Axion-induced EDMs in paramagnetic systems Benjamin M. Roberts - PowerPoint PPT Presentation

Axion-induced EDMs in paramagnetic systems Benjamin M. Roberts Yevgeny V. Stadnik, Vladimir A. Dzuba, Victor V. Flambaum Department of Theoretical Physics, University of New South Wales, Sydney, Australia The Ultra-Light Frontier Mainz Institute for Theoretical Physics, Johannes Gutenberg University, Mainz, Germany 18 June 2015 B. M. Roberts (UNSW Australia) ALP-induced paramagnetic EDMs 18 June 2015 1 / 28

Overview: Axions, ALPs & pseudoscalar fields Conventional searches: axion–photon coupling Quadratic (+higher) in coupling Axion–Gluon Coupling: Linear effects [Graham, Rajendran, PRD 84 , 055013 (2011)] Oscillating EDMs in diamagnetic systems: CASPEr [Budker, Graham, Ledbetter, Rajendran, Sushkov, PRX 4 , 021030 (2014)] New linear effects Axion/ALP–Gluon, –Fermion, and –Photon Oscillating EDMs in paramagnetic systems Tests of CPT Limits on SME parameters WIMP–electron scattering: atomic ionisation Implications for DAMA annual modulation B. M. Roberts (UNSW Australia) ALP-induced paramagnetic EDMs 18 June 2015 2 / 28

Axions Strong CP Problem Observed lack of CP -violation in QCD ( θ < 10 − 10 ) Resolution: Pseudoscalar particle “Axion” [1] Axion Condensate Classical, oscillating field a ( t ) = a 0 cos( m a t ) Cold dark matter candidate [2] [1] Peccei, Quinn, Phys. Rev. Lett. 38 , 1440 (1977); Weinberg, Phys. Rev. Lett. 40 , 223 (1978). [2] Preskill, Wise, Wilczek, Phys. Lett. B 120 , 127 (1983); Sikivie, Phys. Rev. Lett. 51 , 1415 (1983); Dine, Fischler, Phys. Lett. B 120 , 137 (1983). B. M. Roberts (UNSW Australia) ALP-induced paramagnetic EDMs 18 June 2015 3 / 28

Axion–SM Couplings Anomalous effective couplings to SM particles: Fermion Photon Gluon � �� � � �� � � �� � a a ∂ µ a F µν � G µν � ψγ µ γ 5 ψ ¯ F µν G µν f a f a f a ≈ 2 × 10 − 20 eV − 1 � � 1 m a a ( t ) = a 0 cos( m a t ) 10 − 4 eV f a Classical Region: m a ∼ 10 − 6 − 10 − 4 eV ( ∼ MHz – GHz) Anthropic Region: m a ∼ 10 − 10 − 10 − 8 eV ( ∼ kHz – MHz) • Saturates DM density: ⇒ a 0 / f a ∼ 4 × 10 − 19 (QCD axion) • (In general, DM ALP, f a free parameter, a 0 ∼ 1 / m a ) B. M. Roberts (UNSW Australia) ALP-induced paramagnetic EDMs 18 June 2015 4 / 28

Searching for Axions “Standard” Searches: Axion–photon coupling Axion–photon conversion e.g. ADMX, CAST, IAXO, ... P a → γ ∼ (1 / f a ) 2 Quadratic Light shining through a wall e.g. ALPS, BMV, CROWS, ... P γ → a → γ ∼ (1 / f a ) 4 Quartic • Good for ∼ f a < 10 13 GeV ◮ Sikivie, Phys. Rev. Lett. 51 , 1415 (1983). ◮ e.g. : depts.washington.edu/admx/, cast.web.cern.ch/CAST/, alps.desy.de/ B. M. Roberts (UNSW Australia) ALP-induced paramagnetic EDMs 18 June 2015 5 / 28

Emerging Axion Searches: Schiff Moments and CASPEr Gluon–coupling: Axion-induced EDMs d n = 1 . 2 × 10 − 16 θ e cm [1] θ QCD → a / f a ⇒ Also produces observable Nuclear Schiff Moments Dominated by a -induced inter-nucleon force [2] Linear in a 0 / f a ! Good for f a > ∼ 10 16 GeV CASPEr Precision magnetometry [3] Solid-state, diamagnetic atoms [1] Graham, Rajendran, Phys. Rev. D 84 , 055013 (2011); 88 , 035023 (2013). [2] Stadnik, Flambaum, Phys. Rev. D 89 , 043522 (2014). [3] Budker, Graham, Ledbetter, Rajendran, Sushkov, Phys. Rev. X 4 , 021030 (2014). B. M. Roberts (UNSW Australia) ALP-induced paramagnetic EDMs 18 June 2015 6 / 28

Magnetic Quadrupole Moments • As for Schiff moments, θ QCD → a / f a ⇒ MQMs Oscillating EDMs P & T Violating nuclear moment ⇒ EDMs Need I > 1 / 2 Much larger effect in Paramagnetic Systems Nuclear Enhancement Quadrupole deformation ⇒ enhancement (most nuclei!) (Schiff moment needs Octopole) ◮ Roberts, Stadnik, Dzuba, Flambaum, Leefer, Budker, Phys. Rev. D 90 , 096005 (2014). ◮ Roberts, Stadnik, Flambaum, In Preparation B. M. Roberts (UNSW Australia) ALP-induced paramagnetic EDMs 18 June 2015 7 / 28

MQM Sensitivity sin[(2 µ B e − mc 2 ) t / � ] M ≈ np µ E D A sin(2 µ B e ) (2 µ B e − mc 2 ) / � • µ N → µ e ⇒ 10 3 • S → D MQM ⇒ 10 3 or 4 (potentially more in special systems) But: • Paramagnetic ⇒ τ/τ = 10 − 6 B. M. Roberts (UNSW Australia) ALP-induced paramagnetic EDMs 18 June 2015 8 / 28

ALP–Electron Interaction ∂ t a ∇ φ ψγ 0 γ 5 ψ ¯ · ¯ ψ γ γ 5 ψ L int . = + f a f a � �� � � �� � P -even effects P -odd effects (This Work) e e ✁ Pseudoscalar field – atomic electrons Dynamic field: parity-mixing Oscillating EDMs (Paramagnetic) φ Need non-zero J Alkali atoms: d ≈ a 0 a cos( m a t ) ∼ 10 − 38 e cm α 0 m 2 f a ◮ Stadnik, Flambaum, Phys. Rev. D 89 , 043522 (2014); Roberts, Stadnik, Dzuba, Flambaum, Leefer, Budker, Phys. Rev. Lett. 113 , 081601 (2014); Phys. Rev. D 90 , 096005 (2014). B. M. Roberts (UNSW Australia) ALP-induced paramagnetic EDMs 18 June 2015 9 / 28

ALP–Electron Interaction Resonance Dysprosium, Radium, Diatomic molecules Close opposite-parity levels ⇒∼ 10 4 enhancement Magnetically drive resonance: E a − E b = m a ⇒ more? � A | e r | B �� B | γ 5 | A � ( E A − E B + i Γ / 2) 2 − m 2 m 2 a 0 d EDM ≃ − 2 i cos( m a t ) f a ◮ Roberts, Stadnik, Dzuba, Flambaum, Leefer, Budker, Phys. Rev. D 90 , 096005 (2014). ◮ Roberts, Stadnik, Flambaum, In Preparation B. M. Roberts (UNSW Australia) ALP-induced paramagnetic EDMs 18 June 2015 10 / 28

ALP–Electron Interaction However, exact relation: � a | γ 5 | n � = i ∆ E an � a | Σ · r | n � + � a | 2 γ 5 ˆ K | n � Main term, on resonance: ∆ E = m ≫ Γ • D A ∼ a 0 m 2 f a • Independent of m a (for ALP Dark Matter) Main term, off resonance: ∆ E , Γ ≪ m • D A ∼ − ∆ E 2 a 0 f a Other terms: ∆ E ′ ≫ Γ , m • D A ∼ − m 2 ∆ E ′ 2 a 0 f a Enhanced by ( m a / eV ) − 1 c.f. alkali ⇒ several orders of magnitude B. M. Roberts (UNSW Australia) ALP-induced paramagnetic EDMs 18 June 2015 11 / 28

Paramagnetic measurements Oscillating EDMs in Paramagnetic Systems Axion–Electron dominant mechanism in atoms MQM dominant mechanism for solid state (resonance) Different parametric dependence Potential benefits Much larger effects than diamagnetics ..unpaired spins ⇒ higher systematics • Different dependence on m a to CAPSEr ⇒ Complementary! ◮ Roberts, Stadnik, Flambaum, In Preparation B. M. Roberts (UNSW Australia) ALP-induced paramagnetic EDMs 18 June 2015 12 / 28

B. M. Roberts (UNSW Australia) ALP-induced paramagnetic EDMs 18 June 2015 13 / 28

Fermion Interaction Atomic Parity-Violation Pseudoscalar field (e.g. axions) Oscillating PNC amplitudes Observable in Dysprosium? Pseudovector field (from SME[1]) A static or oscillating field Limits from PNC experiments! 0 from Dy; b p , n 0 , d p , n b e 00 from Cs ◮ Roberts, Stadnik, Dzuba, Flambaum, Leefer, Budker, Phys. Rev. D 90 , 096005 (2014) ◮ Roberts, Stadnik, Dzuba, Flambaum, Leefer, Budker, Phys. Rev. Lett. 113 , 081601 (2014) [1] Colladay, Kosteleck´ y, Phys. Rev. D 58 , 116002 (1998). B. M. Roberts (UNSW Australia) ALP-induced paramagnetic EDMs 18 June 2015 14 / 28

Atomic Parity & Time-Reversal Violation Conventional sources Mixing of opposite parity states P -Violating “ E 1” transition: E PNC e-N interaction: Q W N-N interaction: Anapole Moment P , T -Violating Electric Dipole Moments e-N interaction; electron EDM ◮ Zeldovich, Zh. Eksp. Teor. Fiz. 36 , 964 (1959); Bouchiat & Bouchiat, Phys. Lett. B 48 , 111 (1974). ◮ Sandars, Phys. Lett. 14 , 194 (1965). ◮ Recent Review: Roberts, Dzuba, Flambaum, Annu. Rev. Nucl. Part. Sci. 65 , 63 (2015). B. M. Roberts (UNSW Australia) ALP-induced paramagnetic EDMs 18 June 2015 15 / 28

“Cosmic Field”-induced Parity Violation � a | γ 5 | n � = i ∆ E an � a | Σ · r | n � + � a | 2 γ 5 ˆ K | n � • Σ · r : ∼ 1 / c ; No PNC effect; Main EDM effect Pseudoscalar field Static field ⇒ no effects Oscillating field (e.g. axions, ALPs) ⇒ Oscillating PNC E PNC = i ( a 0 / f a ) m a sin( m a t ) K PNC Atomic structure: K PNC ∼ 10 7 | e | GeV − 2 Pseudovector field: L = b µ ¯ ψγ µ γ 5 ψ [1] b 0 ⇒ Static and oscillating PNC E PNC = i b 0 sin( ω b t ) K PNC ◮ Roberts, Stadnik, Dzuba, Flambaum, Leefer, Budker, Phys. Rev. Lett. 113 , 081601 (2014) [1] Colladay, Kosteleck´ y, Phys. Rev. D 58 , 116002 (1998). B. M. Roberts (UNSW Australia) ALP-induced paramagnetic EDMs 18 June 2015 16 / 28

Tests of CPT: Limiting pseudovector field Limit on electron-field coupling From PNC experiment in Dy [1] 0 | < 7 × 10 − 15 GeV | b ( e ) Limit on nucleon-field coupling From Cs anapole moment measurement [2] 0 | < 4 × 10 − 8 GeV 0 | < 2 × 10 − 7 GeV | b ( p ) | b ( n ) ◮ Roberts, Stadnik, Dzuba, Flambaum, Leefer, Budker, Phys. Rev. Lett. 113 , 081601 (2014); Phys. Rev. D 90 , 096005 (2014). [1] Nguyen, Budker, DeMille, Zolotorev, Phys. Rev. A 56 , 3453 (1997). [2] Wood, Bennett, Cho, Masterson, Roberts, Tanner, Wieman, Science 275 , 1759 (1997). B. M. Roberts (UNSW Australia) ALP-induced paramagnetic EDMs 18 June 2015 17 / 28

Fermion Interaction Lead to limits on several other previously unconstrained parameters ◮ Roberts, Stadnik, Dzuba, Flambaum, Leefer, Budker, Phys. Rev. D 90 , 096005 (2014); Phys. Rev. Lett. 113 , 081601 (2014) [1] Kosteleck´ y, Russell, Rev. Mod. Phys. 83 , 11 (2011) [Up-to-date: arXiv:0801.0287v8]. B. M. Roberts (UNSW Australia) ALP-induced paramagnetic EDMs 18 June 2015 18 / 28