  We propose diatomic molecules built from gold and carbon-group atoms as
promising candidates for optical cycling and precision measurements. We show
that this class of molecules (AuX, X = C, Si, Ge, Sn, Pb) features
laser-accessible electronic transitions with nearly diagonal Franck-Condon
factors. The $^2\Pi_{1/2}$ ground states can be easily polarized in the
laboratory frame and have near-zero magnetic moments, valuable features for
quantum science and precision measurement applications. The sensitivities of
AuX molecules to the electron electric dipole moment (EDM) are found to be
favorable, with effective electric fields of 10-30 GV/cm. Together, these
features imply that AuX molecules may enable significantly improved searches
for time-reversal symmetry violation.
