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We present a new set of tools to derive systemic velocities for single-mode RR Lyrae stars from visual and near-infrared spectra. We derived scaling relations and line-of-sight velocity templates using both APOGEE andGaiaspectroscopic products combined with photometricG-band amplitudes. We provide a means to estimate systemic velocities for the RR Lyrae subclasses, RRab and RRc. Our analysis indicates that the scaling relation between the photometric and line-of-sight velocity amplitudes is nonlinear, with a break in a linear relation occurring around ≈0.4 mag in both theV-band andG-band amplitudes. We did not observe such a break in the relation for the first-overtone pulsators. Using stellar pulsation models, we further confirm and examine the nonlinearity in scaling relation for the RRab subclass. We observed little to no variation with stellar parameters (mass, metallicity, and luminosity) in the scaling relation between the photometric and line-of-sight velocity amplitudes for fundamental-mode pulsators. We observed an offset in the scaling relation between the observations and stellar pulsation models, mainly in the low-amplitude RR Lyrae regime. This offset disappears when different sets of convective parameters are used. Thus, the Fourier amplitudes obtained from the photometry and line-of-sight velocity measurements can be utilized to constrain convective parameters of stellar pulsation models. The scaling relations and templates for APOGEE andGaiadata accurately predict systemic velocities compared to literature values. In addition, our tools derived from theGaiaspectra improve the precision of the derived systemic velocities by approximately 50 percent and provide a better description of the uncertainty distribution in comparison with previous studies. Our newly derived tools will be used for RR Lyrae variables observed toward the Galactic bulge. 

We present a new set of period–absolute magnitude–metallicity (PMZ) relations for single-mode RR Lyrae stars calibrated for the opticalG_BP,V,G,G_RP, near-infraredI,J,H, andK_spassbands. We compiled a large dataset (over 100 objects) of fundamental and first-overtone RR Lyrae pulsators consisting of mean intensity magnitudes, reddenings, pulsation properties, iron abundances, and parallaxes measured by theGaiaastrometric satellite in its third data release. Our newly calibrated PMZ relations encapsulate the most up-to-date ingredients in terms of both data and methodology. They are intended to be used in conjunction with large photometric surveys targeting the Galactic bulge, including the Optical Gravitational Lensing Experiment (OGLE), the Vista Variables in the Vía Láctea Survey (VVV), and theGaiacatalog. In addition, our Bayesian probabilistic approach provides accurate uncertainty estimates of the predicted absolute magnitudes of individual RR Lyrae stars. Our derived PMZ relations provide consistent results when compared to benchmark distances to globular clusters NGC 6121 (also known as M 4), NGC 5139 (also known as omega Cen), and Large and Small Magellanic Clouds, which are stellar systems rich in RR Lyrae stars. Lastly, ourK_s-band PMZ relations match well with the previously published PMZ relations based onGaiadata and accurately predict the distance toward the prototype of this class of variables, the eponymic RR Lyr itself.