Milky Way Classical Cepheids Distances from Calibrated Infrared Period-Luminosity-Metallicity Relations

Classical Cepheids (DCEPs) serve as fundamental standard candles for measuring cosmic distances and investigating the structure and evolution of the Milky Way disc. However, accurate distance estimation faces challenges due to severe extinction, particularly toward the Galactic center. Although the $Gaia$ Wesenheit magnitude reduces extinction effects, its reliance on a constant optical extinction law introduces significant uncertainties in regions of heavy obscuration. Infrared Period-Luminosity relations, combined with 3D extinction maps, offer an alternative, but these maps become unreliable beyond approximately 5 kpc. In this work, we calibrate the Period-Luminosity-Metallicity (PLZ) relations for DCEPs across three near-infrared bands ($J, H, K_S$) and four mid-infrared bands ($W1, W2, [3.6]$, and $[4.5]$). This includes the first calibration of the $W1$ and $W2$ bands. To correct for extinction, we employ the infrared multi-passband optimal distance method and the BP-RP method, which complement and validate each other. These homogeneous PLZ relations, combined with reliable extinction corrections, yield the most accurate Galactic DCEP distances to date, covering 3,452 DCEPs with an average relative distance error of 3.1%.