Is there any evidence that ionised outflows quench star formation in
  type 1 quasars at z<1?
  The aim of this paper is to test the basic model of negative AGN feedback.
According to this model, once the central black hole accretes at the Eddington
limit and reaches a certain critical mass, AGN driven outflows blow out gas,
suppressing star formation in the host galaxy and self-regulating black hole
growth. We consider a sample of 224 quasars selected from the SDSS at z<1
observed in the infrared band by Herschel. We evaluate the star formation rate
in relation to several outflow signatures traced by the [OIII]4959,5007 and
[OII]3726,3729 emission lines in about half of the sample with high quality
spectra. Most of the quasars show asymmetric and broad wings in [OIII], which
we interpret as outflow signatures. We separate the quasars in two groups,
``weakly'' and ``strongly'' outflowing, using three different criteria. When we
compare the mean star formation rate in five redshift bins in the two groups,
we find that the SFRs are comparable or slightly larger in the strongly
outflowing quasars. We estimate the stellar mass from SED fitting and the
quasars are distributed along the star formation main sequence, although with a
large scatter. The scatter from this relation is uncorrelated with respect to
the kinematic properties of the outflow. Moreover, for quasars dominated in the
infrared by starburst or by AGN emission, we do not find any correlation
between the star formation rate and the velocity of the outflow, a trend
previously reported in the literature for pure starburst galaxies. We conclude
that the basic AGN negative feedback scenario seems not to agree with our
results. Although we use a large sample of quasars, we did not find any
evidence that the star formation rate is suppressed in the presence of AGN
driven outflows on large scale. A possibility is that feedback is effective
over much longer timescales than those of single episodes of quasar activity.
