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We present newly-calibrated period-$\phi_{31}$-[Fe/H] relations forfundamental mode RR Lyrae stars in the optical and, for the first time,mid-infrared. This work's calibration dataset provides the largest and mostcomprehensive span of parameter space to date with homogeneous metallicitiesfrom $-3<\textrm{[Fe/H]}<0.4$ and accurate Fourier parameters derived from 1980ASAS-SN ($V$-band) and 1083 WISE (NEOWISE extension, $W1$ and $W2$ bands) RRLyrae stars with well-sampled light curves. We compare our opticalperiod-$\phi_{31}$-[Fe/H] with those available in the literature anddemonstrate that our relation minimizes systematic trends in the lower andhigher metallicity range. Moreover, a direct comparison shows that our opticalphotometric metallicities are consistent with both those from high-resolutionspectroscopy and globular clusters, supporting the good performance of ourrelation. We found an intrinsic scatter in the photometric metallicities (0.41dex in the $V$-band and 0.50 dex in the infrared) by utilizing largecalibration datasets covering a broad metallicity range. This scatter becomessmaller when optical and infrared bands are used together (0.37 dex). Overall,the relations derived in this work have many potential applications, includinglarge-area photometric surveys with JWST in the infrared and LSST in theoptical.

Metallicity of Galactic RR Lyrae from Optical and Infrared Light Curves: I. Period-Fourier-Metallicity Relations for Fundamental Mode RR Lyrae