  We employ polarization-resolved Raman spectroscopy to study critical nematic
fluctuations in Ba(Fe$_{1-x}$Au$_x$)$_2$As$_2$ superconductors above and across
well separated tetragonal to orthorhombic phase transition at temperature
$T_S(x)$ and the N\'{e}el transition at $T_N(x)$. The static Raman
susceptibility in $XY$ symmetry channel increases upon cooling from room
temperature following the Curie-Weiss law, with Weiss temperature
$T_{\theta}(x)$ several tens of degrees lower than $T_S(x)$. Data reveals a
hidden nematic quantum critical point at $x_{c} = 0.031$ when the system
becomes superconducting, indicating a direct connection between quantum
critical nematic fluctuations and unconventional superconductivity. We
attribute the origin of the nematicity to charge quadrupole fluctuations due to
electron transfer between the nearly degenerate $d_{xz}/d_{yz}$ orbitals.
