Panchromatic calibration of Ca II triplet luminosity dependence

(ABRIDGED) Context. The line strength of the Ca II triplet (CaT) lines are a proxy to measure metallicity from individual stellar spectra of bright red giant stars. It is a mandatory step to remove the magnitude (proxy for gravity, temperature and luminosity) dependence from the equivalent width (EW) of the lines before converting them into metallicities. The working empirical procedure used for decades is to use the relative magnitude with respect to the horizontal branch level. Aims. The V filter is broadly adopted as the reference magnitude, although a few works have used different filters (I and Ks, for example). In this work we investigate the dependence of the CaT calibration using griz filters from the DECam and the GMOS, G from Gaia, BVI filters from the MCPS, YJKs filters from VIRCAM. We use as a reference FORS2 V filter used in the original analysis of the sample. Methods. Red giant stars from clusters with known metallicity and available CaT equivalent widths are used as reference. Public photometric catalogues are taken from SMASH DR2, VMC, Gaia, MCPS surveys plus VISCACHA-GMOS data, for a selection of Small Magellanic Cloud clusters. The slopes are fitted using two and three lines to be applicable to most of the metallicity scales. Results. The magnitude dependence of the CaT EWs is well described by a linear relation using any filter analysed in this work. The slope increases with wavelength of the filters. The zero point (a.k.a. reduced equivalent width), that is the metallicity indicator, remains the same. Conclusions. If the same line profile function is used with the same bandpasses and continuum regions, and the total EW comes from the same number of lines (2 or 3), then the reduced EW is the same regardless the filter used. Therefore, any filter can be used to convert the CaT equivalent widths into metallicity for a given CaT calibration.