I. Stellar mass at z < 1

et al.[Aims]: Long gamma-ray bursts (LGRBs) are associated with massive stars and are therefore linked to star formation. However, the conditions needed for the progenitor stars to produce LGRBs can affect the relation between the LGRB rate and star formation. By using the power of a complete LGRB sample, our long-term aim is to understand whether such a bias exists and, if it does, what its origin is. [Methods]: To reach our goal we use the Swift/BAT6 complete sample of LGRBs. In this first paper, we build the spectral energy distribution (SED) of the 14 z Black star) from SED fitting. To investigate the presence of a bias in the LGRB-star formation relation we compare the stellar mass distribution of the LGRB host galaxies (i) with star-forming galaxies observed in deep surveys (UltraVISTA) within the same redshift limit; (ii) with semi-analytical models of the z th = 0.3-0.5 Z⊙ is necessary to form a LGRB. Models without a metallicity threshold or with an extreme threshold of Zth = 0.1 Z⊙ are excluded at z ⊙) inferred by the comparison with the simulations can be a consequence of the particular conditions needed for the progenitor star to produce a GRB.A.F.S. acknowledges support from grants AYA2010-22111-C03-02 and AYA2013-48623-C2-2 from the Spanish Ministerio de Economia y Competitividad, and grants Prometeo 2009/064 and PrometeoII 2014/060 from the Generalitat Valenciana.Peer Reviewe