Synthetic horizontal branches are constructed from a grid of horizontal-branch (HB) evolutionary tracks with the alpha-elements (O, Ne, Mg, and Ca) enhanced by a factor of 5 with respect to the solar-scaled mixture ([alpha/Fe] = 0.7) and various surface helium [Y(HB) = 0.20, 0.25) and heavy-element ([Fe/H] = -1.27, -2.27) abundances. The relevant constraints on HB morphology and mean properties of RR Lyrae variables are presented and discussed. The comparison of alpha-enriched with canonical ([alpha/Fe] = 0) computations shows that, with the helium content and the overall metallicity Z fixed, the luminosity log L(3.83) and the mass-to-light ratio A(3.83) of the ZAHB at the mean temperature of the RR Lyrae gap have virtually no dependence on the ratio between alpha-and heavy-element abundances. This leads to general log L(3.83) versus log Z and A(3.83) versus log Z relations which hold irrespective of the adopted enhancement of alpha-elements. From our alpha-enhanced synthetic models of HB, we obtain that the mean luminosity <log L> and mass-to-light ratio <A> of RR Lyrae variables depend on metallicity as well as HB morphology, in agreement with recent canonical calculations by Lee, Demarque, and Zinn. At Y(HB) = 0.25, [alpha/Fe] = 0.7, and -2.3 < [Fe/H] < -1.3, we find <log L> = 1.524 - 0.078[Fe/H] and <A> = 1.743 -0.038[Fe/H], for (B - R)/(B + V + R) < 0.7, while for bluer HB types we get <log L> = 1.445 - 0.076[Fe/H] + 0.111(B - R)/(B + V + R) and <A> = 1.613 - 0.031[Fe/H] + 0.201(B - R) (B + V + R). On these grounds, the observed relationship between mass-to-light ratio and [Fe/H] (Sandage) is analyzed. The result is that all the observational data-except for M15-could be fitted to within the errors with [alpha/Fe] in the range 0.7-0.4 and a constant primordial helium Y(MS) approximately 0.23, eliminating in this way the requirement for a sizable anticorrelation of helium with metals and/or other ad hoc assumptions which had been suggested in previous work. As for M15, several possible explanation are presented, without a satisfactory solution. From HB models and isochrone computations at Y(MS) = 0.23 we find that the predicted difference in bolometric magnitude DELTA-M(bol)(TO - HB) between the main-sequence turnoff and the zero-age horizontal branch at the RR Lyrae gap is rather insensitive to metallicity. This result, when combined with Buonanno, Corsi, and Fusi Pecci's observations of a sample of Galactic globular clusters, yields at [alpha/Fe] = 0, a mean age of 16.9 +/- 1.5 Gyr, with on the average approximately 17.9 Gyr at [Fe/H] = -2.3 and approximately 15.8 Gyr at [Fe/H] = -0.8. Concerning the effect of no scaled-solar mixture, we find that the age is rather independent of the degree of alpha-enhancement. Specifically, if [alpha/Fe] = 0.7 or 0.4, then the slope of the age versus [Fe/H] relationship becomes slightly milder, and the mean age of that sample is reduced by roughly approximately 1 and approximately 0.5 Gyr, respectively. Concerning the problem of the age spread among clusters of the same metallicity, present results seem to confirm the existence of a relation between age and HB morphology which has been recently suggested by Sarajedini & King.
