Manifestations of Dark Matter and Variations of Fundamental - PowerPoint PPT Presentation

Manifestations of Dark Matter and Variations of Fundamental Constants in Atoms and Astrophysical Phenomena Victor Flambaum, Yevgeny Stadnik, Benjamin Roberts, Vladimir Dzuba University of New South Wales, Sydney, Australia Physical Review D 89 , 043522 (2014) Physical Review Letters 113 , 081601 (2014) Physical Review Letters 113 , 151301 (2014) Physical Review D 90 , 096005 (2014) Physical Review Letters 114 , 161301 (2015) arXiv:1503.08540, arXiv:1504.01798 Conference, Location, Month 2015

Motivation Consider a typical “scattering-off-nuclei” search for WIMP dark matter ( χ ) (e.g. CoGeNT, CRESST, DAMA/LIBRA, LUX, Super-CDMS, XENON100, …) Observable is quadratic in αי ( quartic in e י ) which is extremely small!

Motivation We instead propose to search for light bosonic dark matter ( galactic condensates and topological defects ) through observables that are linear in underlying interaction parameters using new high-precision detection methods! Detection methods include the use of terrestrial measurements (atomic clocks, magnetometers, torsion pendula, ultracold neutrons, laser interferometers) and astrophysical observations (pulsar timing, cosmic radiation lensing).

Galactic Condensates of Light Bosons The QCD axion is a good candidate for cold dark matter (along with light pseudoscalar ( ALP ) and scalar particles). Initial θ ~ 1, minimum θ =0. θ (t)=a(t)/f a . An oscillating condensate (on a macroscopic scale) of bosons, a ( t ) = a 0 cos( m a t ), is believed to have been produced during the early Universe. For sufficiently light bosons ( m a < ~1eV), a galactic condensate of bosons remains until the present day and may be detected.

Coherence of Galactic Condensate Galactic condensate is virialised ( v Virial ~ 10 -3 c ).

Zoo of axion effects-linear in interaction strength! • Derivative-type coupling • Produces oscillating effects : – PNC effects – Axion ‘wind’ – EDMs – Energy shifts – Anapole moments [c.f. ] • Axion field modified by Earth’s gravitational field:

“Axion Wind” Effect (Axion and ALPs) As Earth moves through galactic condensate of axions/ALPs ( v ~ 10 -3 c ), spin-precession effects arise from derivative coupling of axion field to axial- vector currents of electrons or nucleons (spatial components of interaction).

“Axion Wind” Effect (Axion and ALPs) Axion-induced spin-precession effects are linear in a 0 / f a !

“Axion Wind” Effect (Axion and ALPs) There are two distinct spin-precession frequencies: Spin-axion momentum couplings can be sought for with a variety of spin-polarised systems: atomic co- magnetometers, torsion pendula and ultracold neutrons .

“Axion Wind” Effect (Axion and ALPs) [Flambaum, Patras Workshop , 2013], [Stadnik, Flambaum, PRD 89 , 043522 (2014)] Distortion of axion/ALP field by gravitational fields of Sun and Earth induces oscillating spin-gravity couplings . Spin-axion momentum and axion-mediated spin- gravity couplings to nucleons may have isotopic dependence ( C p ≠ C n ) – calculations of required proton and neutron spin contents ( 3 He, 21 Ne, 39/41 K, 85/87 Rb, 129 Xe, 133 Cs, 199/201 Hg, …) have been performed in [Stadnik, Flambaum, EPJC 75 , 110 (2015)]

Oscillating P , T -odd Nuclear Electromagnetic Moments (QCD Axion) A galactic condensate consisting of the QCD axion induces oscillating P , T -odd electromagnetic moments in nuclei via two mechanisms: (1) Oscillating nucleon EDMs via axion coupling to gluon fields - dynamical θ (t)=a(t)/f a . [Graham, Rajendran, PRD 84 , 055013 (2011)]

Nuclear EDM: T,P-odd NN interaction gives 40 times larger contribution than nucleon EDM Sushkov, Flambaum, Khriplovich 1984

Screening of external electric field in atoms Dzuba, Flambaum, Sushkov calculation + + + …

Diamagnetic atoms and molecules Source-nuclear Schiff moment SM appears when screening of external electric field by atomic electrons is taken into account. Nuclear T,P-odd moments: • EDM – non-observable due to total screening (Schiff theorem) Nuclear electrostatic potential with screening (Sushkov, Flambaum, Khriplovich calculation following ideas of Schiff and Sandars): ρ ρ ( ) 1 ( ) e r r ∫ ∫ ϕ = + • ∇ 3 3 ( ) ( ) R d r d d r − − | | | | R r Z R r d is nuclear EDM, the term with d is the electron screening term ϕ ( R ) in multipole expansion is reduced to ϕ = π • ∇ δ ( ) 4 ( ) R S R   5 e = − 2 2 where is Schiff moment. S r r r r     10 3 Z This expression is not suitable for relativistic calculations.

• B ∫ 3 L R φ = − ρ = ρ 4 Flambaum,Ginges: ( ) ( ) R R where ( ) R R dR L=S(1 – c Z 2 α 2 ) B Nuclear spin ϕ Electric field induced by T,P-odd nuclear forces which influence proton charge density E R This potential has no singularities and may be used in relativistic calculations. SM electric field polarizes atom and produces EDM. Calculations of nuclear SM: Sushkov,Flambaum,Khriplovich ;Brown et al,Flambaum et al Dmitriev et al,Auerbach et al,Engel et al, Liu et al,Sen’kov et al, Ban et al. Atomic EDM: Sushkov,Flambaum,Khriplovich; Dzuba,Flambaum,Ginges,Kozlov. Best limits from Hg EDM measurement in Seattle – Crucial test of modern theories of CP violation (supersymmetry, etc.)

Nuclear enhancement Auerbach, Flambaum, Spevak 1996 The strongest enhancement is due to octupole deformation (Rn,Ra,Fr,…) Intrinsic Schiff moment: β β 9 ≈ 3 2 3 S eZR intr N π 20 35 β 2 ≈ 0 . 2 - quadrupole deformation β 3 ≈ 0 . 1 - octupole deformation No T,P-odd forces are needed for the Schiff moment and EDM in intri reference frame However, in laboratory frame S=d=0 due to rotation

In the absence of T,P-odd forces: doublet (+) and (-) ( ) 1 Ψ = + − = IMK IM K 0 n and 2 I I n n = • ( ) K I n T,P-odd mixing ( β ) with opposite parity state (-) of doublet: [ ] 1 ∝ β Ψ = + β + − β − ( 1 ) ( 1 ) n I IMK IM K and 2 EDM and Schiff moment ∝ ∝ β , d S n I

Simple estimate (Auerbach, Flambaum, Spevak ): + − | | H ∝ TP S S + − lab body E E − Two factors of enhancement: 1. Large collective moment in the body frame 2. Small energy interval ( E + -E - ), 0.05 instead of 8 MeV eV − ≈ β β η ≈ × η ≈ 2 2 / 3 3 8 3 0 . 05 700 10 fm 500 ( Hg ) S e ZA r e S − 2 3 0 E E + − 225 Ra, 223 Rn, Fr,… -100-1000 times enhancemnt Engel, Friar, Hayes (2000); Flambaum, Zelevinsky (2003): Static octupole deformation is not essential, nuclei with soft octupole vibrations also have the enhancement. Nature 2013 Experiment : Octupole deformation in 224 Ra, 220 Rn, Measurements of 225 Ra EDM: Argonne PRL, 9 June 2015

Atomic EDM produced by nuclear magnetic quadrupole moment Magnetic interaction is not screened! MQM produced by nuclear T,P-odd forces (Khriplovich, Sushkov, Flambaum) Collective enhancement in deformed nuclei (Flambaum).T,P-odd nuclear interaction produces spin hedgehog- correlation (s r) Spherical – magnetic monopole forbidden Deformed- collective magnetic quadrupole Paramagnetic molecules ThO,TaN,YbF,… (Flambaum, DeMille, Kozlov)

Oscillating P , T -odd Nuclear Electromagnetic Moments (QCD Axion) (2) P,T-violating nucleon-nucleon interaction via pion exchange (axion-gluon interaction provides oscillating source of P and T violation at one of the vertices) – Dominant mechanism in most nuclei! [Stadnik, Flambaum, PRD 89 , 043522 (2014)]

Oscillating P , T -odd Nuclear Electromagnetic Moments (QCD Axion) Axion-induced oscillating P , T -odd nuclear electromagnetic moments are linear in a 0 / f a ! Can search for oscillating nuclear Schiff moments using precision magnetometry on diamagnetic atoms in the solid-state (CASPEr) [Budker, Graham, Ledbetter, Rajendran, A. Sushkov, PRX 4 , 021030 (2014)] , or …

Oscillating EDMs of Paramagnetic Atoms and Molecules (Axion and ALPs) [Flambaum, Patras Workshop , 2013], [Stadnik, Flambaum, PRD 89 , 043522 (2014)], [Roberts, Stadnik, Dzuba, Flambaum, Leefer, Budker, PRL 113 , 081601 (2014) + PRD 90 , 096005 (2014)], [Roberts, Stadnik, Flambaum, (In preparation)] A galactic condensate consisting of axions or ALPs induces oscillating EDMs in atoms and molecules via three types of interactions: (1) Oscillating P,T-odd nuclear EM moments (nuclear Schiff moments and magnetic quadrupole moments), produced by coupling of the axion to gluon fields .

Oscillating EDMs of Paramagnetic Atoms and Molecules (Axion and ALPs) [Flambaum, Patras Workshop , 2013], [Stadnik, Flambaum, PRD 89 , 043522 (2014)], [Roberts, Stadnik, Dzuba, Flambaum, Leefer, Budker, PRL 113 , 081601 (2014) + PRD 90 , 096005 (2014)], [Roberts, Stadnik, Flambaum, (In preparation)] (2) Derivative coupling of axion field to axial-vector currents of atomic/molecular electrons (temporal component of interaction).

Oscillating EDMs of Paramagnetic Atoms and Molecules (Axion and ALPs) [Flambaum, Patras Workshop , 2013], [Stadnik, Flambaum, PRD 89 , 043522 (2014)], [Roberts, Stadnik, Dzuba, Flambaum, Leefer, Budker, PRL 113 , 081601 (2014) + PRD 90 , 096005 (2014)], [Roberts, Stadnik, Flambaum, (In preparation)] (3) Perturbation of electromagnetic electron-nucleon interaction by anomalous axion-photon interaction .