1. V. A. Dzuba, V. V. Flambaum, Y. Stadnik
Parity violation in atoms and molecules: neutron skin, neutron quadrupole, search for new physics and dark matter
V. A. Dzuba, V. V. Flambaum, Y. Stadnik
University of New South Wales, Sydney, Australia
B.A. Brown (Michigan State University)
A. Derevianko (University of Nevada),

2. 4 questions:
Can the measurements of parity-violating effects in atoms be used to study neutron skin?
To what extend neutron skin uncertainty affects the search for new physics beyond SM?
Measurements of the quadrupole moments of the neutron distribution in nuclei using parity violation in atoms and molecules, tensor PV interaction
Search for dark matter using PV effects and EDM
3 types of measurements:
Single-isotope measurement of PV violating transition in atom (e.g. the 6s-7s transition in Cs).
Ratios of PV effects for several isotopes.
Enhanced PV effects in molecules
V.A.Dzuba, V.V. Flambaum, I.B. Khriplovich, Z. Phys. D 1, 243 (1986).
A. Derevianko, and S. G. Porsev, PRA 65, (2002);
B. A. Brown, A. Derevianko, and V. V. Flambaum, PRC 79, (2009);
V. A. Dzuba, numerical analysis (unpublished, 2016).
V.V. Flambaum, arxiv:
Y. Stadnik, V. V. Flambaum PRL and PRD papers in

3. Ab initio methods of atomic calculations: perturbation theory in H-HRelativisticHartree-Fock
Nve
Method
Accuracy
Rel. Hartree-Fock+RPA
~ 10% 1
RHF+MBPT All-orders sums
0.1-1%
2-8
RHF+MBPT+CI
1-10%
2-15
Configuration interaction
10-20%
Nve - number of valence electrons
These methods cover all periodic table of elements

4. The highest experimental and theoretical accuracy has been achieved for cesium
Boulder, 1997
Theory is good for alkali atoms with one valence electron (Rb, Cs, Fr, Sr+, Ba+, Ra+, Ac2+,Th3+,Pa4+,U5+), heavy atoms since effect increases as Z3 . Results for Cs:
Epv
Source
0.908(9)
Dzuba, Flambaum, Sushkov (1984,1987,1989)
0.909(9)
Blundell, Johnson, Sapirstein (1990)
0.905(9)
Kozlov, Porsev, Tupitsin (2001)
0.9078(45)
Dzuba, Flambaum, Ginges (2002)
0.8990(24)*
Porsev, Derevianko, Beloy (2009)
0.9079(40)#
Dzuba, Berengut, Flambaum, Roberts (2012)
* Uncertainty was underestimated since important contributions were missed
# Contributions missed in (*) were added.

5. Alkali atoms and similar ions are the best for accurate calculations because of their simple electron structure
(one electron above closed shells). We performed calculations for
Rb, Cs, Fr, Ba+, Ra+, Ac2+,Th3+,Pa4+,U5+.
For accurate theoretical results one needs to include
Many-body effects,
Breit interaction,
QED effects in strong Coulomb field.
Main challenge comes from many-body effects:
Electron core polarization (change of core and its potential by photon electric field and nuclear weak field). Can be treated within Time-Dependent Relativistic Hartree-Fock in external fields (nickname RPA with exchange).
Correlations (beyond mean field wave function). All-orders summation of dominating diagrams

6. Core polarizarion: PV amplitude in RPA
Double CP term
(-0.26% in Cs) missed
in many other calculations.
are corrections due to external field
Weak interaction (W):
Electric field of external photon (D):
Both:

7. All-order correlation potential S.
2nd order S:
=>
Four chains of higher-order diagrams are included:
1. Screening of Coulomb interaction
(similar to screening of external electric
field, i.e. Schiff theorem: E(0)=0 ).
2. Hole-particle interaction
(responsible for discrete spectrum
of Noble gases).
3. Ladder diagrams
(all-order residual Coulomb interaction
of external electron with the core).
4. Iterations of S

8. We do not rely on any single-electron basis!
Im w
Integration
path
G – Green function, P – polarization operator
Core poles
Re w
Valence poles
Without exchange:
With exchange:
Polarization operator:
We do not rely on any single-electron basis!
(We use B-splines to calculate exchange diagrams for S only)

9. Dominating correlation corrections to the PV amplitude
Other correlations corrections:
Higher-order in S terms;
Structure radiation;
Weak correlation potential;
Renormalization.

10. EPV = -0.897(10.5%)10-11 ieaB(-QW/N)
Dzuba,Flambaum,Ginges 2002
EPV = (10.5%)10-11 ieaB(-QW/N)
 QW  QWSM  1.1 
Porsev, Derevianko QW  QWSM  0 .
Dzuba et al 2012 found correction to this result which brings Porsev, Derevianko result into agreement with our number.
QW  QWSM ~ 1 
Tightly constrains possible new physics.
EPV includes -0.8% shift due to strong-field
QED self-energy / vertex corrections to weak
matrix elements Wsp
[Kuchiev,Flambaum; Milstein,Sushkov,Terekhov]
A complete calculation of QED corrections to PV amplitude includes also
QED corrections to energy levels and E1 amplitudes
[Flambaum,Ginges; Shabaev,Pachuki,Tupitsyn,Yerokhin]

11. High-precision atomic calculations
APV
Atomic EDM
HPV is due to electron-nucleon P-odd interactions and nuclear anapole,
HPT is due to nucleon-nucleon, electron-nucleon PT-odd interactions,
electron, proton or neutron EDM.
Atomic wave functions need to be good at all distances!
We check the quality of our wave functions by calculating:
- hyperfine structure constants and isotope shift
- energies
- E1 transition amplitudes
and comparing to measured values.
Also, estimates of higher order diagrams.

12. Radiative potential for QED
Fg(r) – magnetic formfactor
Ff(r) – electric formfactor
Fl(r) – low energy electric formfactor
FU(r) – Uehling potential
FWC(r) – Wichmann-Kroll potential
Ff(r) and Ff(r) have free parameters which are chosen to fit QED corrections to the energies (Mohr, et al) and weak matrix elements
(Kuchiev,Flambaum; Milstein,Sushkov,Terekhov; Sapirstein et al)

13. Accuracy ~0.1% for s-levels. Includes many-body corrections

14. Low-energy theorem to calculate QED radiative corrections to electromagnetic amplitudes
Small parameter=E/w
E=energy of valence electron=10 -5 mc2
w-virtual photon frequency =mc2
Results are expressed in terms of self-energy S and
dS/dE (vertex, normalization)
Radiative potential contribution: a3Z2 ln(a2Z2 )
Other contributions: a3 (Zi +1)2 , Zi –ion charge
In neutral atoms (Zi=0) radiative potential contribution is Z2 times larger!
Actual calculation: all orders in aZ including many-body corrections
Total QED correction to EPV= %(weak)+0.43%(E1)-0.34%(dE)=-0.32%

15. Dependence of PV in atoms on nuclear radius R is due to relativistic effects
calculated at
Atom K
-(3/7)(a Z)2
KDRnp/Rp
133Cs
(5)
138Ba
(6)
221Fr
(16)
222Ra
(16)
DRnp/Rp : Brown, Derevianko, Flambaum, PRC 79, (2009);
High accuracy is needed for both and

16. Experimental accuracy for Cs is 0.35%.
Theoretical accuracy for Cs is 0.44%.
Similar theoretical accuracy can be achieved
for Rb, Ba+, Fr, Ra+, Ac+2, Th+3, Pa+4, U+6
(one electron above closed shells).
Atom
KDRnp/Rp
133Cs
(5)
138Ba
(6)
221Fr
(16)
222Ra
(16)
Then Fr and Ra+ the are the best candidates to study neutron skin.
Other atoms considered for PV measurements (I, Xe, Sm, Dy, Yb, Hg, Tl, Pb, Bi, Th) have complicated electron structure resulting in insufficient theoretical accuracy.
More valence electrons Tl 3%, Pb 8%, Bi 11%,…
Discovery of PV 1978 Barkov, Zolotarev, 6 months later confirmed by SLAC and later by Commins group
Triumph of electroweak theory, Nobel Prize 1979
PV effects may be 2 orders of magnitude bigger than in Cs

17. S-D PV transitions (e.g., the 6s-5d3/2 transition in Ba+).
The PV amplitude
is strongly dominated by a single term
~ 80% of the sum.
If experimental data is used for and theoretical for ,
High accuracy can be achieved.
The same is true for Ra+!
The neutron skin contribution is -0.3% for Ba+ and -0.7% for Ra+.

18. PV : Chain of isotopes Dzuba, Flambaum, Khriplovich 1986
Rare-earth atoms:
close opposite parity levels-enhancement
Many stable isotopes
Ratio of PV effects gives ratio of weak charges. Uncertainty in atomic calculations cancels out. Experiments:
Berkeley: Dy and Yb; PV amplitude 100 x Cs!
Ra+ - Groningen, Fr- TRIUMF
Fortson,Pang,Wilets - neutron distribution problem
Test of Standard model or neutron distribution?
Brown, Derevianko,Flambaum Uncertainties in neutron distributions cancel in differences of PV effects in isotopes of the same element. Error reduced 4-10 times.
Measurements of ratios of PV effects in isotopic chain can compete with other tests of Standard model!

19. Ratio of PV effects on different isotopes
KPV cancels out in the ratio EPV (A1)/EPV (A2)
Enhancement of PV due to close levels of opposite parity
(Dzuba, Flambaum, Khriplovich, Z. Phys. D 1, 243 (1986)).
More accurately –dependence on nuclear radii due to the relativistic effects
[Neutron skin contribution] b
2g-2 Cs
-0.182
-0.168 Ba
-0.188
-0.175 Dy
-0.266
-0.247 Yb
-0.302
-0.281 Fr
-0.489
-0.455 Ra
-0.502
-0.467
Numerical test of analytical formula.
The uncertainties due to Rp and Qw are small, e.g.
Change due to b instead of 2g-2 ~ 2 x 10-4.
Calculations of neutron skin contribution for all usable isotopes, A= Brown, Derevianko, Flambaum,2009

20. Taking DRnp from Brown, Derevianko, Flambaum, PRC 79, 035501 (2009)
leads to
Atom
Stable isotopes
Unstable
(t>1 day)
Maximal difference of neutrom skin corrections to EPV Cs
133
0.0012(2) Ba
0.0012(2) -> (2) Sm
0.0024(3) Dy
0.0012(3) -> (3) Yb
0.0017(4) Hg
0.0016(5) Tl
203,205
0.0004(5) -> (5) Pb
0.0008(5) -> (5) Bi
209
0.0010(5) Fr
(t>1m)
0.0028(5) Ra
0.0029(5)
Best candidates:
Sm, Yb, Hg, Fr, Ra.
The ratio APV(A1)/APV(A2) needs to be measured to ~10-3 accuracy.

21. Neutron skin vs new physics
Atomic PV can be used in search for new physics if neutron skin is small or known from independent sources.
Single isotope measurements.
133Cs: DRnp =0.13(4) fm from antiprotonic data,
Trzcinska et al, PRL 87, (2001).
DRnp =0.158(37) fm from nuclear calculations,
Brown, Derevianko, Flambaum , PRC 79, (2009).

22. Theoretical PV amplitude in Cs [10-11 i(-QW/N) a.u.]
Experiment:
Wood et al, Science 275, 1759 (1997).
Theoretical PV amplitude in Cs [10-11 i(-QW/N) a.u.]
Contribution
Value
Many-body
0.9079(40)
Breit
-0.055(1)
QED
(3)
Neutron skin
(5)
Total
0.8977(40)
- Two times smaller than
theoretical uncertainty
Comparing theoretical and experimental data tests SM and
constrains new physics.

23. Using experimental values for EPV/b and b
[b=26.957(51) a.u. Bennet and Wieman, PRL 82, 2484 (1999)]
leads to QW(133Cs)=-72.58(29)exp(32)theor,
while QWSM =-73.23(2).
DQW=QW - QWSM=0.65(43) s
Using DQW =-0.800S-0.007T [Rosner, PRD 65, (2002)]
leads to S=-0.81(54).
Using DQW =0.4(2N+Z)(MW/MZx)2
[Marciano and Rosner, PRL 65, 2963 (1990)]
leads to MZx >710 GeV.

24. Another way of describing new physics
DQnew=Nhn+Zhp
For cesium
78hn+55hp=0.65(43).
This leads to |hn|<0.014; |hp|<0.020.
The single-isotope measurements are more sensitive to hn.

25. Similar or better results can be obtained for Rb, Ba+, Fr, Ra+.
Atom
PV transition
Value [10-12 iea0(-Qw/N)]
Neutron skin
Experiment
85Rb
[Kr]5s – [Kr]6s
1.39
0.07%
TRIUMF(?)
133Cs
[Xe]6s – [Xe]7s
8.97
0.2%
Boulder, 1997 Purdue
138Ba+
[Xe]6s – [Xe]5d3/2
21.7
0.3%
Seattle
221Fr
[Rn]7s – [Rn]8s
159
0.7%
TRIUMF
222Ra+
[Rn]7s – [Rn]6d3/2
429
KVI
Expected theoretical accuracy ~ 0.4% or better.

26. Single isotope measurements are more sensitive to hn.
B. Isotope ratio measurements.
New physics
Single isotope measurements are more sensitive to hn.
Isotope ratio measurements are sensitive to hp:
R0 is the ratio with no new physics.
Sensitivity function
F=0 means no new physics.
Derevianko and Porsev, PRA 65, (2002).

27. The uncertainty dF comes from experiment (dR) and theory (dR0),
The latter is due to the neutron skin:
Atom A1 A2
dFNS x103
hp* Cs
129
137
2.1
0.0020 Ba
130
138
2.3
0.0022 Sm
144
154
4.2
0.0039 Dy
156
164
2.7
0.0025 Yb
168
176
10.2
0.0096 Tl
203
205
7.2
0.0068 Pb
204
208
7.7
0.0072 Fr
209
221
8.8
0.0084 Ra
210
222
8.9
QpW=0.064(12);
Qweak collaboration,
PRL 111, (2013);
=> hp<0.012.
Isotope chain
measurements are
competitive wth the
PVES measurements
* Limits on hp from nuclear skin uncertainty.

28. Single isotope measurements Isotope ratio measurements
Summary
Atomic PV measurements can be used to study neutron skin and to search for new physics.
Single isotope measurements
Neutron skin
New physics
Sensitive to
DRnp hn
Theoretical error
<1%
Experimental error
Best candidates
Fr, Ra+ , Ac+2 ,Th+3
Rb, Cs, Ba+, Fr, Ra+,Th+3
Isotope ratio measurements
dDRnp hp
Small
~10-3
Fr, Ra+, Yb
Rb, Cs, Ba+, Dy

29. Nuclear anapole moment
Source of nuclear spin-dependent PV effects in atoms
Nuclear magnetic multipole violating parity
Arises due to parity violation inside the nucleus
Interacts with atomic electrons via usual magnetic interaction (PV hyperfine interaction): B j
 a
[Flambaum,Khriplovich 1980, Flambaum,Khriplovich,Sushkov 1984]
EPV  Z2 A2/3 measured as difference of PV effects for transitions between hyperfine components
Cs: |6s,F=3> – |7s,F‘=4> and |6s,F’=4> – |7s,F=3>
Probe of weak nuclear forces via atomic experiments!

30. Boulder Cs: g=6(1) in units of Fermi constant Seattle Tl: g=-2(3)
Nuclear anapole moment is produced by PV nuclear forces. Measurements +our calculations give the strength constant g.
Boulder Cs: g=6(1) in units of Fermi constant
Seattle Tl: g=-2(3)
More accurate nuclear calculations Flambaum,Hanhart; Haxton,Liu,Ramsey-Musolf; Auerbach, Brown; Dmitriev, Khriplovich,Telitsin:
problem remains.
Experiments and proposals: Fr (TRIUMF),
103 enhancement in Ra atom due to close opposite parity state; Dy,Yb,…(Berkeley)

31. Enhancement of nuclear anapole effects in molecules
105 enhancement of the anapole contribution in diatomic molecules due to mixing of close rotational levels of opposite parity.
Theorem: only nuclear-spin-dependent (anapole) contribution to PV is enhanced (Labzovsky;Sushkov,Flambaum 1978).
Weak charge can not mix opposite parity rotational levels and L-doublet. Anapole can.
W=1/2 terms: S1/2 , P1/2 . Heavy molecules, effect Z2 A2/3 R(Za)
YbF,BaF, PbF,LuS,LuO,LaS,LaO,HgF,…Cl,Br,I,…BiO,BiS,…
Cancellation between hyperfine and rotational intervals-enhancement.
Interval between the opposite parity levels may be reduced to zero by magnetic field – further enhancement.
Molecular experiments : Yale, Groningen, NWU.
New calculations for many molecules and molecular ions: Borschevsky,Ilias,Beloy,Dzuba,Flambaum,Schwerdtfeger 2012

32. PV to measure quadrupole moments of neutron distribution (NQM)
Sushkov, Flambaum 1978: Nuclear quadrupole moment generates tensor weak interaction WT=WikIiIk which mixes opposite parity electron energy levels up to J1-J2=2. In atoms this contribution may be separated by measurements of PV on different hyperfine components
Cs, Ba, Yb, Dy, Fr, Ra+,…
WT mixes very close levels of opposite parity (omega=+1,-1 doublet) in molecules ThO, TaN, ThF+, HfF+, PbO, WC used to measure electron EDM. Huge enhancement of WT
In the Standard model neutron weak charge -1, proton weak charge So, we measure NQM.
NQM is calculated using deformed oscillator model for all nuclei of experimental interest, PRL 2106,arxiv:

33. V. Flambaum, Y. Stadnik, B. Roberts, V. Dzuba
Dark Matter and violation of symmetries
V. Flambaum, Y. Stadnik, B. Roberts, V. Dzuba
University of New South Wales, Sydney, Australia
Physical Review Letters 116, (2016) Physical Review Letters 115, (2015) Physical Review Letters 114, (2015) Physical Review Letters 113, (2014) Physical Review Letters 113, (2014) Physical Review D 89, (2014) Physical Review D 90, (2014) European Physical Journal C 75, 110 (2015) arXiv: , , Nature Physics 12, 465 (2016)

34. Motivation
Traditional “scattering-off-nuclei” searches for heavy WIMP dark matter particles (χ) have not yet produced a strong positive result.
Observable is quartic in the interaction constant eי, which is extremely small! 34

35. Motivation
We propose to search for other well-motivated forms of dark matter: low-mass spin-0 particles, which form a coherently * oscillating classical † field: φ(t) = φ0 cos(mφt), via effects that are linear in the interaction constant (ΛX = new-physics energy scale).
Consideration of linear effects has already allowed us to improve on existing constraints on some interactions of dark matter by up to 15 orders of magnitude, as well as derive the first constraints on some other interactions of dark matter.
1 parsec = 3.26 light years; R_{dwarf galaxy} ~ 1 kpc.
Energy scales: Hubble scale ~ 10^{-33} eV; Planck scale ~ 10^{28} eV. i.e. ~ 61 orders of magnitude in range.
Need consistency in a/phi!
* Coherently oscillating field => cold, Eφ = mφc2
† nφ(λdB/2π)3 >> 1 35

36. Low-mass Spin-0 Dark Matter
Scalars:
Even-parity
Pseudoscalars
(Axions, ALPs):
Odd-parity
→ ‘Slow’ evolution and oscillating variation of fundamental constants
→ Oscillating spin-dependent effects, EDM,
P,T, Lorentz and Einstein symmetry violation
Switch these parity around, and add details of measurements!
RA: Less talk? Just say there are different types of dark matter (with different properties), which produce different effects.
Atomic clocks
Highly-charged ions
Molecules
Nuclear clocks
Laser interferometers
Atomic magnetometry
Ultracold neutrons
Solid-state magnetometry
Electric dipole moments 36

37. Axion-Induced Oscillating Parity Non-Conservation in Atoms and Molecules
[Stadnik, Flambaum, PRD 89, (2014)], [Roberts, Stadnik, Dzuba, Flambaum, Leefer, Budker, PRL 113, (2014) + PRD 90, (2014)]
Interaction of the oscillating axion field with atomic/molecular electrons mixes opposite-parity states, producing oscillating PNC effects in nuclei, atoms and molecules.
In nuclei- oscillating anapole 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. 37

38. Axion-Induced Oscillating Neutron EDM
[Graham, Rajendran, PRD 84, (2011)]
An oscillating axion field induces an oscillating neutron electric dipole moment via its coupling to gluons.
Make all key effects in bold!
Add d_n estimate; and add in the relevant diagram (soft pion limit??) 38

39. Axion-Induced Oscillating Atomic and Molecular EDMs
[Stadnik, Flambaum, PRD 89, (2014)]
Oscillating atomic and molecular EDMs are induced through oscillating Schiff (J ≥ 1/2) and oscillating magnetic quadrupole (J ≥ 1, no Schiff screening) moments of nuclei, which arise from intrinsic oscillating nucleon EDMs and oscillating P,T-violating intranuclear forces (larger by factor of several – 1000).
Add: by factor of ~ few – 1000!; Add estimates for d_{Hg} and d_{Ra}; put in \bar{g}_{\pi NN} into the right-hand diagram!! 39

40. Axion-Induced Oscillating EDMs of Paramagnetic Atoms and Molecules
[Stadnik, Flambaum, PRD 89, (2014)], [Roberts, Stadnik, Dzuba, Flambaum, Leefer, Budker, PRL 113, (2014) + PRD 90, (2014)]
In paramagnetic atoms and molecules, oscillating EDMs are also induced through mixing of opposite-parity states via the interaction of the oscillating axion field with atomic/molecular electrons. 40

41. Dark Matter-Induced Cosmological Evolution of the Fundamental Constants
[Stadnik, Flambaum, PRL 115, (2015)]
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.
Update references… Explain that electromagnetic fine-structure constant governs the strength of all electromagnetic processes in Nature and interactions.
RA: less talk --- only explain cos()^2 part…
‘Slow’ drifts [Astrophysics (high ρDM): BBN, CMB]
Oscillating variations [Laboratory (high precision)] 41

42. [Stadnik, Flambaum, PRL 115, 201301 (2015)]
Dark Matter-Induced Cosmological Evolution of the Fundamental Constants
[Stadnik, Flambaum, PRL 115, (2015)]
We can consider a wide range of quadratic-in-φ interactions with the SM sector:
Photon:
Fermions:
Bosons W,Z (mediators of weak interactions): 42

43. [Van Tilburg, Leefer, Bougas, Budker, PRL 115, 011802 (2015)]
Laboratory Search for Oscillating Variations in Fundamental Constants using Atomic Dysprosium
[Van Tilburg, Leefer, Bougas, Budker, PRL 115, (2015)]
Circle the states!? 43

44. Constraints on Quadratic Interaction of Scalar Dark Matter with the Photon
BBN, CMB, Dy and Rb/Cs constraints: [Stadnik, Flambaum, PRL 115, (2015) + arXiv: ] orders of magnitude improvement!
Emphasise 15 orders of magnitude improvement for the lightest masses! – Mention also constraints on other interactions (photon, electron, light quarks (u,d), massive vector bosons (W+/-,Z) 44

45. Constraints on Quadratic Interactions of Scalar Dark Matter with Light Quarks
BBN and Rb/Cs constraints: [Stadnik, Flambaum, PRL 115, (2015) + arXiv: ]
Emphasise 15 orders of magnitude improvement for the lightest masses! – Mention also constraints on other interactions (photon, electron, light quarks (u,d), massive vector bosons (W+/-,Z) 45

46. BBN and CMB constraints: [Stadnik, Flambaum, PRL 115, 201301 (2015)]
Constraints on Quadratic Interaction of Scalar Dark Matter with the Electron
BBN and CMB constraints: [Stadnik, Flambaum, PRL 115, (2015)]
Emphasise 15 orders of magnitude improvement for the lightest masses! – Mention also constraints on other interactions (photon, electron, light quarks (u,d), massive vector bosons (W+/-,Z) 46

47. BBN 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, (2015)]
Emphasise 15 orders of magnitude improvement for the lightest masses! – Mention also constraints on other interactions (photon, electron, light quarks (u,d), massive vector bosons (W+/-,Z) 47

48. Constraints on Linear Interaction of Scalar Dark Matter with the Higgs Boson
Dy and Rb/Cs constraints: [Stadnik, Flambaum, PRA2016,arXiv: ]
Emphasise 15 orders of magnitude improvement for the lightest masses! – Mention also constraints on other interactions (photon, electron, light quarks (u,d), massive vector bosons (W+/-,Z) 48

49. Conclusions
New classes of dark matter effects that are linear in the underlying interaction constant (traditionally-sought effects of dark matter scale as second or fourth power)
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 with the Higgs boson.
First limits on linear and quadratic interactions of scalar dark matter with vector bosons (W+,W-,Z0)
Oscillating effects of variation of fundamental constants and violation of the fundamental symmetries: P, T, EDM, Lorentz, Einstein equivalence principle
Enormous potential for low-energy atomic experiments to search for dark matter with unprecedented sensitivity
Update formula to have: obs \propto (1/\Lambda)^n !
A summary slide with all effects and systems (pseudoscalar ~ spin-dep.) versus (scalar ~ VFCs) would be nice --- can also use for the conclusions…
And also mention that for scalars, these are new possibilities for VFCs… (some methods are modification of existing methods, while others are new) 49

50. 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 a finite coherence time and finite coherence length:
RA: Less talk? 50