Searching for Scalar Dark Matter Asimina Arvanitaki Perimeter - - PowerPoint PPT Presentation

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

L ⊃ di φ MP l OSM OSM ≡ mee¯ e, mqq¯ q, G2

s, F 2 EM, ...

Constraints on Light Scalars

• Mediates new interactions in matter
• Generates a fifth force in matter
• Generates Equivalence Principle violation

F ∼ (diQi)2 4πM 2

P l

M1M2 r2 e−mφr

Light Scalar Dark Matter

• Produced by the misalignment mechanism

Potential Energy scalar field

Frozen when: Hubble > mφ

Light Scalar Dark Matter

• Produced by the misalignment mechanism

Potential Energy scalar field

Frozen when: Hubble > mφ Oscillates when: Hubble < mφ ρφ scales as a-3 just like Dark Matter Initial conditions set by inflation

Light Scalar Dark Matter Today

• If mφ < 0.1 eV, can still be thought of as a scalar field today

Potential Energy scalar field

mφ 2 φo2 cos2 (mφ t) ~ ρφ Amplitude compared to MPl in the galaxy: Coherent for υvir-2 ~106 periods

Oscillating Fundamental Constants

From the local oscillation of Dark Matter

• Ex. for the electron mass:

δme me ≈ dmeφo MP l cos(mφt) = 6 × 10−13 cos(mφt)10−18 eV mφ dme 1 Need an extremely sensitive probe… dme φ MP lmee¯ e Fractional variation set by square root of DM abundance

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
• Hyperfine Splittings
• Nuclear Splittings

∆Eoptical ∝ α2

EMme ~ eV

ΔE (mp, αs, αEM)~ 1 MeV ~ 10-6 eV DM appears as a signature in atomic (or nuclear) clocks ∆Ehyperfine ∝ ∆Eopticalα2

EM

✓me mp ◆

Atomic Clocks

• Kept tuned to an atomic energy level splitting
• Have shown stability of 1 part in 1018
• Have won several Nobel prizes in the past 20 years

Current definition of a second: the duration of 9192631770 periods of the radiation corresponding to the transition between the two hyperfine levels

• f the ground state of the caesium 133 atom

Compared to 1 part in 1013 expected by DM

How does and Atomic Clock Work?

Keep a laser tuned to a long-lived (> minutes) atomic transition τcycling of order the lifetime δf f ∼ Γatom f 1 √Natoms r τcycling texperiment

How do you take the measurements?

• Observe two clocks every τcycling
• Calculate ratio of frequencies taking into account:
• Take Fourier transform to look for oscillations with period longer

than τcycling

Atomic Clock DM searches are broadband searches δfA fA = (ξA + 2)δαEM αEM + ζA δme me − ζA δmp mp fA = αξA+2

EM

✓me mp ◆ζA

Table of atomic transitions used (or to be used)

δfA fA = (ξA + 2)δαEM αEM + ζA δme me − ζA δmp mp

Table of atomic transitions used (or to be used)

Accidental cancellations in Dysprosium optical transitions are very sensitive to EM coupling variations

δfA fA = (ξA + 2)δαEM αEM + ζA δme me − ζA δmp mp

Table of atomic transitions used (or to be used)

Thorium nuclear transition cancellations increase sensitivity to EM coupling and quark mass coupling variations Not measured yet…

δfA fA = (ξA + 2)δαEM αEM + ζA δme me − ζA δmp mp

What type of comparisons can we do?

• Hyperfine to Optical transitions
• Sensitive to me, mq, and αs (less to αΕΜ)
• Optical to Optical transitions
• Sensitive to αΕΜ
• Nuclear to Optical transitions
• Sensitive to me, αΕΜ, mq, and αs

Hyperfine to Optical Transition Comparison

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2 4 6 8 10 log10@mfêeVD log10 dg log10@ffêHzD

CI EP CD EP QCD axion

• ptical-MW clock
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2 4 6 8 10 log10@mfêeVD log10 dm

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log10@ffêHzD

CI EP CD EP Q C D a x i

• n
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t i c a l

• M

W c l

• c

k

coupling to αs relative to gravity

Current Sensitivity to αs and mq variations

coupling to mq relative to gravity

Experiments run for 106 sec or 3 years

Hyperfine to Optical Transition Comparison

Current Sensitivity to me variations

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2 4 6 8 10 log10@mfêeVD log10 dme log10@ffêHzD

CI EP CD EP MW-optical clock

Reduced sensitivity to variations of the EM coupling

Optical to Optical Comparison

Current sensitivity to αEM variations

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CI EP CD EP QCD axion

• ptical-optical clock

The Dysprosium Clock Comparison

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5F de EP de Dy de natural de

Analysis performed with existing data

Ken Van Tilburg and the Budker group (2015)

sensitivity to αEM variations

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

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• ptical-optical clock

CI EP CD EP nuclear-optical clock QCD axion

Nuclear to Optical Clock Comparison

Future Sensitivity

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MW-optical clock CI EP CD EP nuclear-optical clock QCD axion

coupling to αΕΜ relative to gravity coupling to mq relative to gravity

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
• rB ~ (α me)-1
• The size of solids changes with DM
• L ~ N (α me)-1

For a single atom δrB~ 10-30 m Need macroscopic objects to get a detectable signal δrB rB = − ✓δαEM αEM + δme me ◆ δL L = − ✓δαEM αEM + δme me ◆

The simple harmonic oscillator

• f mass M, resonant frequency ω and equilibrium length L

L = Lo ✓ 1 + δL Lo cos(mφt) ◆

If the equilibrium size changes with time (with D=x-L):

The simple harmonic oscillator

• f mass M, resonant frequency ω and equilibrium length L

L = Lo ✓ 1 + δL Lo cos(mφt) ◆

If the equilibrium size changes with time (with D=x-L): Driving force from change in the equilibrium position

The Simple Harmonic Oscillator

Dark Matter Driving Force: FDM = −Mω2Loh h = − ✓δαEM αEM + δme me ◆ with 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
• Today: AURIGA, NAUTILUS, MiniGrail

Strain sensitivity h~10-17 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
• Can cover frequencies from 1 kHz all the way to 1 GHz
• Need to worry about bandwidth coverage

Improves with higher quality factor object size and (effective) mass

Jn : mode overlap with DM signal —drops like n-2

hmin ∼ s 4T Mω3

nJ2 nQn

The Sun and The Earth as Resonant-Mass Detectors

• Earth’s acoustic mode with frequency (20 min)-1 and Q~7500
• Sun’s acoustic modes with frequency ~1 mHz and Q~1000
• Can potentially use other astrophysical objects

Strain sensitivity h~10-17 Good only for setting bounds

What can be done with current resonant-mass detectors?

• AURIGA: Ten years of data taking available
• Quartz: Experiment by M. Tobar using Q > 1010 piezoelectrics
• Earth: Using a single monopole seismic mode observed over several months
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5F dme 5F de EP dme EP de Dy de natural dme natural de Earth AURIGA Hex.L quartz Hex.L Electron charge or mass coupling relative to Gravity

What can be done in the future?

• Dual Mass detectors
• Xylophone
• Copper-Silicon alloy sphere: variations of few percent in sound

speed between 4 — 100 K

• Use temperature to scan resonant frequency

Need to increase bandwidth

The scanning resonant-mass detector

• Use Fabry-Perot cavity to pick up displacement as small as

10-19 m/(Hz)1/2

• Change operating temperature between 4-100 K at 2 mK

increments

• Pick up ALL modes at once: continuous coverage above 10kHz

FP laser photodiode Cu-Si

What can be done in the future?

• Probe even the theoretically biased regime of natural couplings

and masses

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5F dme 5F de EP dme EP de Dy de natural dme natural de Earth AURIGA Hex.L DUAL Hfut.L Cu-Si sphere Hfut.L quartz Hex.L Electron charge or mass coupling relative to Gravity

δme me < 10−20 ✓10 TeV Λ ◆2 Ex.

What about naturalness?

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5F dme 5F de EP dme EP de Dy de mic.-opt. dme Hex.L

• pt.-opt. de Hex.L

nuc.-opt. de Hfut.L natural dme natural de Earth AURIGA Hex.L DUAL Hfut.L Cu-Si sphere Hfut.L quartz Hex.L

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5F EP mic.-opt. Hex.L nuc.-opt. Hfut.L natural dm

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Electron charge or mass coupling relative to Gravity Quark mass coupling relative to Gravity

Summary

• Several orders of magnitude improvement in searches for moduli

Dark Matter

• Based on existing and well-established techniques
• There are several more possibilities in particular pushing to

higher frequencies

This is only scratching the surface…

The High Energy Frontier

LHC

The Length Scales in the Universe

80% of the energy scale left to explore

1026

Scale in m

10-4

Hubble Planck

LHC Standard Model Neutrinos Dark Energy

10-12 10-18 10-35