Consistent lensing and clustering in a low-$S_8$ Universe with BOSS, DES
  Year 3, HSC Year 1 and KiDS-1000
  We evaluate the consistency between lensing and clustering probes of
large-scale structure based on measurements of projected galaxy clustering from
BOSS combined with overlapping galaxy-galaxy lensing from three surveys: DES
Y3, HSC Y1, and KiDS-1000. An intra-lensing-survey study finds good agreement
between these lensing data. We model the observations using the Dark Emulator
and fit the data at two fixed cosmologies: Planck, with $S_8=0.83$, and a
Lensing cosmology with $S_8=0.76$. For a joint analysis limited to scales with
$R>5.25h^{-1}$Mpc, we find that both cosmologies provide an acceptable fit to
the data. Full utilisation of the small-scale clustering and lensing
measurements is hindered by uncertainty in the impact of baryon feedback and
assembly bias, which we account for with a reasoned theoretical error budget.
We incorporate a systematic scaling parameter for each redshift bin, $A$, that
decouples the lensing and clustering to capture any inconsistency. When a wide
range of scales ($0.15<R<60h^{-1}$Mpc) are incorporated, we find different
results for the consistency of clustering and lensing between the two
cosmologies. Limiting the analysis to the bins for which the impact of the
selection of the lens sample is expected to be minimal, for the low-$S_8$
Lensing cosmology, the measurements are consistent with $A$=1; $A=0.91\pm0.04$
using DES+KiDS and $A=0.97\pm0.06$ using HSC. For the Planck cosmology case, we
find a discrepancy: $A=0.79\pm0.03$ using DES+KiDS and $A=0.84\pm0.05$ using
HSC. We demonstrate that a kSZ-based estimate for baryonic effects alleviates
some of the discrepancy in the Planck cosmology. This analysis demonstrates the
statistical power of these small-scale measurements, but also indicates that
caution is still warranted given current uncertainties in modelling baryonic
effects, assembly bias, and selection effects in the foreground sample.
