Searching for Scalar Dark Matter Asimina Arvanitaki Perimeter Institute with Ken Van Tilburg Junwu Huang (2014) and Savas Dimopoulos (2015)
Theories of Light Scalars • Moduli, Dilaton, Axions… • Couples non-derivatively to the Standard Model φ L ⊃ d i O SM M P l q, G 2 s , F 2 O SM ≡ m e e ¯ e, m q q ¯ EM , ...
Constraints on Light Scalars • Mediates new interactions in matter • Generates a fifth force in matter F ∼ ( d i Q i ) 2 M 1 M 2 e − m φ r 4 π M 2 r 2 P l • Generates Equivalence Principle violation
Light Scalar Dark Matter • Produced by the misalignment mechanism Frozen when: Hubble > m φ Potential Energy scalar field
Light Scalar Dark Matter • Produced by the misalignment mechanism Frozen when: Hubble > m φ Potential Energy Oscillates when: Hubble < m φ ρ φ scales as a -3 just like Dark Matter scalar field Initial conditions set by inflation
Light Scalar Dark Matter Today • If m φ < 0.1 eV, can still be thought of as a scalar field today Potential Energy m φ 2 φ o2 cos 2 (m φ t) ~ ρ φ Coherent for υ vir-2 ~10 6 periods scalar field Amplitude compared to M Pl in the galaxy:
Oscillating Fundamental Constants From the local oscillation of Dark Matter Ex. for the electron mass: φ d m e M P lm e e ¯ e δ m e ≈ d m e φ o cos( m φ t ) m e M P l = 6 × 10 − 13 cos( m φ t )10 − 18 eV d m e 1 m φ Fractional variation set by square root of DM abundance Need an extremely sensitive probe…
Light Scalar Dark Matter Detection • Detecting Dark Matter with Atomic Clocks • Detecting Dark Matter with Resonant-Mass Detectors
Keeping the DM time with Atomic Clocks with Junwu Huang and Ken Van Tilburg (2014)
Oscillating Atomic and Nuclear Energy Splittings • Optical Splittings ∆ E optical ∝ α 2 EM m e ~ eV • Hyperfine Splittings ✓ m e ◆ ∆ E hyperfine ∝ ∆ E optical α 2 ~ 10 -6 eV EM m p • Nuclear Splittings Δ E (m p , α s , α EM )~ 1 MeV DM appears as a signature in atomic (or nuclear) clocks
Atomic Clocks • Kept tuned to an atomic energy level splitting Current definition of a second: the duration of 9192631770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium 133 atom • Have shown stability of 1 part in 10 18 Compared to 1 part in 10 13 expected by DM • Have won several Nobel prizes in the past 20 years
How does and Atomic Clock Work? Keep a laser tuned to a long-lived (> minutes) atomic transition r τ cycling δ f f ∼ Γ atom 1 √ N atoms f t experiment τ cycling of order the lifetime
How do you take the measurements? • Observe two clocks every τ cycling • Calculate ratio of frequencies taking into account: ◆ ζ A ✓ m e δ f A = ( ξ A + 2) δα EM δ m e δ m p f A = α ξ A +2 + ζ A − ζ A EM m p α EM f A m e m p • Take Fourier transform to look for oscillations with period longer than τ cycling Atomic Clock DM searches are broadband searches
Table of atomic transitions used (or to be used) δ f A = ( ξ A + 2) δα EM δ m e δ m p + ζ A − ζ A f A α EM m e m p
Table of atomic transitions used (or to be used) δ f A = ( ξ A + 2) δα EM δ m e δ m p + ζ A − ζ A f A α EM m e m p Accidental cancellations in Dysprosium optical transitions are very sensitive to EM coupling variations
Table of atomic transitions used (or to be used) δ f A = ( ξ A + 2) δα EM δ m e δ m p + ζ A − ζ A f A α EM m e m p Thorium nuclear transition cancellations increase sensitivity to EM coupling and quark mass coupling variations Not measured yet…
What type of comparisons can we do? • Hyperfine to Optical transitions • Sensitive to m e , m q , and α s (less to α ΕΜ ) • Optical to Optical transitions • Sensitive to α ΕΜ • Nuclear to Optical transitions • Sensitive to m e , α ΕΜ , m q , and α s
Hyperfine to Optical Transition Comparison log 10 @ f f ê Hz D Current Sensitivity to α s and m q variations coupling to α s relative to gravity - 8 - 6 - 4 - 2 0 2 4 6 8 10 0 CI EP - 2 - 4 log 10 d g CD EP Experiments run for 10 6 sec or 3 years optical - MW clock - 6 QCD axion - 8 - 10 - 24 - 22 - 20 - 18 - 16 - 14 - 12 - 10 - 8 - 6 - 4 log 10 @ f f ê Hz D coupling to m q relative to gravity log 10 @ m f ê eV D - 8 - 6 - 4 - 2 0 2 4 6 8 10 0 CI EP - 2 - 4 k CD EP c o l c log 10 d m W ` M - 6 - l a c i t p n o o i - 8 x a D C Q - 10 - 12 - 24 - 22 - 20 - 18 - 16 - 14 - 12 - 10 - 8 - 6 - 4 log 10 @ m f ê eV D
Hyperfine to Optical Transition Comparison Current Sensitivity to m e variations log 10 @ f f ê Hz D - 8 - 6 - 4 - 2 0 2 4 6 8 10 0 CI EP CD EP - 2 - 4 MW - optical clock log 10 d m e - 6 - 8 - 10 - 12 - 24 - 22 - 20 - 18 - 16 - 14 - 12 - 10 - 8 - 6 - 4 log 10 @ m f ê eV D Reduced sensitivity to variations of the EM coupling
Optical to Optical Comparison Current sensitivity to α EM variations log 10 @ f f ê Hz D - 8 - 6 - 4 - 2 0 2 4 6 8 10 0 CI EP - 2 CD EP - 4 log 10 d e - 6 optical - optical clock - 8 QCD axion - 10 - 12 - 24 - 22 - 20 - 18 - 16 - 14 - 12 - 10 - 8 - 6 - 4 log 10 @ m f ê eV D
The Dysprosium Clock Comparison Ken Van Tilburg and the Budker group (2015) sensitivity to α EM variations log 10 @ f f ê Hz D - 8 - 6 - 4 - 2 0 2 4 6 8 10 2 5F d e 0 - 2 EP d e log 10 d e - 4 - 6 Dy d e natural d e - 8 - 10 - 12 24 - 22 - 20 - 18 - 16 - 14 - 12 - 10 - 8 - 6 - 4 log 10 @ m f ê eV D Analysis performed with existing data
What are possible future improvements? • Optical clock improvements by four orders of magnitude • Using more than one atom • Using entangled atoms • The thorium clock under development: Nuclear-Optical Clock comparison
Nuclear to Optical Clock Comparison Future Sensitivity log 10 @ f f ê Hz D coupling to α ΕΜ relative to gravity - 8 - 6 - 4 - 2 0 2 4 6 8 10 0 CI EP CD EP - 4 optical - optical clock log 10 d e - 8 nuclear - optical clock - 12 QCD axion - 16 log 10 @ f f ê Hz D coupling to m q relative to gravity - 24 - 22 - 20 - 18 - 16 - 14 - 12 - 10 - 8 - 6 - 4 - 8 - 6 - 4 - 2 0 2 4 6 8 10 0 log 10 @ m f ê eV D CI EP CD EP MW - optical clock - 4 log 10 d m ` - 8 QCD axion nuclear - optical clock - 12 - 16 - 24 - 22 - 20 - 18 - 16 - 14 - 12 - 10 - 8 - 6 - 4 log 10 @ m f ê eV D
Keeping the DM time with Atomic Clocks • Several orders of magnitude improvement possible now compared to 5th force and EP violation searches • Nuclear clocks if ever built will give several orders of magnitude improvement in the reach
The Sound of Dark Matter with Ken Van Tilburg and Savas Dimopoulos (2015)
Oscillating interatomic distances • The Bohr radius changes with DM • r B ~ ( α m e ) -1 ✓ δα EM ◆ δ r B + δ m e = − α EM r B m e • The size of solids changes with DM • L ~ N ( α m e ) -1 ✓ δα EM ◆ δ L + δ m e L = − α EM m e For a single atom δ r B ~ 10 -30 m Need macroscopic objects to get a detectable signal
The simple harmonic oscillator of mass M, resonant frequency ω and equilibrium length L If the equilibrium size changes with time (with D=x-L): ✓ ◆ 1 + δ L L = L o cos( m φ t ) L o
The simple harmonic oscillator of mass M, resonant frequency ω and equilibrium length L If the equilibrium size changes with time (with D=x-L): ✓ ◆ 1 + δ L L = L o cos( m φ t ) L o Driving force from change in the equilibrium position
The Simple Harmonic Oscillator Dark Matter Driving Force: F DM = − M ω 2 L o h with ✓ δα EM ◆ + δ m e h = − α EM m e Just like a scalar gravitational wave of same strain Can use resonant-mass detectors to enhance and measure the acoustic waves produced the signal
Resonant-Mass Detectors • In the 1960’s: The Weber Bar Strain sensitivity h~10 -17 • Today: AURIGA, NAUTILUS, MiniGrail Strain sensitivity h~10 -23
Resonant-Mass Detectors • Resonant frequency set by size and speed of sound in the material • For sizes ~ 1 m resonant frequency of ~1 kHz • Can take advantage of higher acoustic modes • Increases the bandwidth covered by a single device
Resonant-Mass Detectors • Ultimate sensitivity limited by thermal noise s 4 T h min ∼ M ω 3 n J 2 n Q n Improves with higher quality factor object size and (effective) mass J n : mode overlap with DM signal —drops like n -2 • Can cover frequencies from 1 kHz all the way to 1 GHz • Need to worry about bandwidth coverage
The Sun and The Earth as Resonant-Mass Detectors • Earth’s acoustic mode with frequency (20 min) -1 and Q~7500 Strain sensitivity h~10 -17 • Sun’s acoustic modes with frequency ~1 mHz and Q~1000 • Can potentially use other astrophysical objects Good only for setting bounds
What can be done with current resonant-mass detectors? Electron charge or mass coupling relative to Gravity log 10 @ f f ê Hz D - 8 - 6 - 4 - 2 0 2 4 6 8 10 4 5F d m e 2 5F d e 0 quartz log 10 d i H ex. L EP d m e - 2 EP d e - 4 Earth AURIGA H ex. L - 6 Dy d e natural d m e natural d e - 8 - 22 - 20 - 18 - 16 - 14 - 12 - 10 - 8 - 6 - 4 log 10 @ m f ê eV D • AURIGA: Ten years of data taking available • Quartz: Experiment by M. Tobar using Q > 10 10 piezoelectrics • Earth: Using a single monopole seismic mode observed over several months
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