Australia
52nd Rencontres de Moriond Gravitation, La Thuile, March 2017
PRL 113, 081601 (2014); PRL 113, 151301 (2014);
PRL 114, 161301 (2015); PRL 115, 201301 (2015);
PRL 117, 271601 (2016);
PRD 89, 043522 (2014); PRD 90, 096005 (2014);
EPJC 75, 110 (2015); PRA 93, 063630 (2016);
PRD 93, 115037 (2016); PRA 94, 022111 (2016).
In collaboration with: Dmitry Budker (Helmholtz Institute Mainz)
Motivation Overwhelming astrophysical evidence for existence
of dark matter (~5 times more dark matter than
ordinary matter).
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?”
Motivation Traditional “scattering-off-nuclei” searches for
heavy WIMP dark matter particles (χ) have not yet
produced a strong positive result.
Motivation Traditional “scattering-off-nuclei” searches for
heavy WIMP dark matter particles (χ) have not yet
produced a strong positive result.
Problem: Observable is quartic in the interaction
constant eי, which is extremely small (e1 >> י)!
† nφ(λdB/2π)3 >> 1 * Coherently oscillating field => cold, i.e., Eφ ≈ mφc2
Low-mass Spin-0 Dark Matter We propose to search for other well-motivated forms of dark
matter: low-mass spin-0 particles, which form a coherently *
oscillating classical † field (<ρφ> ≈ mφ2φ0
2/2):
φ(t) = φ0 cos(mφc2t/ℏ)
† nφ(λdB/2π)3 >> 1 * Coherently oscillating field => cold, i.e., Eφ ≈ mφc2
Low-mass Spin-0 Dark Matter We propose to search for other well-motivated forms of dark
matter: low-mass spin-0 particles, which form a coherently *
oscillating classical † field (<ρφ> ≈ mφ2φ0
2/2):
φ(t) = φ0 cos(mφc2t/ℏ) – “cosmic laser”
† nφ(λdB/2π)3 >> 1 * Coherently oscillating field => cold, i.e., Eφ ≈ mφc2
Low-mass Spin-0 Dark Matter We propose to search for other well-motivated forms of dark
matter: low-mass spin-0 particles, which form a coherently *
oscillating classical † field (<ρφ> ≈ mφ2φ0
2/2):
φ(t) = φ0 cos(mφc2t/ℏ), via effects that are linear in the
interaction constant .
† nφ(λdB/2π)3 >> 1
• 10-22 eV ≤ mφ ≤ 0.1 eV <=> 10-8 Hz ≤ f ≤ 1013 Hz
* Coherently oscillating field => cold, i.e., Eφ ≈ mφc2
Low-mass Spin-0 Dark Matter We propose to search for other well-motivated forms of dark
matter: low-mass spin-0 particles, which form a coherently *
oscillating classical † field (<ρφ> ≈ mφ2φ0
2/2):
φ(t) = φ0 cos(mφc2t/ℏ), via effects that are linear in the
interaction constant .
† nφ(λdB/2π)3 >> 1
• 10-22 eV ≤ mφ ≤ 0.1 eV <=> 10-8 Hz ≤ f ≤ 1013 Hz
• Inaccessible to traditional “scattering-off-nuclei” and collider searches
* Coherently oscillating field => cold, i.e., Eφ ≈ mφc2
Low-mass Spin-0 Dark Matter We propose to search for other well-motivated forms of dark
matter: low-mass spin-0 particles, which form a coherently *
oscillating classical † field (<ρφ> ≈ mφ2φ0
2/2):
φ(t) = φ0 cos(mφc2t/ℏ), via effects that are linear in the
interaction constant .
† nφ(λdB/2π)3 >> 1
• 10-22 eV ≤ mφ ≤ 0.1 eV <=> 10-8 Hz ≤ f ≤ 1013 Hz
• Inaccessible to traditional “scattering-off-nuclei” and collider searches
• Ultra-low-mass spin-0 DM with mass mφ ~ 10-22 eV has been
proposed to resolve several “small-scale crises” of the cold DM model (cusp-core problem and others)
* Coherently oscillating field => cold, i.e., Eφ ≈ mφc2
Low-mass Spin-0 Dark Matter We propose to search for other well-motivated forms of dark
matter: low-mass spin-0 particles, which form a coherently *
oscillating classical † field (<ρφ> ≈ mφ2φ0
2/2):
φ(t) = φ0 cos(mφc2t/ℏ), via effects that are linear in the
interaction constant .
† nφ(λdB/2π)3 >> 1
• 10-22 eV ≤ mφ ≤ 0.1 eV <=> 10-8 Hz ≤ f ≤ 1013 Hz
• Inaccessible to traditional “scattering-off-nuclei” and collider searches
• Ultra-low-mass spin-0 DM with mass mφ ~ 10-22 eV has been
proposed to resolve several “small-scale crises” of the cold DM model (cusp-core problem and others)
• f ~ 10-8 Hz (mφ ~ 10-22 eV) <=> T ~ 1 year
* Coherently oscillating field => cold, i.e., Eφ ≈ mφc2
Low-mass Spin-0 Dark Matter We propose to search for other well-motivated forms of dark
matter: low-mass spin-0 particles, which form a coherently *
oscillating classical † field (<ρφ> ≈ mφ2φ0
2/2):
φ(t) = φ0 cos(mφc2t/ℏ), via effects that are linear in the
interaction constant .
† nφ(λdB/2π)3 >> 1
• Consideration of linear effects of dark matter in low-energy
atomic and astrophysical phenomena has already allowed us
to improve the sensitivity to some interactions of dark matter
by up to 15 orders of magnitude (!)
* Coherently oscillating field => cold, i.e., Eφ ≈ mφc2
Low-mass Spin-0 Dark Matter We propose to search for other well-motivated forms of dark
matter: low-mass spin-0 particles, which form a coherently *
oscillating classical † field (<ρφ> ≈ mφ2φ0
2/2):
φ(t) = φ0 cos(mφc2t/ℏ), via effects that are linear in the
interaction constant .
Low-mass Spin-0 Dark Matter
Dark Matter
Low-mass Spin-0 Dark Matter
Dark Matter
Scalars:
Even-parity
Pseudoscalars
(Axions, ALPs):
Odd-parity
Low-mass Spin-0 Dark Matter
Dark Matter
Scalars:
Even-parity
Pseudoscalars
(Axions, ALPs):
Odd-parity
→ Oscillating spin-
dependent effects
→ ‘Slow’ evolution and oscillating variation of
fundamental constants
Low-mass Spin-0 Dark Matter
Dark Matter
Scalars:
Even-parity
→ ‘Slow’ evolution and oscillating variation of
fundamental constants
Cosmological Evolution of the
Fundamental Constants • Dirac’s large numbers hypothesis: G ∝ 1/t
Cosmological Evolution of the
Fundamental Constants • Dirac’s large numbers hypothesis: G ∝ 1/t
• Values of fundamental constants cannot be predicted,
but must be determined from experiment:
e.g., α(q2 = 0) ≈ 1/137 locally (in space and time)
Cosmological Evolution of the
Fundamental Constants • Dirac’s large numbers hypothesis: G ∝ 1/t
• Values of fundamental constants cannot be predicted,
but must be determined from experiment:
e.g., α(q2 = 0) ≈ 1/137 locally (in space and time) • Contemporary dark-energy-type models:
Cosmological evolution of fundamental constants driven
by (nearly) massless exotic boson that couples to matter
Cosmological Evolution of the
Fundamental Constants • Dirac’s large numbers hypothesis: G ∝ 1/t
• Values of fundamental constants cannot be predicted,
but must be determined from experiment:
e.g., α(q2 = 0) ≈ 1/137 locally (in space and time) • Contemporary dark-energy-type models:
Cosmological evolution of fundamental constants driven
by (nearly) massless exotic boson that couples to matter
“Can a cosmological evolution of the
fundamental constants be driven by dark matter?”
Dark Matter-Induced Cosmological
Evolution of the Fundamental Constants
Consider an oscillating classical scalar field,
φ(t) = φ0 cos(mφt), that interacts with SM fields
(e.g., a fermion f) via quadratic couplings in φ.
[Stadnik, Flambaum, PRL 115, 201301 (2015)]
Dark Matter-Induced Cosmological
Evolution of the Fundamental Constants
Consider an oscillating classical scalar field,
φ(t) = φ0 cos(mφt), that interacts with SM fields
(e.g., a fermion f) via quadratic couplings in φ.
[Stadnik, Flambaum, PRL 115, 201301 (2015)]
Dark Matter-Induced Cosmological
Evolution of the Fundamental Constants
Consider an oscillating classical scalar field,
φ(t) = φ0 cos(mφt), that interacts with SM fields
(e.g., a fermion f) via quadratic couplings in φ.
[Stadnik, Flambaum, PRL 115, 201301 (2015)]
Dark Matter-Induced Cosmological
Evolution of the Fundamental Constants
Consider an oscillating classical scalar field,
φ(t) = φ0 cos(mφt), that interacts with SM fields
(e.g., a fermion f) via quadratic couplings in φ.
[Stadnik, Flambaum, PRL 115, 201301 (2015)]
Dark Matter-Induced Cosmological
Evolution of the Fundamental Constants
Consider an oscillating classical scalar field,
φ(t) = φ0 cos(mφt), that interacts with SM fields
(e.g., a fermion f) via quadratic couplings in φ.
[Stadnik, Flambaum, PRL 115, 201301 (2015)]
‘Slow’ drifts [Astrophysics
(high ρDM): BBN, CMB]
Dark Matter-Induced Cosmological
Evolution of the Fundamental Constants
Consider an oscillating classical scalar field,
φ(t) = φ0 cos(mφt), that interacts with SM fields
(e.g., a fermion f) via quadratic couplings in φ.
[Stadnik, Flambaum, PRL 115, 201301 (2015)]
‘Slow’ drifts [Astrophysics
(high ρDM): BBN, CMB]
Oscillating variations [Laboratory (high precision)]
Dark Matter-Induced Cosmological
Evolution of the Fundamental Constants
We can consider a wide range of quadratic-in-φ
interactions with the SM sector:
Photon:
Fermions:
W and Z Bosons (mediators of weak interactions):
[Stadnik, Flambaum, PRL 115, 201301 (2015)]
Astrophysical Constraints on ‘Slow’ Drifts in Fundamental Constants Induced by Scalar Dark Matter (BBN)
• Largest effects of scalar dark matter are in the early
Universe (highest ρDM => highest φ02).
[Stadnik, Flambaum, PRL 115, 201301 (2015)]
Astrophysical Constraints on ‘Slow’ Drifts in Fundamental Constants Induced by Scalar Dark Matter (BBN)
• Largest effects of scalar dark matter are in the early
Universe (highest ρDM => highest φ02).
• Earliest cosmological epoch that we can probe is Big
Bang nucleosynthesis (from tweak ≈ 1s until tBBN ≈ 3 min).
[Stadnik, Flambaum, PRL 115, 201301 (2015)]
Astrophysical Constraints on ‘Slow’ Drifts in Fundamental Constants Induced by Scalar Dark Matter (BBN)
• Largest effects of scalar dark matter are in the early
Universe (highest ρDM => highest φ02).
• Earliest cosmological epoch that we can probe is Big
Bang nucleosynthesis (from tweak ≈ 1s until tBBN ≈ 3 min). • Primordial 4He abundance is sensitive to relative
abundance of neutrons to protons (almost all neutrons
are bound in 4He by the end of BBN).
[Stadnik, Flambaum, PRL 115, 201301 (2015)]
Astrophysical Constraints on ‘Slow’ Drifts in Fundamental Constants Induced by Scalar Dark Matter (BBN)
• Largest effects of scalar dark matter are in the early
Universe (highest ρDM => highest φ02).
• Earliest cosmological epoch that we can probe is Big
Bang nucleosynthesis (from tweak ≈ 1s until tBBN ≈ 3 min). • Primordial 4He abundance is sensitive to relative
abundance of neutrons to protons (almost all neutrons
are bound in 4He by the end of BBN).
[Stadnik, Flambaum, PRL 115, 201301 (2015)]
Astrophysical Constraints on ‘Slow’ Drifts in Fundamental Constants Induced by Scalar Dark Matter (BBN)
• Largest effects of scalar dark matter are in the early
Universe (highest ρDM => highest φ02).
• Earliest cosmological epoch that we can probe is Big
Bang nucleosynthesis (from tweak ≈ 1s until tBBN ≈ 3 min). • Primordial 4He abundance is sensitive to relative
abundance of neutrons to protons (almost all neutrons
are bound in 4He by the end of BBN).
[Stadnik, Flambaum, PRL 115, 201301 (2015)]
Astrophysical Constraints on ‘Slow’ Drifts in Fundamental Constants Induced by Scalar Dark Matter (BBN)
• Largest effects of scalar dark matter are in the early
Universe (highest ρDM => highest φ02).
• Earliest cosmological epoch that we can probe is Big
Bang nucleosynthesis (from tweak ≈ 1s until tBBN ≈ 3 min). • Primordial 4He abundance is sensitive to relative
abundance of neutrons to protons (almost all neutrons
are bound in 4He by the end of BBN).
[Stadnik, Flambaum, PRL 115, 201301 (2015)]
Laboratory Searches for Oscillating Variations in
Fundamental Constants Induced by Scalar Dark Matter [Arvanitaki, Huang, Van Tilburg, PRD 91, 015015 (2015); Stadnik, Flambaum, PRL 115, 201301 (2015)]
• In the laboratory, we can search for oscillating variations in
the fundamental constants induced by scalar DM, using
clock frequency comparison measurements.
Laboratory Searches for Oscillating Variations in
Fundamental Constants Induced by Scalar Dark Matter [Arvanitaki, Huang, Van Tilburg, PRD 91, 015015 (2015); Stadnik, Flambaum, PRL 115, 201301 (2015)]
• In the laboratory, we can search for oscillating variations in
the fundamental constants induced by scalar DM, using
clock frequency comparison measurements.
= mφ (linear) or = 2mφ (quadratic),
10-22 eV ≤ mφ ≤ 0.1 eV => 10-8 Hz* ≤ f ≤ 1014 Hz (f ~ 10-8 Hz corresponds to T ~ 1 year)
Laboratory Searches for Oscillating Variations in
Fundamental Constants Induced by Scalar Dark Matter [Arvanitaki, Huang, Van Tilburg, PRD 91, 015015 (2015); Stadnik, Flambaum, PRL 115, 201301 (2015)]
• In the laboratory, we can search for oscillating variations in
the fundamental constants induced by scalar DM, using
clock frequency comparison measurements.
• Sensitivity coefficients KX calculated extensively by
Flambaum group and co-workers (1998 – present).
= mφ (linear) or = 2mφ (quadratic),
10-22 eV ≤ mφ ≤ 0.1 eV => 10-8 Hz* ≤ f ≤ 1014 Hz (f ~ 10-8 Hz corresponds to T ~ 1 year)
Laboratory Searches for Oscillating Variations in
Fundamental Constants Induced by Scalar Dark Matter [Arvanitaki, Huang, Van Tilburg, PRD 91, 015015 (2015); Stadnik, Flambaum, PRL 115, 201301 (2015)]
• In the laboratory, we can search for oscillating variations in
the fundamental constants induced by scalar DM, using
clock frequency comparison measurements.
• Sensitivity coefficients KX calculated extensively by
Flambaum group and co-workers (1998 – present).
• Precision of latest state-of-the-art optical clocks is
approaching the 10-18 fractional level (clocks lose or gain less
than 1 second over 14 billion years).
= mφ (linear) or = 2mφ (quadratic),
10-22 eV ≤ mφ ≤ 0.1 eV => 10-8 Hz* ≤ f ≤ 1014 Hz (f ~ 10-8 Hz corresponds to T ~ 1 year)
Effects of Varying Fundamental Constants
on Atomic Transitions [Dzuba, Flambaum, Webb, PRL 82, 888 (1999) + PRA 59, 230 (1999);
Dzuba, Flambaum, Marchenko, PRA 68, 022506 (2003); Angstmann, Dzuba, Flambaum,
PRA 70, 014102 (2004); Dzuba, Flambaum, PRA 77, 012515 (2008)]
• Atomic optical transitions:
Effects of Varying Fundamental Constants
on Atomic Transitions [Dzuba, Flambaum, Webb, PRL 82, 888 (1999) + PRA 59, 230 (1999);
Dzuba, Flambaum, Marchenko, PRA 68, 022506 (2003); Angstmann, Dzuba, Flambaum,
PRA 70, 014102 (2004); Dzuba, Flambaum, PRA 77, 012515 (2008)]
• Atomic optical transitions:
Effects of Varying Fundamental Constants
on Atomic Transitions [Dzuba, Flambaum, Webb, PRL 82, 888 (1999) + PRA 59, 230 (1999);
Dzuba, Flambaum, Marchenko, PRA 68, 022506 (2003); Angstmann, Dzuba, Flambaum,
PRA 70, 014102 (2004); Dzuba, Flambaum, PRA 77, 012515 (2008)]
• Atomic optical transitions:
Effects of Varying Fundamental Constants
on Atomic Transitions [Dzuba, Flambaum, Webb, PRL 82, 888 (1999) + PRA 59, 230 (1999);
Dzuba, Flambaum, Marchenko, PRA 68, 022506 (2003); Angstmann, Dzuba, Flambaum,
PRA 70, 014102 (2004); Dzuba, Flambaum, PRA 77, 012515 (2008)]
• Atomic optical transitions:
Kα(Sr) = 0.06, Kα(Yb) = 0.3, Kα(Hg) = 0.8
Increasing Z
Effects of Varying Fundamental Constants
on Atomic Transitions [Dzuba, Flambaum, Webb, PRL 82, 888 (1999) + PRA 59, 230 (1999);
Dzuba, Flambaum, Marchenko, PRA 68, 022506 (2003); Angstmann, Dzuba, Flambaum,
PRA 70, 014102 (2004); Dzuba, Flambaum, PRA 77, 012515 (2008)]
• Atomic optical transitions:
Kα(Sr) = 0.06, Kα(Yb) = 0.3, Kα(Hg) = 0.8
Increasing Z
• Atomic hyperfine transitions:
Effects of Varying Fundamental Constants
on Atomic Transitions [Dzuba, Flambaum, Webb, PRL 82, 888 (1999) + PRA 59, 230 (1999);
Dzuba, Flambaum, Marchenko, PRA 68, 022506 (2003); Angstmann, Dzuba, Flambaum,
PRA 70, 014102 (2004); Dzuba, Flambaum, PRA 77, 012515 (2008)]
• Atomic optical transitions:
Kα(Sr) = 0.06, Kα(Yb) = 0.3, Kα(Hg) = 0.8
Increasing Z
• Atomic hyperfine transitions:
Kα(1H) = 2.0, Kα(
87Rb) = 2.3, Kα(133Cs) = 2.8
Increasing Z
Effects of Varying Fundamental Constants
on Atomic Transitions [Dzuba, Flambaum, Webb, PRL 82, 888 (1999) + PRA 59, 230 (1999);
Dzuba, Flambaum, Marchenko, PRA 68, 022506 (2003); Angstmann, Dzuba, Flambaum,
PRA 70, 014102 (2004); Dzuba, Flambaum, PRA 77, 012515 (2008)]
• Atomic optical transitions:
Kα(Sr) = 0.06, Kα(Yb) = 0.3, Kα(Hg) = 0.8
Increasing Z
• Atomic hyperfine transitions:
Kα(1H) = 2.0, Kα(
87Rb) = 2.3, Kα(133Cs) = 2.8
Increasing Z
Kme/mN= 1
Enhanced Effects of Varying Fundamental
Constants on Atomic Transitions [Numerous papers by Flambaum group and co-workers]
• Sensitivity coefficients may
be greatly enhanced for
transitions between nearly
degenerate levels:
- Atoms (e.g.,
|Kα(Dy)| ~ 106 – 107)
Enhanced Effects of Varying Fundamental
Constants on Atomic Transitions [Numerous papers by Flambaum group and co-workers]
• Sensitivity coefficients may
be greatly enhanced for
transitions between nearly
degenerate levels:
- Atoms (e.g.,
|Kα(Dy)| ~ 106 – 107)
- Molecules
- Highly-charged ions
- Nuclei
Laboratory Searches for Oscillating Variations in
Fundamental Constants Induced by Scalar Dark Matter
System Laboratory Constraints 162,164Dy/133Cs UC Berkeley/Mainz Van Tilburg, Leefer, Bougas, Budker,
PRL 115, 011802 (2015);
Stadnik, Flambaum, PRL 115, 201301
(2015) + PRA 94, 022111 (2016)
87Rb/133Cs LNE-SYRTE Paris Hees, Guena, Abgrall, Bize, Wolf,
PRL 117, 061301 (2016);
Stadnik, Flambaum,
PRA 94, 022111 (2016)
Constraints on Quadratic Interaction of
Scalar Dark Matter with the Photon BBN, CMB, Dy and Rb/Cs constraints:
[Stadnik, Flambaum, PRL 115, 201301 (2015) + PRA 94, 022111 (2016)]
15 orders of magnitude improvement!
Constraints on Quadratic Interactions of
Scalar Dark Matter with Light Quarks BBN and Rb/Cs constraints:
[Stadnik, Flambaum, PRL 115, 201301 (2015) + PRA 94, 022111 (2016)]
Constraints on Quadratic Interaction of
Scalar Dark Matter with the Electron BBN and CMB constraints:
[Stadnik, Flambaum, PRL 115, 201301 (2015)]
Constraints on Quadratic Interactions of
Scalar Dark Matter with W and Z Bosons BBN constraints:
[Stadnik, Flambaum, PRL 115, 201301 (2015)]
Laboratory Searches for Oscillating Variations in
Fundamental Constants Induced by Scalar Dark Matter [Stadnik, Flambaum, PRL 114, 161301 (2015) + PRA 93, 063630 (2016)]
LIGO interferometer,
L ~ 4 km Small-scale cavity,
L ~ 0.2 m
Laboratory Searches for Oscillating Variations in
Fundamental Constants Induced by Scalar Dark Matter [Stadnik, Flambaum, PRL 114, 161301 (2015) + PRA 93, 063630 (2016)]
• Alternatively, we can compare interferometer arm length
with photon wavelength. LIGO enhancement ~ 1014.
Laboratory Searches for Oscillating Variations in
Fundamental Constants Induced by Scalar Dark Matter [Stadnik, Flambaum, PRL 114, 161301 (2015) + PRA 93, 063630 (2016)]
• Alternatively, we can compare interferometer arm length
with photon wavelength. LIGO enhancement ~ 1014.
• Accumulated phase in an arm, Φ = L/c, changes if the
fundamental constants change (L ~ NaB and atomic
depend on the fundamental constants).
Laboratory Searches for Oscillating Variations in
Fundamental Constants Induced by Scalar Dark Matter [Stadnik, Flambaum, PRL 114, 161301 (2015) + PRA 93, 063630 (2016)]
• Alternatively, we can compare interferometer arm length
with photon wavelength. LIGO enhancement ~ 1014.
• Accumulated phase in an arm, Φ = L/c, changes if the
fundamental constants change (L ~ NaB and atomic
depend on the fundamental constants).
Laboratory Searches for Oscillating Variations in
Fundamental Constants Induced by Scalar Dark Matter [Stadnik, Flambaum, PRL 114, 161301 (2015) + PRA 93, 063630 (2016)]
• Alternatively, we can compare interferometer arm length
with photon wavelength. LIGO enhancement ~ 1014.
• Accumulated phase in an arm, Φ = L/c, changes if the
fundamental constants change (L ~ NaB and atomic
depend on the fundamental constants).
• Multiple reflections enhance observable effects due to
variation of the fundamental constants by the effective
mean number of passages Neff (e.g., Neff ~ 105 in small-
scale interferometer with highly reflective mirrors).
0D object – Monopole
1D object – String
2D object – Domain wall
Topological Defect Dark Matter
0D object – Monopole
1D object – String
2D object – Domain wall
Take a simple scalar field and give it a self-potential,
e.g., V(φ) = (φ2-v2)2 . If φ = -v at x = -∞ and φ = +v at
x = +∞, then a stable domain wall will form in between,
e.g., φ(x) = v tanh(xmφ) with mφ = 1/2 v .
Topological Defect Dark Matter
0D object – Monopole
1D object – String
2D object – Domain wall
Take a simple scalar field and give it a self-potential,
e.g., V(φ) = (φ2-v2)2 . If φ = -v at x = -∞ and φ = +v at
x = +∞, then a stable domain wall will form in between,
e.g., φ(x) = v tanh(xmφ) with mφ = 1/2 v .
Topological defects produce transient-in-time effects.
Topological Defect Dark Matter
0D object – Monopole
1D object – String
2D object – Domain wall
Take a simple scalar field and give it a self-potential,
e.g., V(φ) = (φ2-v2)2 . If φ = -v at x = -∞ and φ = +v at
x = +∞, then a stable domain wall will form in between,
e.g., φ(x) = v tanh(xmφ) with mφ = 1/2 v .
Topological defects produce transient-in-time effects.
Detection of topological defects via transient-in-time
effects requires searching for correlated signals using
a terrestrial or space-based network of detectors.
Topological Defect Dark Matter
Global Network of Laser Interferometers (LIGO,
Virgo, GEO600, TAMA300 and Small-scale)
[Stadnik, Flambaum, PRL 114, 161301 (2015) + PRA 93, 063630 (2016)
+ Ongoing collaboration with LIGO and Virgo (Klimenko, Mitselmakher; Ward)]
vTD ~ 10-3 c
Recent Search for Domain Walls with
Strontium Clock – Optical Cavity System [Wcislo et al., Nature Astronomy 1, 0009 (2016)]
[Wcislo et al., Nature Astronomy 1, 0009 (2016)]
Recent Search for Domain Walls with
Strontium Clock – Optical Cavity System
• Pulsars are highly-magnetised, rapidly rotating neutron
stars (Trot ~ 1 ms – 10 s), with very high long-term period
stability (~10-15).
[Stadnik, Flambaum, PRL 113, 151301 (2014)]
Pulsar Timing Searches
• Pulsars are highly-magnetised, rapidly rotating neutron
stars (Trot ~ 1 ms – 10 s), with very high long-term period
stability (~10-15).
• Can search for correlated effects of topological defects with
pulsar networks and binary pulsar systems.
[Stadnik, Flambaum, PRL 113, 151301 (2014)]
Pulsar Timing Searches
• Pulsars are highly-magnetised, rapidly rotating neutron
stars (Trot ~ 1 ms – 10 s), with very high long-term period
stability (~10-15).
• Can search for correlated effects of topological defects with
pulsar networks and binary pulsar systems.
• Advantage: Pulsars are abundant!
[Stadnik, Flambaum, PRL 113, 151301 (2014)]
Pulsar Timing Searches
Non-Cosmological Sources of Exotic Bosons
Non-Cosmological Sources of Exotic Bosons • Mediators of fifth-forces
Non-Cosmological Sources of Exotic Bosons • Mediators of fifth-forces and inter-conversion with SM
particles
Non-Cosmological Sources of Exotic Bosons • Mediators of fifth-forces and inter-conversion with SM
particles
• Emission from stars, supernovae and white dwarves
Yukawa-type Fifth-Forces Yukawa-type interactions, e.g., between a spin-0 boson φ
and a SM fermion f, produce an attractive Yukawa-type
potential between two fermions:
Yukawa-type Fifth-Forces Yukawa-type interactions, e.g., between a spin-0 boson φ
and a SM fermion f, produce an attractive Yukawa-type
potential between two fermions:
Alternative (equivalent) formulation: Fermions act as a
source of φ and modify the masses of distant fermions:
Yukawa-type Fifth-Forces Yukawa-type interactions, e.g., between a spin-0 boson φ
and a SM fermion f, produce an attractive Yukawa-type
potential between two fermions:
Alternative (equivalent) formulation: Fermions act as a
source of φ and modify the masses of distant fermions:
Hence varying the distance away from a massive body
alters the fundamental constants and particle masses
[Leefer, Gerhardus, Budker, Flambaum, Stadnik, PRL 117, 271601 (2016)]
Variation of Fundamental Constants
Induced by a Massive Body
We can search for these alterations in the fundamental
constants, using clock frequency comparison
measurements, in the presence of a massive body at two
different distances away from the clock pair.
[Leefer, Gerhardus, Budker, Flambaum, Stadnik, PRL 117, 271601 (2016)]
Variation of Fundamental Constants
Induced by a Massive Body
We can search for these alterations in the fundamental
constants, using clock frequency comparison
measurements, in the presence of a massive body at two
different distances away from the clock pair.
e = 0.017
[Leefer, Gerhardus, Budker, Flambaum, Stadnik, PRL 117, 271601 (2016)]
Variation of Fundamental Constants
Induced by a Massive Body
We can search for these alterations in the fundamental
constants, using clock frequency comparison
measurements, in the presence of a massive body at two
different distances away from the clock pair.
e ≈ 0.05
[Leefer, Gerhardus, Budker, Flambaum, Stadnik, PRL 117, 271601 (2016)]
Variation of Fundamental Constants
Induced by a Massive Body
We can search for these alterations in the fundamental
constants, using clock frequency comparison
measurements, in the presence of a massive body at two
different distances away from the clock pair.
Movable 300kg
Pb mass
Spectroscopy constraints: [Leefer, Gerhardus, Budker, Flambaum, PRL 117, 271601 (2016)]
Spectroscopy (DM) constraints: [Van Tilburg, Leefer, Bougas, Budker, PRL 115, 011802 (2015);
Hees, Guena, Abgrall, Bize, Wolf, PRL 117, 061301 (2016)]
Constraints on Linear Yukawa Interaction
of a Scalar Boson with the Photon
[Leefer, Gerhardus, Budker, Flambaum, Stadnik, PRL 117, 271601 (2016)]
Constraints on Linear Yukawa Interaction
of a Scalar Boson with the Electron
[Leefer, Gerhardus, Budker, Flambaum, Stadnik, PRL 117, 271601 (2016)]
Constraints on Linear Yukawa Interaction
of a Scalar Boson with the Nucleons
[Leefer, Gerhardus, Budker, Flambaum, Stadnik, PRL 117, 271601 (2016)]
Constraints on a Combination of Linear
Yukawa Interactions of a Scalar Boson
[Leefer, Gerhardus, Budker, Flambaum, Stadnik, PRL 117, 271601 (2016)]
How to Probe Weaker Interactions?
1. Use different systems in the laboratory.
[Leefer, Gerhardus, Budker, Flambaum, Stadnik, PRL 117, 271601 (2016)]
How to Probe Weaker Interactions?
1. Use different systems in the laboratory.
2. Implement different experimental geometries
[Leefer, Gerhardus, Budker, Flambaum, Stadnik, PRL 117, 271601 (2016)]
How to Probe Weaker Interactions?
1. Use different systems in the laboratory.
2. Implement different experimental geometries (e.g., the size
of the effect may be increased by up to 4 orders of
magnitude by measuring the difference in 1/ 2 in the
laboratory and on a space probe incident towards the Sun).
[Leefer, Gerhardus, Budker, Flambaum, Stadnik, PRL 117, 271601 (2016)]
How to Probe Weaker Interactions?
1. Use different systems in the laboratory.
2. Implement different experimental geometries (e.g., the size
of the effect may be increased by up to 4 orders of
magnitude by measuring the difference in 1/ 2 in the
laboratory and on a space probe incident towards the Sun).
Conclusions • New classes of dark matter effects that are linear in the
underlying interaction constant (traditionally-sought
effects of dark matter are either quadratic or quartic)
Conclusions • New classes of dark matter effects that are linear in the
underlying interaction constant (traditionally-sought
effects of dark matter are either quadratic or quartic)
• 15 orders of magnitude improvement on quadratic
interactions of scalar dark matter with the photon,
electron, and light quarks (u,d)
Conclusions • New classes of dark matter effects that are linear in the
underlying interaction constant (traditionally-sought
effects of dark matter are either quadratic or quartic)
• 15 orders of magnitude improvement on quadratic
interactions of scalar dark matter with the photon,
electron, and light quarks (u,d)
• Improved limits on linear interaction of scalar dark
matter with the Higgs boson
Conclusions • New classes of dark matter effects that are linear in the
underlying interaction constant (traditionally-sought
effects of dark matter are either quadratic or quartic)
• 15 orders of magnitude improvement on quadratic
interactions of scalar dark matter with the photon,
electron, and light quarks (u,d)
• Improved limits on linear interaction of scalar dark
matter with the Higgs boson
• First limits on linear and quadratic interactions of scalar
dark matter with the W and Z bosons
Conclusions • New classes of dark matter effects that are linear in the
underlying interaction constant (traditionally-sought
effects of dark matter are either quadratic or quartic)
• 15 orders of magnitude improvement on quadratic
interactions of scalar dark matter with the photon,
electron, and light quarks (u,d)
• Improved limits on linear interaction of scalar dark
matter with the Higgs boson
• First limits on linear and quadratic interactions of scalar
dark matter with the W and Z bosons
• Enormous potential for new low-energy atomic and
astrophysical experiments to search for dark matter and
exotic bosons with unprecedented sensitivity
Conclusions • New classes of dark matter effects that are linear in the
underlying interaction constant (traditionally-sought
effects of dark matter are either quadratic or quartic)
• 15 orders of magnitude improvement on quadratic
interactions of scalar dark matter with the photon,
electron, and light quarks (u,d)
• Improved limits on linear interaction of scalar dark
matter with the Higgs boson
• First limits on linear and quadratic interactions of scalar
dark matter with the W and Z bosons
• Enormous potential for new low-energy atomic and
astrophysical experiments to search for dark matter and
exotic bosons with unprecedented sensitivity
• New results to be published soon!
Low-mass Spin-0 Dark Matter Non-thermal production of coherently oscillating classical
field, φ(t) = φ0 cos(mφt)
†, in the early Universe, e.g., via the misalignment mechanism. [10-22 eV ≤ mφ ≤ 0.1 eV]
Sufficiently low-mass and feebly-interacting bosons are practically stable (mφ ≤ 24 eV for the QCD axion), and survive to the present day to form galactic DM haloes (where they may be detected).
† Natural units adopted henceforth: ℏ = c = 1
Low-mass Spin-0 Dark Matter The mass range 10-22 eV ≤ mφ ≤ 0.1 eV is inaccessible
to traditional “scattering-off-nuclei” and collider searches, but large regions are accessible to low-
energy atomic experiments that search for oscillating
signals produced by φ(t) = φ0 cos(mφt)
[10-8 Hz* ≤ f ≤ 1013 Hz].
In particular, ultra-low-mass spin-0 DM with mass
mφ ~ 10-22 eV has been proposed to resolve several
long-standing “small-scale crises” of the cold DM model (cusp-core problem, missing satellite problem,
etc.), due to its effects on structure formation†.
* f ~ 10-8 Hz (mφ ~ 10-22 eV) corresponds to T ~ 1 year.
† On sub-wavelength length scales, the gravitational collapse of DM is prevented
by quantum pressure.
Coherence of Galactic DM Gravitational interactions between DM and ordinary
matter during galactic structure formation result in
the virialisation of the DM particles (vvir ~ 10-3 c),
which gives the galactic DM field the finite
coherence time and finite coherence length:
Dark Matter-Induced Oscillating Variation
of the Fundamental Constants Also possible to have linear-in-φ interactions with the SM
sector, which may be generated, e.g., through the super-
renormalisable interaction of φ with the Higgs boson*
[Piazza, Pospelov, PRD 82, 043533 (2010)]:
* Produces logarithmically-divergent corrections to (mφ)2, i.e., technically natural for
A < mφ. Minimum of potential is stable (without adding extra φ4 terms) for (A/mφ)2 < 2λ.
Constraints on Linear Interaction of
Scalar Dark Matter with the Higgs Boson Dy and Rb/Cs constraints:
[Stadnik, Flambaum, PRA 94, 022111 (2016)]
Gravitational test constraints (fifth-force searches):
Exchange of a pair of virtual spin-0 bosons produces
an attractive ~1/r 3 potential* between two SM particles.
[Olive, Pospelov, PRD 77, 043524 (2008)]
Generic Constraints on Quadratic
Scalar Interactions
* Similar to the 1-loop quantum correction to Newton’s Law of Gravitation, see, e.g., [Kirilin, Khriplovich, JETP 95, 981 (2002)] and [Bjerrum-Bohr, Donoghue, Holstein,
PRD 67, 084033 (2003)], and to theories with two large extra dimensions.
Astrophysical constraints (stellar energy loss bounds):
Pair annihilation of photons and bremsstrahlung-like
emission processes can produce pairs of φ-quanta,
increasing stellar energy loss rate.
[Olive, Pospelov, PRD 77, 043524 (2008)]
Generic Constraints on Quadratic
Scalar Interactions
Astrophysical Constraints on ‘Slow’ Drifts in Fundamental Constants Induced by Scalar Dark Matter (CMB)
• Weaker astrophysical constraints come from CMB
measurements (lower ρDM).
• Variations in α and me at the time of electron-proton
recombination affect the ionisation fraction and
Thomson scattering cross section, σThomson = 8πα2/3me2,
changing the mean-free-path length of photons at
recombination and leaving distinct signatures in the
CMB angular power spectrum.
[Stadnik, Flambaum, PRL 115, 201301 (2015)]
Laboratory Searches for Oscillating Variations in
Fundamental Constants Induced by Scalar Dark Matter
System Λˊγ Λˊe ΛˊN Λˊq
Atomic (electronic) + - - -
Atomic (hyperfine) + + + +
Highly charged ionic + - - -
Molecular (rotational/hyperfine) + + + +
Molecular (fine-structure/vibrational) + + + +
Molecular (Ω-doubling/hyperfine) + + + +
Nuclear (e.g., 229Th) + - + +
Laser interferometer + + + +
Calculations performed by Flambaum group and co-workers (>100 systems!)
Take a simple scalar field and give it a self-potential,
e.g., V(φ) = (φ2-v2)2 . If φ = -v at x = -∞ and φ = +v at
x = +∞, then a stable domain wall will form in between,
e.g., φ(x) = v tanh(xmφ) with mφ = 1/2 v .
The characteristic “span” of this object is d ~ 1/mφ, and
it is carrying energy per area ~ v2/d ~ v2mφ . Networks of
such topological defects can give contributions to dark
matter/dark energy and act as seeds for structure
formation.
0D object – a Monopole
1D object – a String
2D object – a Domain wall
Topological Defect Dark Matter
Topological defects may have large amplitude, large
transverse size (possibly macroscopic) and large
distances (possibly astronomical) between them.
=> Signatures of topological defects are very different
from other forms of dark matter!
Topological defects produce transient-in-time effects.
Topological Defect Dark Matter
Detection of topological defects via transient-in-time
effects requires searching for correlated signals using
a terrestrial or space-based network of detectors.
Searching for Topological Defects
Proposals include:
Magnetometers [Pospelov et
al., PRL 110, 021803 (2013)]
Pulsar Timing [Stadnik,
Flambaum, PRL 113, 151301 (2014)]
Atomic Clocks [Derevianko,
Pospelov, Nature Physics 10, 933
(2014)]
Laser Interferometers [Stadnik, Flambaum, PRL 114,
161301 (2015); PRA 93, 063630
(2016)]
Adiabatic passage of a topological defect though a
pulsar produces a smooth modulation in the pulsar
rotational frequency profile
[Stadnik, Flambaum, PRL 113, 151301 (2014)]
Pulsar Timing Searches
Non-adiabatic passage of a topological defect through a
pulsar may trigger a pulsar ‘glitch’ event (which have
already been observed, but their underlying cause is still
disputed); e.g., via unpinning of vortices in neutron superfluid
core (vortices initially pinned to neutron crust).
[Stadnik, Flambaum, PRL 113, 151301 (2014)]
Pulsar Timing Searches
Glitch Theory • Model pulsar as 2-component system: neutron
superfluid core, surrounded by neutron crust
• 2 components can rotate independently of one
another
• Rotation of neutron superfluid core quantified by
area density of quantised vortices (which carry
angular momentum)
• Strong vortex ‘pinning’ to neutron crust
• Can vortices be unpinned by topological defect?
• Vortices avalanche = pulsar glitch
Yukawa-type Fifth-Forces Yukawa-type interactions, e.g., between a spin-0 boson φ
and a SM fermion f, produce an attractive Yukawa-type
potential between two fermions:
Yukawa-type fifth-forces are traditionally sought for with
measurements of vector quantities, usually the difference
in acceleration of two test bodies in the presence of a
massive body (Earth or Sun):
– Torsion pendulum experiments
– Lunar laser ranging
– Atom interferometry
Variation of Fundamental Constants
Induced by a Massive Body
Consider the Yukawa-type interactions again:
The equations of motion for φ read:
SM fields source φ:
[Leefer, Gerhardus, Budker, Flambaum, Stadnik, PRL 117, 271601 (2016)]
Variation of Fundamental Constants
Induced by a Massive Body
Varying the distance away from a massive body hence alters
the fundamental constants, in the presence of Yukawa-type
interactions:
We can search for such alterations in the fundamental
constants, using clock frequency comparison
measurements ( 1/ 2 => scalar quantities), in the presence
of a massive body at two different distances away from the
clock pair:
– Sun (elliptical orbit, e = 0.0167)
– Moon (e ≈ 0.05, with seasonal variation and effect of finite Earth size)
– Massive objects in the laboratory (e.g., moveable 300kg Pb mass)
Yevgeny Stadnik, Victor Flambaum
New Low-Energy Probes for Low-Mass
Dark Matter and Exotic Bosons
Helmholtz Institute Mainz, Germany
University of New South Wales, Sydney, Australia
ALPS Collaboration Meeting, Johannes Gutenberg University Mainz, March 2017
PRL 113, 081601 (2014); PRL 113, 151301 (2014);
PRL 114, 161301 (2015); PRL 115, 201301 (2015);
PRL 117, 271601 (2016);
PRD 89, 043522 (2014); PRD 90, 096005 (2014);
EPJC 75, 110 (2015); PRA 93, 063630 (2016);
PRD 93, 115037 (2016); PRA 94, 022111 (2016).
In collaboration with: Dmitry Budker*; Nicholas Ayres‖,
Phillip Harris‖, Klaus Kirch†, Michal Rawlik‡ (nEDM collaboration)
* Helmholtz Institute Mainz, Germany ‖ University of Sussex, United Kingdom
† Paul Scherrer Institute, Switzerland ‡ ETH Zurich, Switzerland
Low-mass Spin-0 Dark Matter
Dark Matter
Pseudoscalars
(Axions, ALPs):
Odd-parity
→ Oscillating spin-
dependent effects
• Atomic magnetometry
• Ultracold neutrons
• Solid-state magnetometry
QCD axion resolves
strong CP problem
“Axion Wind” Spin-Precession Effect
Motion of Earth through galactic axion
dark matter gives rise to the interaction
of fermion spins with a time-dependent
pseudo-magnetic field Beff(t), producing
spin-precession effects.
[Flambaum, talk at Patras Workshop, 2013], [Graham, Rajendran, PRD 88, 035023 (2013)],
[Stadnik, Flambaum, PRD 89, 043522 (2014)]
Axion-Induced Oscillating Spin-Gravity Coupling
Distortion of axion field by gravitational
field of Sun or Earth induces oscillating
spin-gravity couplings.
[Stadnik, Flambaum, PRD 89, 043522 (2014)]
Axion-Induced Oscillating Spin-Gravity Coupling
Distortion of axion field by gravitational
field of Sun or Earth induces oscillating
spin-gravity couplings.
[Stadnik, Flambaum, PRD 89, 043522 (2014)]
Spin-axion momentum and axion-induced oscillating
spin-gravity couplings to nucleons may have isotopic
dependence (Cp ≠ Cn) – calculations of proton and
neutron spin contents for nuclei of experimental
interest have been performed, see, e.g., [Stadnik, Flambaum, EPJC 75, 110 (2015)].
Oscillating Electric Dipole Moments EDM = parity (P) and time-reversal-invariance (T)
violating electric moment
Axion-Induced Oscillating Neutron EDM
An oscillating axion field induces an oscillating neutron
electric dipole moment via its coupling to gluons.
[Crewther, Di Vecchia, Veneziano, Witten, PLB 88, 123 (1979)],
[Pospelov, Ritz, PRL 83, 2526 (1999)], [Graham, Rajendran, PRD 84, 055013 (2011)]
Axion-Induced Oscillating Neutron EDM
An oscillating axion field induces an oscillating neutron
electric dipole moment via its coupling to gluons.*
[Crewther, Di Vecchia, Veneziano, Witten, PLB 88, 123 (1979)],
[Pospelov, Ritz, PRL 83, 2526 (1999)], [Graham, Rajendran, PRD 84, 055013 (2011)]
* dn receives main contribution from the chirally enhanced process above, rather than
from the process with the external photon line attached to the internal proton line
(where there is no chiral-log enhancement factor).
Schiff’s Screening Theorem [Schiff, Phys. Rev. 132, 2194 (1963)]
Schiff’s Theorem: “For a neutral, non-relativistic system consisting
of pointlike charged particles, which possess permanent EDMs and
interact with each other only electrostatically, there is complete
shielding of the constituent EDMs when the system is exposed to an
external electric field.”
Schiff’s Screening Theorem [Schiff, Phys. Rev. 132, 2194 (1963)]
Schiff’s Theorem: “For a neutral, non-relativistic system consisting
of pointlike charged particles, which possess permanent EDMs and
interact with each other only electrostatically, there is complete
shielding of the constituent EDMs when the system is exposed to an
external electric field.”
Classical explanation (for nuclear EDM): A neutral atom does not
accelerate in an external electric field. Atomic electrons fully screen
the external electric field at the centre of the atom.
Schiff’s Screening Theorem [Schiff, Phys. Rev. 132, 2194 (1963)]
Schiff’s Theorem: “For a neutral, non-relativistic system consisting
of pointlike charged particles, which possess permanent EDMs and
interact with each other only electrostatically, there is complete
shielding of the constituent EDMs when the system is exposed to an
external electric field.”
Classical explanation (for nuclear EDM): A neutral atom does not
accelerate in an external electric field. Atomic electrons fully screen
the external electric field at the centre of the atom.
Schiff’s Screening Theorem [Schiff, Phys. Rev. 132, 2194 (1963)]
Schiff’s Theorem: “For a neutral, non-relativistic system consisting
of pointlike charged particles, which possess permanent EDMs and
interact with each other only electrostatically, there is complete
shielding of the constituent EDMs when the system is exposed to an
external electric field.”
Lifting of Schiff’s Theorem in physical atomic systems (for nuclear EDM): Incomplete screening of external electric field due to
finite nuclear size, parametrised by nuclear Schiff moment.
Axion-Induced Oscillating Atomic and Molecular EDMs
Oscillating atomic and molecular EDMs are induced through
oscillating Schiff (J ≥ 0) moments of nuclei
[O. Sushkov, Flambaum, Khriplovich, JETP 60, 873 (1984)],
[Stadnik, Flambaum, PRD 89, 043522 (2014)]
Axion-Induced Oscillating Atomic and Molecular EDMs
Oscillating atomic and molecular EDMs are induced through
oscillating Schiff (J ≥ 0) and oscillating magnetic quadrupole (J ≥ 1/2, no Schiff screening) moments of nuclei
[O. Sushkov, Flambaum, Khriplovich, JETP 60, 873 (1984)],
[Stadnik, Flambaum, PRD 89, 043522 (2014)]
Axion-Induced Oscillating Atomic and Molecular EDMs
Oscillating atomic and molecular EDMs are induced through
oscillating Schiff (J ≥ 0) and oscillating magnetic quadrupole
(J ≥ 1/2, no Schiff screening) moments of nuclei, which arise from
(1) intrinsic oscillating nucleon EDMs
[O. Sushkov, Flambaum, Khriplovich, JETP 60, 873 (1984)],
[Stadnik, Flambaum, PRD 89, 043522 (2014)]
(1)
Axion-Induced Oscillating Atomic and Molecular EDMs
Oscillating atomic and molecular EDMs are induced through
oscillating Schiff (J ≥ 0) and oscillating magnetic quadrupole (J ≥ 1/2, no Schiff screening) moments of nuclei, which arise from
(1) intrinsic oscillating nucleon EDMs and (2) oscillating P,T-violating
intranuclear forces * (larger by ~1–3 orders of magnitude).
[O. Sushkov, Flambaum, Khriplovich, JETP 60, 873 (1984)],
[Stadnik, Flambaum, PRD 89, 043522 (2014)]
(1) (2)
Axion-Induced Oscillating Atomic and Molecular EDMs [O. Sushkov, Flambaum, Khriplovich, JETP 60, 873 (1984)],
[Stadnik, Flambaum, PRD 89, 043522 (2014)]
(1) (2)
1-loop-level process Tree-level process
Axion-Induced Oscillating Atomic and Molecular EDMs [O. Sushkov, Flambaum, Khriplovich, JETP 60, 873 (1984)],
[Stadnik, Flambaum, PRD 89, 043522 (2014)]
(1) (2)
Heavy spherical nuclei:
Factors of nuclear origin
1-loop-level process Tree-level process
(Lack of) loop
suppression factor
Axion-Induced Oscillating Atomic and Molecular EDMs [O. Sushkov, Flambaum, Khriplovich, JETP 60, 873 (1984)],
[Stadnik, Flambaum, PRD 89, 043522 (2014)]
(1) (2)
Heavy spherical nuclei:
Deformed nuclei: Additional enhancement compared with spherical
nuclei, due to close-level and collective enhancement mechanisms.
Factors of nuclear origin
1-loop-level process Tree-level process
(Lack of) loop
suppression factor
Axion-Induced Oscillating EDMs of
Paramagnetic Atoms and Molecules [Stadnik, Flambaum, PRD 89, 043522 (2014)], [Roberts, Stadnik, Dzuba, Flambaum,
Leefer, Budker, PRL 113, 081601 (2014) + PRD 90, 096005 (2014)]
In paramagnetic atoms and molecules, oscillating EDMs are
also induced through mixing of opposite-parity
atomic/molecular states via the interaction of the oscillating
axion field with atomic/molecular electrons.
Axion-Induced Oscillating EDMs of
Paramagnetic Atoms and Molecules [Stadnik, Flambaum, PRD 89, 043522 (2014)], [Roberts, Stadnik, Dzuba, Flambaum,
Leefer, Budker, PRL 113, 081601 (2014) + PRD 90, 096005 (2014)]
In paramagnetic atoms and molecules, oscillating EDMs are
also induced through mixing of opposite-parity
atomic/molecular states via the interaction of the oscillating
axion field with atomic/molecular electrons.
Axion-Induced Oscillating EDMs of
Paramagnetic Atoms and Molecules [Stadnik, Flambaum, PRD 89, 043522 (2014)], [Roberts, Stadnik, Dzuba, Flambaum,
Leefer, Budker, PRL 113, 081601 (2014) + PRD 90, 096005 (2014)]
In paramagnetic atoms and molecules, oscillating EDMs are
also induced through mixing of opposite-parity
atomic/molecular states via the interaction of the oscillating
axion field with atomic/molecular electrons.
• Ongoing search for “axion wind” spin-precession effect and
axion-induced oscillating neutron EDM by the nEDM
collaboration at PSI and Sussex
Search for Axion Dark Matter with
Ultracold Neutrons Ongoing work with the nEDM collaboration (Ayres, Harris, Kirch, Rawlik et al.)
10-22 eV ≤ ma ≤ 0.1 eV => 10-8 Hz* ≤ f ≤ 1013 Hz (f ~ 10-8 Hz corresponds to T ~ 1 year)
• Ongoing search for “axion wind” spin-precession effect and
axion-induced oscillating neutron EDM by the nEDM
collaboration at PSI and Sussex
• Use a dual neutron/199Hg co-magnetometer to measure the
ratio of the neutron and 199Hg Larmor precession frequencies
in an applied B-field (and E-field for oscillating dn):
Search for Axion Dark Matter with
Ultracold Neutrons Ongoing work with the nEDM collaboration (Ayres, Harris, Kirch, Rawlik et al.)
10-22 eV ≤ ma ≤ 0.1 eV => 10-8 Hz* ≤ f ≤ 1013 Hz (f ~ 10-8 Hz corresponds to T ~ 1 year)
• Ongoing search for “axion wind” spin-precession effect and
axion-induced oscillating neutron EDM by the nEDM
collaboration at PSI and Sussex
• Use a dual neutron/199Hg co-magnetometer to measure the
ratio of the neutron and 199Hg Larmor precession frequencies
in an applied B-field (and E-field for oscillating dn):
• Equivalent magnetic-field sensitivity at the ~10-14 Tesla level
(magnetic fields generated by human brain during cognitive
processes are typically at the ~10-13 Tesla level).
Search for Axion Dark Matter with
Ultracold Neutrons Ongoing work with the nEDM collaboration (Ayres, Harris, Kirch, Rawlik et al.)
10-22 eV ≤ ma ≤ 0.1 eV => 10-8 Hz* ≤ f ≤ 1013 Hz (f ~ 10-8 Hz corresponds to T ~ 1 year)
Expected Sensitivity (Interaction of
Axion Dark Matter with Nucleons) Ongoing work with the nEDM collaboration (Ayres, Harris, Kirch, Rawlik et al.)
Expected Sensitivity (Interaction of
Axion Dark Matter with Gluons) Ongoing work with the nEDM collaboration (Ayres, Harris, Kirch, Rawlik et al.)
Expected Sensitivity (Interaction of
Axion Dark Matter with Gluons) Ongoing work with the nEDM collaboration (Ayres, Harris, Kirch, Rawlik et al.)
Core-polarisation Corrections to ab initio
Nuclear Shell Model Calculations [Stadnik, Flambaum, EPJC 75, 110 (2015)]
Minimal model correction scheme:
Axion-Induced Oscillating PNC Effects in
Atoms and Molecules [Stadnik, Flambaum, PRD 89, 043522 (2014)], [Roberts, Stadnik, Dzuba, Flambaum,
Leefer, Budker, PRL 113, 081601 (2014) + PRD 90, 096005 (2014)]
Interaction of the oscillating axion field with atomic/molecular
electrons mixes opposite-parity states, producing oscillating
PNC effects in atoms and molecules.
Axion-induced oscillating atomic PNC effects are determined
entirely by relativistic corrections (in the non-relativistic
approximation, KPNC = 0)*.
* Compare with the Standard Model static atomic PNC effects in atoms, which are
dominated by Z0-boson exchange between atomic electrons and nucleons in the
nucleus, where the effects arise already in the non-relativistic approximation, see,
e.g., [Ginges, Flambaum, Phys. Rept. 397, 63 (2004)] for an overview.
Axion-Induced Oscillating Nuclear
Anapole Moments [Stadnik, Flambaum, PRD 89, 043522 (2014)], [Roberts, Stadnik, Dzuba, Flambaum,
Leefer, Budker, PRL 113, 081601 (2014) + PRD 90, 096005 (2014)]
Interaction of the oscillating axion field with nucleons in nuclei
induces oscillating nuclear anapole moments.
Expected Sensitivity (Interaction of
Axion Dark Matter with Electrons)
WIMP-Nucleon Scattering • Search for annual modulation in σ N (velocity dependent)
Figure: https://www.hep.ucl.ac.uk/darkMatter/pictures/wind.jpg
WIMP-Nucleon Scattering • Search for annual modulation in σ N (velocity dependent)
WIMP-Electron Ionising Scattering • Search for annual modulation in σ e (velocity dependent)
WIMP-Electron Ionising Scattering • Search for annual modulation in σ e (velocity dependent)
• Previous analyses treated atomic electrons non-
relativistically
WIMP-Electron Ionising Scattering • Search for annual modulation in σ e (velocity dependent)
• Previous analyses treated atomic electrons non-
relativistically
• Non-relativistic treatment of atomic electrons
inadequate for m > 1 GeV!
WIMP-Electron Ionising Scattering • Search for annual modulation in σ e (velocity dependent)
• Previous analyses treated atomic electrons non-
relativistically
• Non-relativistic treatment of atomic electrons
inadequate for m > 1 GeV!
• Need relativistic atomic calculations for m > 1 GeV!
Why are electron relativistic effects
so important? [Roberts, Flambaum, Gribakin, PRL 116, 023201 (2016)],
[Roberts, Dzuba, Flambaum, Pospelov, Stadnik, PRD 93, 115037 (2016)]
Why are electron relativistic effects
so important?
• Consider m ~ 10 GeV, <v > ~ 10-3
[Roberts, Flambaum, Gribakin, PRL 116, 023201 (2016)],
[Roberts, Dzuba, Flambaum, Pospelov, Stadnik, PRD 93, 115037 (2016)]
Why are electron relativistic effects
so important?
• Consider m ~ 10 GeV, <v > ~ 10-3
• <q> ~ <p > ~ 10 MeV >> me
[Roberts, Flambaum, Gribakin, PRL 116, 023201 (2016)],
[Roberts, Dzuba, Flambaum, Pospelov, Stadnik, PRD 93, 115037 (2016)]
Why are electron relativistic effects
so important?
• Consider m ~ 10 GeV, <v > ~ 10-3
• <q> ~ <p > ~ 10 MeV >> me
=> Relativistic process on atomic scale!
[Roberts, Flambaum, Gribakin, PRL 116, 023201 (2016)],
[Roberts, Dzuba, Flambaum, Pospelov, Stadnik, PRD 93, 115037 (2016)]
Why are electron relativistic effects
so important?
• Consider m ~ 10 GeV, <v > ~ 10-3
• <q> ~ <p > ~ 10 MeV >> me
=> Relativistic process on atomic scale!
• Large q ~ 1000 a.u. corresponds to small r ~ 1/q << aB/Z
[Roberts, Flambaum, Gribakin, PRL 116, 023201 (2016)],
[Roberts, Dzuba, Flambaum, Pospelov, Stadnik, PRD 93, 115037 (2016)]
Why are electron relativistic effects
so important?
• Consider m ~ 10 GeV, <v > ~ 10-3
• <q> ~ <p > ~ 10 MeV >> me
=> Relativistic process on atomic scale!
• Large q ~ 1000 a.u. corresponds to small r ~ 1/q << aB/Z
• Largest contribution to σ e comes from innermost atomic
orbitals
[Roberts, Flambaum, Gribakin, PRL 116, 023201 (2016)],
[Roberts, Dzuba, Flambaum, Pospelov, Stadnik, PRD 93, 115037 (2016)]
Why are electron relativistic effects
so important?
• Consider m ~ 10 GeV, <v > ~ 10-3
• <q> ~ <p > ~ 10 MeV >> me
=> Relativistic process on atomic scale!
• Large q ~ 1000 a.u. corresponds to small r ~ 1/q << aB/Z
• Largest contribution to σ e comes from innermost atomic
orbitals – for <ΔE> ~ <T > ~ 5 keV:
– Na (1s)
– Ge (2s)
– I (3s/2s)
– Xe (3s/2s)
– Tl (3s)
[Roberts, Flambaum, Gribakin, PRL 116, 023201 (2016)],
[Roberts, Dzuba, Flambaum, Pospelov, Stadnik, PRD 93, 115037 (2016)]
Why are electron relativistic effects
so important?
• Non-relativistic and relativistic contributions to σ e are very
different for large q, for scalar, pseudoscalar, vector and
pseudovector interaction portals:
[Roberts, Flambaum, Gribakin, PRL 116, 023201 (2016)],
[Roberts, Dzuba, Flambaum, Pospelov, Stadnik, PRD 93, 115037 (2016)]
Why are electron relativistic effects
so important?
• Non-relativistic and relativistic contributions to σ e are very
different for large q, for scalar, pseudoscalar, vector and
pseudovector interaction portals:
Non-relativistic [s-wave, ∝ r 0 (1 - Zr/aB) as r → 0)]*:
[Roberts, Flambaum, Gribakin, PRL 116, 023201 (2016)],
[Roberts, Dzuba, Flambaum, Pospelov, Stadnik, PRD 93, 115037 (2016)]
* We present the leading atomic-structure contribution to the cross-sections here
Why are electron relativistic effects
so important?
• Non-relativistic and relativistic contributions to σ e are very
different for large q, for scalar, pseudoscalar, vector and
pseudovector interaction portals:
Non-relativistic [s-wave, ∝ r 0 (1 - Zr/aB) as r → 0)]*:
dσ e ∝ 1/q 8
[Roberts, Flambaum, Gribakin, PRL 116, 023201 (2016)],
[Roberts, Dzuba, Flambaum, Pospelov, Stadnik, PRD 93, 115037 (2016)]
* We present the leading atomic-structure contribution to the cross-sections here
Why are electron relativistic effects
so important?
• Non-relativistic and relativistic contributions to σ e are very
different for large q, for scalar, pseudoscalar, vector and
pseudovector interaction portals:
Non-relativistic [s-wave, ∝ r 0 (1 - Zr/aB) as r → 0)]*:
dσ e ∝ 1/q 8
Relativistic [s1/2, p1/2-wave, ∝ r γ-1 as r → 0, γ2 = 1 - (Zα)2]*:
[Roberts, Flambaum, Gribakin, PRL 116, 023201 (2016)],
[Roberts, Dzuba, Flambaum, Pospelov, Stadnik, PRD 93, 115037 (2016)]
* We present the leading atomic-structure contribution to the cross-sections here
Why are electron relativistic effects
so important?
• Non-relativistic and relativistic contributions to σ e are very
different for large q, for scalar, pseudoscalar, vector and
pseudovector interaction portals:
Non-relativistic [s-wave, ∝ r 0 (1 - Zr/aB) as r → 0)]*:
dσ e ∝ 1/q 8
Relativistic [s1/2, p1/2-wave, ∝ r γ-1 as r → 0, γ2 = 1 - (Zα)2]*:
dσ e ∝ 1/q 6-2(Zα)2
(dσ e ∝ 1/q 5.7 for Xe and I)
[Roberts, Flambaum, Gribakin, PRL 116, 023201 (2016)],
[Roberts, Dzuba, Flambaum, Pospelov, Stadnik, PRD 93, 115037 (2016)]
* We present the leading atomic-structure contribution to the cross-sections here
Why are electron relativistic effects
so important?
• Non-relativistic and relativistic contributions to σ e are very
different for large q, for scalar, pseudoscalar, vector and
pseudovector interaction portals:
Non-relativistic [s-wave, ∝ r 0 (1 - Zr/aB) as r → 0)]*:
dσ e ∝ 1/q 8
Relativistic [s1/2, p1/2-wave, ∝ r γ-1 as r → 0, γ2 = 1 - (Zα)2]*:
dσ e ∝ 1/q 6-2(Zα)2
(dσ e ∝ 1/q 5.7 for Xe and I)
[Roberts, Flambaum, Gribakin, PRL 116, 023201 (2016)],
[Roberts, Dzuba, Flambaum, Pospelov, Stadnik, PRD 93, 115037 (2016)]
* We present the leading atomic-structure contribution to the cross-sections here
Why are electron relativistic effects
so important?
• Non-relativistic and relativistic contributions to σ e are very
different for large q, for scalar, pseudoscalar, vector and
pseudovector interaction portals:
Non-relativistic [s-wave, ∝ r 0 (1 - Zr/aB) as r → 0)]*:
dσ e ∝ 1/q 8
Relativistic [s1/2, p1/2-wave, ∝ r γ-1 as r → 0, γ2 = 1 - (Zα)2]*:
dσ e ∝ 1/q 6-2(Zα)2
(dσ e ∝ 1/q 5.7 for Xe and I)
• Relativistic contribution to σ e dominates by several orders of
magnitude for large q!
[Roberts, Flambaum, Gribakin, PRL 116, 023201 (2016)],
[Roberts, Dzuba, Flambaum, Pospelov, Stadnik, PRD 93, 115037 (2016)]
* We present the leading atomic-structure contribution to the cross-sections here
Why are electron relativistic effects
so important? [Roberts, Flambaum, Gribakin, PRL 116, 023201 (2016)],
[Roberts, Dzuba, Flambaum, Pospelov, Stadnik, PRD 93, 115037 (2016)]
Calculated atomic-structure functions for ionisation of I from 3s atomic orbital as a function of q; ΔE = 4 keV, vector interaction portal
[Roberts, Flambaum, Gribakin, PRL 116, 023201 (2016)],
[Roberts, Dzuba, Flambaum, Pospelov, Stadnik, PRD 93, 115037 (2016)]
Accurate relativistic atomic calculations
• Performed accurate (ab initio Hartree-Fock) relativistic
atomic calculations of σ e for Na, Ge, I, Xe and Tl, and
event rates of various experiments:
– DAMA
– XENON10
– XENON100
[Roberts, Flambaum, Gribakin, PRL 116, 023201 (2016)],
[Roberts, Dzuba, Flambaum, Pospelov, Stadnik, PRD 93, 115037 (2016)]
Accurate relativistic atomic calculations
• Performed accurate (ab initio Hartree-Fock) relativistic
atomic calculations of σ e for Na, Ge, I, Xe and Tl, and
event rates of various experiments:
– DAMA
– XENON10
– XENON100
• 3 parameter problem: m , mV, α
[Roberts, Flambaum, Gribakin, PRL 116, 023201 (2016)],
[Roberts, Dzuba, Flambaum, Pospelov, Stadnik, PRD 93, 115037 (2016)]
Accurate relativistic atomic calculations
• Performed accurate (ab initio Hartree-Fock) relativistic
atomic calculations of σ e for Na, Ge, I, Xe and Tl, and
event rates of various experiments:
– DAMA
– XENON10
– XENON100
• 3 parameter problem: m , mV, α
[Roberts, Flambaum, Gribakin, PRL 116, 023201 (2016)],
[Roberts, Dzuba, Flambaum, Pospelov, Stadnik, PRD 93, 115037 (2016)]
Accurate relativistic atomic calculations
Calculated differential σ e as a function of total energy deposition (ΔE);
m = 10 GeV, mV = 10 MeV, α = 1, vector interaction portal
[Roberts, Flambaum, Gribakin, PRL 116, 023201 (2016)],
[Roberts, Dzuba, Flambaum, Pospelov, Stadnik, PRD 93, 115037 (2016)]
Can the DAMA result be explained by the
ionising scattering of WIMPs on electrons?
[Roberts, Flambaum, Gribakin, PRL 116, 023201 (2016)],
[Roberts, Dzuba, Flambaum, Pospelov, Stadnik, PRD 93, 115037 (2016)]
Can the DAMA result be explained by the
ionising scattering of WIMPs on electrons?
XENON10 (expected/observed ratio)
[Roberts, Flambaum, Gribakin, PRL 116, 023201 (2016)],
[Roberts, Dzuba, Flambaum, Pospelov, Stadnik, PRD 93, 115037 (2016)]
Can the DAMA result be explained by the
ionising scattering of WIMPs on electrons?
XENON10 (expected/observed ratio) XENON100 (expected/observed ratio)
[Roberts, Flambaum, Gribakin, PRL 116, 023201 (2016)],
[Roberts, Dzuba, Flambaum, Pospelov, Stadnik, PRD 93, 115037 (2016)]
Can the DAMA result be explained by the
ionising scattering of WIMPs on electrons?
• Using results of XENON10 and XENON100, we find no
region of parameter space in m and mV that is
consistent with interpretation of DAMA result in terms of
“ionising scattering on electrons” scenario.
XENON10 (expected/observed ratio) XENON100 (expected/observed ratio)