Limits on the Carroll-Field-Jackiw electrodynamics from geomagnetic data

Abstract

Lorentz-symmetry violation may be described via the CPT-odd, dimension-3, Carroll-Field-Jackiw term, which couples the electromagnetic fields to a constant 4-vector $k_{\mathrm{AF}}$ selecting a preferred direction in spacetime. We solve the field equations using the Green's method for a static point-like magnetic dipole and find the $k_{\mathrm{AF}}$-dependent corrections to the standard dipolar magnetic field that strongly dominates the near-Earth magnetic field. Given the very good agreement between current models and ground- and satellite-based geomagnetic data, our strongest constraints on the components of $k_{\mathrm{AF}}$ in the Sun-centered frame read $|(k_{\mathrm{AF}}{)}_Z|\lesssim 4\times 10^{-25}\mathrm{GeV}$ for $|(k_{\mathrm{AF}}{)}_X|,|(k_{\mathrm{AF}}{)}_Y|\lesssim 10^{-24}\mathrm{GeV}$ at the two-sigma level. This represents an improvement of about four orders of magnitude over earlier bounds based on other geophysical phenomena.

Comments: 58 pages, 16 figures. Constructive comments are welcome