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

What is the axion? ( /f)

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

? mh’ = mp

? mh’ = mp 985 MeV 140 MeV Way off!

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

? 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

cf4 ei(q - a/f) Det U + h.c. - c’f4 cos(q - a/f ) ? 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:

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’

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:

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

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

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

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

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.

Axion Decoupling

Axion Decoupling Display manifest gauge invariance:

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

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.

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

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

“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.

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

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

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

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

No! But generally: / 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: /

Do a simple calculation: Electron Magnetic Moment axion anomaly axion

Do a simple calculation:

Do a simple calculation:

Do a simple calculation:

Do a simple calculation: note decoupling

Do a simple calculation:

Do a simple calculation: The resulting OEDM is:

Do a simple calculation: The resulting OEDM is:

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

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

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

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

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

Do a less simple calculation:

Do a less simple calculation:

Do a less simple calculation:

Do a less simple calculation:

Do a less simple calculation: The effective action:

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

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

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

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

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

Magnetic monopoles acquire electric charge in presence of a nonzero q angle, “Witten Effect.” A magnetic monopole–antimonopole pair will have a magnetic dipole; this becomes an electric dipole moment For nonzero q angle. Oscillating axion field implies a nonzero oscillating q angle.

Magnetic Dipole An infinitesimally small dipole is indistinguishable from a monopole-anti-monopole pair.

Electric Dipole

Electric Dipole

Theorem: A space-time filling coherent oscillating axion field will cause any magnetic N-pole to become an oscillating electric N-pole through the anomalous coupling of the axion to electromagnetic fields.

Axion in a Source-free Magnetic Field:

Axion in a Source-free Magnetic Field: Non - propagating

Axionic Electrodynamics RF Cavity Energetics Conducting wall r = R

Axionic Electrodynamics RF Cavity Energetics Conducting wall r = R Particular Solution: The particular solution doesn’t satisfy the conducting boundary condition:

Axionic Electrodynamics RF Cavity Energetics Conducting wall r = R Particular Solution: Homogeneous Solution:

Axionic Electrodynamics RF Cavity Energetics Conducting wall r = R Full Solution:

Axionic Electrodynamics RF Cavity Energetics Conducting wall r = R Impose boundary condition: Cavity solution.

Axionic Electrodynamics RF Cavity Energetics Finite Q:

Axionic Electrodynamics RF Cavity Energetics Finite Q: Only need B in the wall!!!

Axionic Electrodynamics RF Cavity Energetics At Large Q

Axionic Electrodynamics RF Cavity Energetics

How does the axion induce a physical signal? Vector potential Vacuum Ohm’s Law Conductor

How does the axion induce a physical signal?

How does the axion induce a physical signal? We only need B in the conductor

Radiation from axion induced OEDM Dipole source Dipole “plume”

Radiation from axion induced OEDM Dipole “plume”

Radiation from axion induced OEDM Dipole source

Radiation from axion induced OEDM Near zone:

Radiation from axion induced OEDM Far zone: Electric Dipole Radiation:

Radiation from axion induced OEDM

Radiation from axion induced OEDM

Radiation from axion induced OEDM

Radiation from axion induced OEDM

Radiation from axion induced OEDM

Radiation from axion induced OEDM

Radiation from axion induced OEDM

Radiation from axion induced OEDM

Radiation from axion induced OEDM

Radiation from axion induced OEDM Summary: Agrees with classical calculation

Radiation from axion induced OEDM

Estimates 2

Power Radiated by a single electron in the axion cosmic field

Power from coherent assemblage of electrons

Slab Radiator Power Output

A Simple Experiment: Slab Radiator Power Output (3s) 0.1K

Possible Advantages of Magnetic Arrays: Non-resonant, broadband radiator Enhanced configurations, eg. scalable , X or XYZ ? Signal can be modulated by multiple arrays, eg XY + X’Y’ Power levels comparable to cavities; may have physical advantages in axion ``sweet-spot’’

Axion electrodynamics in a nut-shell: Axial anomaly a g g In background strong magnetic field induce non-propagating induces a propagating and in a conducting material or source Detectable Poynting Vector x

The axion serves an essential role in QCD Axion is a compelling Dark Matter Candidate Essentially defined by two parameters: faxion and ganomaly Detection is challenging but may be doable: Broadband Radiator Cavity Experiment

END

My Idiosyncratic system of units:

Result:

Result:

Result: Consistent with Pauli-Schroedinger Result:

Estimate of the RF Cavity Energetics

Estimate of the RF Cavity Energetics 2

Power from coherent assemblage of electrons

Estimate of the RF Cavity Energetics

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

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

Power Radiated by a single electron Immersed in the axion cosmic field

Power from coherent assemblage of electrons

Power from coherent assemblage of electrons