We obtain stringent constraints on the actual efficiency of mass loss for red giant branch stars in the Galactic globular cluster 47 Tuc, by comparing synthetic modeling based on stellar evolution tracks with the observed distribution of stars along the horizontal branch in the colour-magnitude-diagram. We confirm that the observed, wedge-shaped distribution of the horizontal branch can be reproduced only by accounting for a range of initial He abundances --in agreement with inferences from the analysis of the main sequence-- and a red giant branch mass loss with a small dispersion. We have carefully investigated several possible sources of uncertainty that could affect the results of the horizontal branch modeling, stemming from uncertainties in both stellar model computations and the cluster properties such as heavy element abundances, reddening and age. We determine a firm lower limit of ~0.17$Mo for the mass lost by red giant branch stars, corresponding to horizontal branch stellar masses between ~0.65Mo and ~0.73Mo (the range driven by the range of initial helium abundances). We also derive that in this cluster the amount of mass lost along the asymptotic giant branch stars is comparable to the mass lost during the previous red giant branch phase. These results confirm for this cluster the disagreement between colour-magnitude-diagram analyses and inferences from recent studies of the dynamics of the cluster stars, that predict a much less efficient red giant branch mass loss. A comparison between the results from these two techniques applied to other clusters is required, to gain more insights about the origin of this disagreement.
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