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Understanding Axion Electrodynamics - Properties and Interactions

Learn about the axion, a particle associated with Peccei-Quinn symmetry breaking, its mass terms, role as dark matter, and coupling to electromagnetic fields. Discover its implications in theoretical physics.

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Understanding Axion Electrodynamics - Properties and Interactions

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  1. Axion Electrodynamics Christopher T. Hill Fermilab U of Durham, UK, April 16, 2016

  2. What is the axion? ( /f)

  3. What is the axion? ( /f) Kinetic Terms Mass Terms

  4. ? mh’ = mp

  5. ? mh’ = mp 985 MeV 140 MeV Way off!

  6. ? mh’ >> mp Remedy I: cf4 Det U + h.c.

  7. ? But! This can have a strong CP-phase: cf4 eiq Det U + h.c. p , h , h’ predicts neutron EDM much too large: g5 sin(q) q < 10-12

  8. ? Remedy II: The axion cf4 ei(q - a/f) Det U + h.c. The axion potential: - c’f4 cos(q - a/f ) The axion mass:

  9. Axions: The axion is a pNGB associated with the spontaneous breaking of Peccei-Quinn symmetry. Typically the PQ symmetry breaks at a high scale At the QCD scale, instantons activate the U(1) axial current anomaly. The axion acquires a potential by mixing with develops a VEV which cancels the QCD CP-violating phase . Small oscillations about this minimum are associated with the axion mass and can constitute dark matter. p , h , h’

  10. Axions: The axion is an “angular variable” in the effective action on scales much less than It is useful to write axion expressions in terms of the angle Variable: The axion kinetic+mass term action can be written:

  11. Axions: The axion mass is controlled by mixing with the pseudoscalar nonet of mesons. The axion mass is then : The prefactor, c, is where and vanishes as QCD: 2p 20.7

  12. Cosmic Axions = Dark Matter? Assume a cosmic axion field: The axion energy density is: Equate this to the galactic halo dark matter density: Hence:

  13. Axion Electrodynamics The axion couples to the electromagnetic field via the U(1) axial current anomaly: Where: and = anomaly coefficient.

  14. Axion Electrodynamics The axion couples to the electromagnetic field via the U(1) axial current anomaly: Where: and = anomaly coefficient. See the PDG article.

  15. Axion Electrodynamics The action for axion electrodynamics: Note that is a total divergence in the limit that The axion anomaly can we written in two ways: Gauge inv. but not chiral. Chiral inv. but not gauge inv.

  16. Axion Decoupling

  17. Axion Decoupling Display manifest gauge invariance:

  18. Axion Decoupling Display manifest gauge invariance: Integrate by parts; Display manifest shift invariance:

  19. Axion Decoupling Display manifest gauge invariance: Integrate by parts; Display manifest shift invariance: Since these differ only by a total divergence, both symmetries must be present in perturbation theory.

  20. “The axion interactions induced perturbatively (ala Feynman diagrams) must always display derivative coupling.”

  21. “The axion interactions induced perturbatively (ala Feynman diagrams) must always display derivative coupling.” False!

  22. “The axion interactions induced perturbatively (ala Feynman diagrams) must always display derivative coupling.” False! Since manifest gauge and shift symmetries differ only by a total divergence, both symmetries must be present in perturbation theory, but need not be simultaneously manifest.

  23. Can an (oscillating) electric dipole moment be generated from the anomaly perturbatively?

  24. Can an (oscillating) electric dipole moment be generated from the anomaly perturbatively? We define a covariant OEDM for the electron:

  25. Can an (oscillating) electric dipole moment be generated from the anomaly perturbatively? We define a covariant OEDM for the electron: Integrate by parts:

  26. Can an (oscillating) electric dipole moment be generated from the anomaly perturbatively? We define a covariant OEDM for the electron: Integrate by parts: Requires:

  27. Can an (oscillating) electric dipole moment be generated from the anomaly perturbatively? We define a covariant OEDM for the electron: Integrate by parts: No! But generally: /

  28. Do a simple calculation: Electron Magnetic Moment axion anomaly axion

  29. Do a simple calculation:

  30. Do a simple calculation:

  31. Do a simple calculation:

  32. Do a simple calculation: note decoupling

  33. Do a simple calculation:

  34. Do a simple calculation: The resulting OEDM is:

  35. Do a simple calculation: The resulting OEDM is:

  36. Do a simple calculation: The resulting OEDM is: Callous sophisticates, US west coast:

  37. Do a simple calculation: The resulting OEDM is: Callous sophisticates, US west coast: No! Doesn’t Decouple!

  38. What has happened to axion shift symmetry?: Integrate by parts: Decoupling requires:

  39. What has happened to axion shift symmetry?: Integrate by parts: Decoupling requires: Easy to check:

  40. What has happened to axion shift symmetry?: Integrate by parts: Decoupling requires: The effective action:

  41. Do a less simple calculation:

  42. Do a less simple calculation:

  43. Do a less simple calculation:

  44. Do a less simple calculation:

  45. Do a less simple calculation: The effective action:

  46. Do a less simple calculation: The effective action: To the callous sophisticates: YES! It Decouples!

  47. This result is subtle and echoes the behavior of the anomaly itself:

  48. This result is subtle and echoes the behavior of the anomaly itself:

  49. This result is subtle and echoes the behavior of the anomaly itself:

  50. Magnetic monopoles acquire electric charge in presence of a nonzero q angle, “Witten Effect.”

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