Tame D-tadpoles in gauge mediation

We revisit models of gauge mediated supersymmetry breaking where messenger parity is violated. Such a symmetry is usually invoked in order to set to zero potentially dangerous hypercharge D-term tadpoles. A milder hypothesis is that the D-tadpole vanishes only at the first order in the gauge coupling constant. Then the next order leads to a contribution to the sfermion masses which is of the same magnitude as the usual radiative one. This enlarges the parameter space of gauge mediated models. We first give a completely general characterization of this contribution, in terms of particular three-point functions of hidden sector current multiplet operators. We then explore the parameter space by means of two simple weakly coupled models, where the D-tadpole arising at two-loops has actually a mild logarithmic divergence.