We have analyzed a sample of LBGs from z =3.5 to z=6 selected from the GOODS-S field as B,V and i-dropouts, and with spectroscopic observations showing that they have the Lyalpha line in emission. Our main aim is to investigate their physical properties and their dependence on the emission line characteristics, to shed light on the relation between galaxies with Lyalpha emission and the general LBG population.The objects were selected from their continuum colors and then spectroscopically confirmed by the GOODS collaboration and other campaigns. From the spectra we derived the line flux and EW. We then used U-band to mid-IR photometry from GOODS-MUSIC to derive the physical properties of the galaxies, such as total stellar mass, age and so on, through standard SED fitting techniques.Although most galaxies are fit by young stellar populations, a small but non negligible fraction has SEDs that require considerably older stellar component, up to 1 Gyr. There is no apparent relation between age and EW: some of the oldest galaxies have large EW, and should be also selected in narrow band surveys. Therefore not all Lyalpha emitters are primeval galaxies in the very early stages of formation,as is commonly assumed. We also find a large range of stellar populations, with masses from 5x10^8 Msol to 5x10^10 Msol and SFR from few to 60 Msol/yr. Although there is no correlation between mass and EW, we find a significant lack of massive galaxies with high EW, which could be explained if the most massive galaxies were more dusty and/or contained more neutral gas than less massive objects. Finally we find that more than half of the galaxies contain small but non negligible amounts of dust: the mean E(B-V) and the EW are well correlated, although with a large scatter, as already found at lower redshift
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