  Thanks to the outstanding capabilites of the HST, our current knowledge about
the M31 globular clusters (GCs) is similar to our knowledge of the Milky Way
GCs in the 1960s-1970s, which set the basis for studying the halo and galaxy
formation using these objects as tracers, and established their importance in
defining the cosmic distance scale. We intend to derive a new calibration of
the M_V(HB)-[Fe/H] relation by exploiting the large photometric database of old
GCs in M31 in the HST archive. We collected the BVI data for 48 old GCs in M31
and analysed them by applying the same methods and procedures to all objects.
We obtained a set of homogeneous colour-magnitude diagrams (CMDs) that were
best-fitted with the fiducial CMD ridge lines of selected Milky Way template
GCs. Reddening, metallicity, Horizontal Branch (HB) luminosity and distance
were determined self-consistently for each cluster. There are three main
results of this study: i) the relation
M_V(HB)=(0.25+/-0.02)[Fe/H]+(0.89+/-0.03), which is obtained from the above
parameters and is calibrated on the distances of the template Galactic GCs; ii)
the distance modulus to M31 of (m-M)_0=24.42+/-0.06 mag, obtained by
normalising this relation at the reference value of [Fe/H]=-1.5 to a similar
relation using V_0(HB). This is the first determination of the distance to M31
based on the characteristics of its GC system which is calibrated on Galactic
GCs; iii) the distance to the Large Magellanic Cloud (LMC), which is estimated
to be 18.54+/-0.07 mag as a consequence of the previous results. These values
agree excellently with the most recent estimate based on HST parallaxes of
Galactic Cepheid and RR Lyrae stars, as well as with recent methods.
