Axion Dark Matter Coupling to Resonant Photons via Magnetic Field

Abstract

We show that the magnetic component of the photon field produced by dark matter axions via the two-photon coupling mechanism in a Sikivie Haloscope is an important parameter passed over in previous analysis and experiments. The interaction of the produced photons will be resonantly enhanced as long as they couple to the electric or magnetic mode structure of the Haloscope cavity. For typical Haloscope experiments the electric and magnetic coupling is the same and implicitly assumed in past sensitivity calculations. However, for future planned searches such as those at high frequency, which synchronize multiple cavities, the sensitivity will be altered due to different magnetic and electric couplings. We define the complete electromagnetic form factor and discuss its implications for current and future high and low mass axion searches, including some effects which have been overlooked, due to the assumption that the two couplings are the same.Axions are a type of Weakly Interacting Slim Particle (WISP) originating from the Peccei Quinn solution to the strong CP problem in QCD [1]. They can be formulated as highly motivated and compelling components of Cold Dark Matter (CDM) [2][3][4][5]. Cosmological constraints provide upper and lower limits on the mass of the axion [6], yet still leave a large area of parameter space to be searched. One of the most mature and sensitive experiments is the Sikivie Haloscope [7,8], which exploits the inverse Primakoff effect whereby a magnetic field provides a source of virtual photons in order to induce axion-to-photon conversion via a two photon coupling, with the generated real photon frequency being dictated by the axion mass. This signal is then resonantly enhanced by a cavity structure and resolved above the thermal noise of the measurement system. It has been well established that in a Haloscope with an axial DC magnetic field the expected power due to axion-tophoton conversion is given by [7][8][9] where g γ is a dimensionless model-dependent parameter of O(1) [10][11][12], α the fine structure constant, f a the Peccei-Quinn energy breaking scale which dictates the axion mass and coupling strength, m a the axion mass, ρ a the local density of axions, V the cavity volume, B 0 the applied magnetic field, Q the cavity quality factor (assuming the bandwidth is greater than the expected spread of the axion signal) and C the Haloscope form factor describing the overlap between the electric field created by the converted axions and the electric field structure of the resonant mode in the cavity.To date Haloscope searches have excluded some areas of the parameter space [9,13], with further experiments currently under way and future efforts in various stages of planning [14][15][16]. All of this work fundamentally relies on Eq. (1) to set constraints on f a and hence the mass of the axion and the strength of axion-photon coupling. In deriving Eq. (1) the coupling of an axion to a photon electric field is explicitly considered in the form factor, C, and it is then assumed that the c...

The ORGAN experiment: An axion haloscope above 15 GHz

“…Here B is the field strength of the external magnetic field, C is a mode dependent form factor of order 1 [29], which represents the degree of overlap between the cavity mode electromagnetic field and the electromagnetic field induced due to axion photon conversion (it is an integral of the dot product of these two fields), V is the volume of the detecting cavity, Q L is the loaded cavity quality factor (provided it is lower than the expected axion signal quality factor ∼ 10 6 ), and ρ a is the local axion dark matter density. The signal powers in axion haloscopes are extremely weak, even ADMX, which operates with a very large volume and high magnetic field system expects signal powers on the order of 10 −22 W. The challenges faced in the move to high frequency haloscopes are evident in equation 1.…”

Effective approximation of electromagnetism for axion haloscope searches

“…However, because of the axion anomaly, this set of Maxwell's equations doesn't naturally satisfy certain boundary conditions. The general haloscope conditions that have been assumed in many previous approaches are [15,16] • zero current : J e = 0,…”

“…In Refs. [15,16], this problem was avoided by forcing the non-zero term in Eq.6 as a relationship of new fields E a and B a as…”

Axion detection via topological Casimir effect

“…This anomalous current points along magnetic field in contrast with ordinary E&M , where the current is always orthogonal to B. Most of the recent proposals [14][15][16][17][18][19][20][21][22][23][24][25][26] to detect the dark matter axions are precisely based on this extra current (5).…”

“…Still, it remains one of the most interesting resolutions of the strong CP problem to date, which has also led to numerous proposals for direct dark matter searches. Here we list but a fraction of the new (and old) ideas [14][15][16][17][18][19][20][21][22][23][24][25][26] On the other hand, one may also discuss a similar theta term in QED. It is normally assumed that a similar θ QED parameter in the abelian Maxwell Electrodynamics is unphysical (if magnetic monopoles are absent), and can be always removed from the system.…”