We present new nonlinear, time-dependent convective hydrodynamical models of RR Lyrae stars computed assuming a constant helium-to-metal enrichment ratio and a broad range in metal abundances (Z = 0.0001-0.02). The stellar masses and luminosities adopted to construct the pulsation models were fixed according to detailed central He burning Horizontal Branch evolutionary models. The pulsation models cover a broad range in stellar luminosity and effective temperatures and the modal stability is investigated for both fundamental and first overtones. We predict the topology of the instability strip as a function of the metal content and new analytical relations for the edges of the instability strip in the observational plane. Moreover, a new analytical relation to constrain the pulsation mass of double pulsators as a function of the period ratio and the metal content is provided. We derive new Period-Radius-Metallicity relations for fundamental and first-overtone pulsators. They agree quite well with similar empirical and theoretical relations in the literature. From the predicted bolometric light curves, transformed into optical (U BVRI) and near-infrared (JHK) bands, we compute the intensity-averaged mean magnitudes along the entire pulsation cycle and, in turn, new and homogenous metaldependent (RI JHK) Period-Luminosity relations. Moreover, we compute new dual and triple band optical, optical-NIR and NIR Period-Wesenheit-Metallicity relations. Interestingly, we find that the optical Period-W(V, B − V) is independent of the metal content and that the accuracy of individual distances is a balance between the adopted diagnostics and the precision of photometric and spectroscopic datasets.

We present new distance determinations to the nearby globular M4 (NGC 6121) based on accurate optical and Near Infrared (NIR) mean magnitudes for fundamental (FU) and first overtone (FO) RR Lyrae variables (RRLs), and new empirical optical and NIR Period-Luminosity (PL) and Period-Wesenheit (PW) relations. We have found that optical-NIR and NIR PL and PW relations are affected by smaller standard deviations than optical relations. The difference is the consequence of a steady decrease in the intrinsic spread of cluster RRL apparent magnitudes at fixed period as longer wavelengths are considered. The weighted mean visual apparent magnitude of 44 cluster RRLs is V = 13.329 ± 0.001 (standard error of the mean) ±0.177 (weighted standard deviation) mag. Distances were estimated using RR Lyr itself to fix the zero-point of the empirical PL and PW relations. Using the entire sample (FU+FO) we found weighted mean true distance moduli of 11.35±0.03±0.05 mag and 11.32±0.02±0.07 mag. Distances were also evaluated using predicted metallicity dependent PLZ and PWZ relations. We found weighted mean true distance moduli of 11.283±0.010±0.018 mag (NIR PLZ) and 11.272±0.005±0.019 mag (optical-NIR and NIR PWZ). The above weighted mean true distance moduli agree within 1σ. The same result is found from distances based on PWZ relations in which the color index is independent of the adopted magnitude (11.272±0.004±0.013 mag). These distances agree quite well with the geometric distance provided by (Kaluzny et al. 2013) based on three eclipsing binaries. The available evidence indicates that this approach can provide distances to globulars hosting RRLs with a precision better than 2-3%.