A vindication of the RR Lyrae Fourier light curve decomposition for the
  calculation of metallicity and distance in globular clusters
  We report the mean metallicity and absolute magnitude of RR Lyrae stars in a
sample of 37 globular clusters, calculated via the Fourier decomposition of
their light curves and ad hoc semiempirical calibrations, in an unprecedented
homogeneous approach. This enabled a new discussion of the metallicity
dependence of the horizontal branch (HB) luminosity, as a fundamental distance
indicator. The calibration for the RRab and RRc stars should be treated
separately. For the RRab the dispersion is larger and non-linear. For the RRc
stars the correlation is less steep, very tight and linear. The relevance of
the HB structural parameter L, is highlighted and offer a non-linear
calibration of the form MV ([Fe/H],L). Excellent agreement is found between
values of [Fe/H] and MV from the light curve decomposition with spectroscopic
values and distances obtained via Gaia-DR3 and HST. The variable stars census
in 35 clusters includes 326 stars found by our program.
