  We investigate the accuracy and reliability of the semiempirical period -
blue amplitude - V-band luminosity relationship for ab-type RR Lyrae stars
originally obtained by Castellani & De Santis (1994) and De Santis (1996). We
infer that the zero point of this relationship does depend on the metallicity,
by studying a sample of both field and cluster variables. We also show that the
use of this relationship can still be useful for those stellar systems showing
an intrinsic metallicity spread, since in this case the metallicity effect has
a negligible effect on the final distance modulus estimate. We compare the
adopted semiempirical relationship with the fully empirical one recently
provided by Kovacs & Walker (2001). When the zero point of the latter relation
is fixed consistently with the former one, the two equations are equivalent. By
appling the semiempirical period - blue amplitude - V-band luminosity relation,
as well as the technique proposed by Cassisi, De Santis & Piersimoni (2001), to
the globular cluster $\omega$ Cen, we show that the empirical slope of the
relationship between the mass of the fundamental RR Lyrae pulsators and their
metallicity, is in fair agreement with the one predicted by updated
evolutionary models for Horizontal-Branch stars.
