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 $k_{\rm AF}$ 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 $k_{\rm AF}$-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 $k_{\rm AF}$ in the Sun-centered frame read $|(k_{\rm AF})_Z| \lesssim 4 \times 10^{-25} \, {\rm GeV}$ for $|(k_{\rm AF})_X|, |(k_{\rm AF})_Y| \lesssim 10^{-24} \, {\rm GeV}$ at the two-sigma level. This represents an improvement of about four orders of magnitude over earlier bounds based on other geophysical phenomena.

Figures (16)

• Figure 1: From top to bottom: time variation of the radial, polar and azimuthal (only its quadratic part) components of the CFJ field, cf. Eqs. \ref{['eq_second_term_phi']}, \ref{['eq_B_r_lab_full']} and \ref{['eq_B_theta_lab_full']}, over a sidereal day for different co-latitudes. Here we set $k_X = 1$, $k_Y = 0.5$ and $k_Z = 1.5$ in units of $10^{-24} \, {\rm GeV}$.
• Figure 2: Time-averaged radial and polar components of the CFJ field for an Earth-bound observer at the surface at $r = R_\oplus$: radial \ref{['eq_Br_avg_T']} in the top panel and polar \ref{['eq_Btheta_avg_T']} in the bottom panel. The components of the background in the SCF are expressed in units of $10^{-24} \, {\rm GeV}$. Since the polar angle satisfies $0 \leq \theta \leq \pi$, the radial projection will change sign when crossing the geographic equator due to the global factor of $c_\theta$, whereas the polar projection is negative for any co-latitude.
• Figure 3: Locations of the 144 ground observatories contributing to the International Real-Time Magnetic Observatory Network (INTERMAGNET) used in this section.
• Figure 4: Distributions of the filtered residuals in the non-empty angular patches of size $\Delta = 5^\circ$ following Eqs. \ref{['eq_def_mean_residuals_T_obs']} and \ref{['eq_def_std_residuals_j_obs']}. The height of each bin is the number of data in that bin divided by the total number; the sum of all heights is equal to one.
• Figure 5: Two-sigma bounds on combinations of the CFJ background in the SCF derived from ground data. In blue and yellow are the bounds from the radial and polar components, respectively. The region within the curves is allowed.