Constraining the photon mass via Schumann resonances

Abstract

The photon is the paradigm for a massless particle, and current experimental tests set severe upper bounds on its mass. Probing such a small mass, or equivalently large Compton wavelength, is challenging at laboratory scales, but planetary or astrophysical phenomena may potentially reach much better sensitivities. In this work, we consider the effect of a finite photon mass on Schumann resonances in the Earth-ionosphere cavity, since the transverse magnetic modes circulating Earth have eigenfrequencies of order $\mathcal{O}(10\text{ }\text{ }\mathrm{Hz})$ that could be sensitive to ${m}_{\ensuremath{\gamma}}\ensuremath{\approx}{10}^{\ensuremath{-}14}\text{ }\text{ }{\mathrm{eV}/\mathrm{c}}^{2}$. In particular, we update the limit from Kroll [Phys. Rev. Lett. 27, 340 (1971)], ${m}_{\ensuremath{\gamma}}\ensuremath{\le}2.4\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}13}\text{ }\text{ }{\mathrm{eV}/\mathrm{c}}^{2}$, by considering realistic conductivity profiles for the atmosphere. We find the conservative upper bound ${m}_{\ensuremath{\gamma}}\ensuremath{\le}2.5\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}14}\text{ }\text{ }{\mathrm{eV}/\mathrm{c}}^{2}$, a factor 9.6 more strict than Kroll's earlier projection.