  Photometric metallicity formulae of fundamental-mode RR Lyr (RRab) stars are
presented using globular-cluster data exclusively. The aim is to check whether
this selection may help increasing the overall accuracy of the fits and
eliminating the systematic bias of the photometric results, namely that they
tend to overestimate [Fe/H] of the most metal-poor variables. The $G$-band
time-series data available in the Gaia DR3 archive and a new compilation of the
published spectroscopic globular cluster [Fe/H] values on a uniform solar
reference metallicity scale are utilized. We have derived a new
${\mathrm{[Fe/H]}}_{\mathrm{phot}}- P,\varphi_{31}$ formula, and have diagnosed
that no significant increase in the accuracy of the fit can be achieved using
non-linear or multi-parameter formulae. The best result is obtained when
different formulae are applied for variables with Oosterhoff-type I and II
properties. However, even this solution cannot eliminate the systematic bias of
the results completely. This separation of the variables has also led to the
conclusion that the photometric estimates of the [Fe/H] are less reliable for
the Oo-type II variables than for the Oo-type I sample. Published
${\mathrm{[Fe/H]}}_{\mathrm{phot}}$ values and the results of the available
photometric formulae in the Gaia $G$-band are compared with the present
results. It is found that each of the solutions yields very similar results,
with similar accuracy and systematic biases. Major differences are detected
only in the zero-points of the [Fe/H] scales, and these offsets are larger than
differences in the accepted solar reference values would explain.
