Phenomenological Implications of a Magnetic 5th Force

A 5th force coupling to baryon number $B$ has been proposed to account for the correlations between the acceleration differences $\Delta a_{ij}$ of the samples studied in the E\"{o}tv\"{o}s experiment, and the corresponding differences in the baryon-to-mass ratios $\Delta(B/\mu)_{ij}$. To date the E\"{o}tv\"{o}s results have not been supported by modern experiments. Here we investigate the phenomenological implications of a possible magnetic analog $\vec{\mathscr{B}}_5$ of the conventional 5th force electric field, $\vec{\mathscr{E}}_5$, arising from the Earth's rotation. We demonstrate that, in the presence of couplings proportional to $\vec{\mathscr{B}}_5$, both the magnitude and direction of a possible 5th force field could be quite different from what would otherwise be expected and warrants further investigation.