  The correlation between emission-line luminosity (L) and profile width
(sigma) for HII Galaxies provides a powerful method to measure the distances to
galaxies over a wide range of redshifts. In this paper we use SDSS
spectrophotometry to explore the systematics of the correlation using the
[OIII]5007 lines instead of Halpha or Hbeta to measure luminosities and line
widths. We also examine possible systematic effects involved in measuring the
profile-widths and the luminosities through different apertures. We find that
the green L-sigma relation defined using [OIII]5007 luminosities is
significantly more sensitive than Hbeta to the effects of age and the physical
conditions of the nebulae, which more than offsets the advantage of the higher
strength of the [OIII]5007 lines. We then explore the possibility of mixing
[OIII]5007 profile-widths with SDSS Hbeta luminosities using the Hubble
constant H0 to quantify the possible systematic effects. We find the mixed
L(Hbeta) sigma[OIII] relation to be at least as powerful as the canonical
L-sigma relation as a distance estimator, and we show that the evolutionary
corrections do not change the slope and the scatter of the correlation, and
therefore, do not bias the L-sigma distance indicator at high redshifts.
Locally, however, the luminosities of the Giant HII Regions that provide the
zero-point calibrators are sensitive to evolutionary corrections and may bias
the Hubble constant if their mean ages, as measured by the equivalent widths of
Hbeta, are significantly different from the mean age of the HII Galaxies. Using
a small sample of 16 ad-hoc zero point calibrators we obtain a value of H0 =
66.4\pm4.5 km s^-1 Mpc^-1 for the Hubble constant, which is fully consistent
with the best modern determinations, and that is not biased by evolutionary
corrections.
