RR Lyrae variables in Galactic globular clusters: IV. Synthetic HB and   RR Lyrae predictions
  We present theoretical predictions concerning horizontal branch stars in globular clusters, including RR Lyrae variables, as derived from synthetic procedures collating evolutionary and pulsational constraints. On this basis, we explore the predicted behavior of the pulsators as a function of the horizontal branch morphology and over the metallicity range Z=0.0001 to 0.006, revealing an encouraging concordance with the observed distribution of fundamentalised periods with metallicity. Theoretical relations connecting periods to K magnitudes and BV or VI Wesenheit functions are presented, both appearing quite independent of the horizontal branch morphology only with Z greater or equal than 0.001. Predictions concerning the parameter R are also discussed and compared under various assumptions about the horizontal branch reference luminosity level. 
S. Cassisi, M. Castellani, F. Caputo, V. Castellani