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The amount of mass lost by stars during the red-giant branch (RGB) phase isone of the main parameters to understand and correctly model the late stages ofstellar evolution. Nevertheless, a fully-comprehensive knowledge of the RGBmass loss is still missing.  Galactic Globular Clusters (GCs) are ideal targets to derive empiricalformulations of mass loss, but the presence of multiple populations withdifferent chemical compositions has been a major challenge to constrain stellarmasses and RGB mass losses. Recent work has disentangled the distinct stellarpopulations along the RGB and the horizontal branch (HB) of 46 GCs, thusproviding the possibility to estimate the RGB mass loss of each stellarpopulation. The mass losses inferred for the stellar populations with pristinechemical composition (called first-generation or 1G stars) tightly correlatewith cluster metallicity. This finding allows us to derive an empirical RGBmass-loss law for 1G stars.  In this paper we investigate seven GCs with no evidence of multiplepopulations and derive the RGB mass loss by means of high-precision {\itHubble-Space Telescope} photometry and accurate synthetic photometry.  We find a cluster-to-cluster variation in the mass loss ranging from$\sim$0.1 to $\sim$0.3 $M_{\odot}$.  The RGB mass loss of simple-population GCs correlates with the metallicity ofthe host cluster. The discovery that simple-population GCs and 1G stars ofmultiple population GCs follow similar mass-loss vs. metallicity relationssuggests that the resulting mass-loss law is a standard outcome of stellarevolution.

Mass loss law for red giant stars in simple population globular clusters