Earth as a transducer for dark-photon dark-matter detection

Earth as a transducer for axion dark-matter detection

“…It is very similar to the one recently pointed out in Refs. [59,60] for kinetically mixed dark-photon dark matter, which in turn has the same conceptual origin as the signal in the DM Radio experiment [61].…”

“…In Ref. [59], this was sufficient to give rise to a dark-photon dark-matter induced magnetic field at the surface of the Earth. Provided that m A 1/R, where R ∼ (3 × 10 −14 eV) −1 is the radius of the Earth, the electric field was suppressed by a fac-tor (m A R) 2 because of the large natural shield.…”

“…grangian, in the presence of a static background magnetic field B 0 : L ⊃ +g aγ aE • B ∼ g aγ (∂ t a)B 0 • A ∼ −im a g aγ aB 0 • A, where we used E ∼ −∂ t A (ignoring the EM scalar potential) integrated by parts dropping the boundary term, and used ∂ t a ∼ −im a a as relevant for a non-relativistic axion. This term has the same mathematical structure as the mass-mixing term that appears in a Lagrangian describing a dark photon that is kinetically coupled to the SM photon, when expressed in the interaction basis [59]: L ⊃ εm 2 A A • A ∼ −εm 2 A A • A (again ignoring the scalar potential), where m A is the dark-photon mass, and ε is the kinetic mixing parameter. The axion coupling must thus source similar physical effects to the dark-photon coupling.…”

“…As for the dark-photon case considered in Ref. [59], our axion signal however does not arise from considering a human-engineered shielding box (as employed, e.g., in other axion searches such as resonant cavity experiments [36,[62][63][64][65][66] and LC circuits [37,61,67]); instead, in our mass range of interest, Nature provides us with a ready-made shield. As explained in Ref.…”

“…As explained in Ref. [59], the near-Earth environment itself can be modeled as a conducting spherical cavity with a vacuum gap: the lower layer of the atmosphere is a poor conductor sandwiched on one side by the conductive innermost layers of the Earth, and on the other side by the conductive ionosphere and/or interplanetary medium. The conductive inner-Earth, ionosphere, and interplanetary medium are thick enough to damp the electromagnetic active mode, at least in our mass range of interest.…”