Reconciling Planck cluster counts and cosmology? Chandra/XMM
  instrumental calibration and hydrostatic mass bias
  The mass of galaxy clusters can be inferred from the temperature of their
X-ray emitting gas, $T_{\mathrm{X}}$. Their masses may be underestimated if it
is assumed that the gas is in hydrostatic equilibrium, by an amount
$b^{\mathrm{hyd}}\sim(20\pm10)$ % suggested by simulations. We have previously
found consistency between a sample of observed \textit{Chandra} X-ray masses
and independent weak lensing measurements. Unfortunately, uncertainties in the
instrumental calibration of {\em Chandra} and {\em XMM-Newton} observatories
mean that they measure different temperatures for the same gas. In this paper,
we translate that relative instrumental bias into mass bias, and infer that
\textit{XMM-Newton} masses of $\sim 10^{14}\,\mbox{M}_{\odot}$ ($> 5\cdot
10^{14} \mbox{M}_{\odot}$) clusters are unbiased ($\sim 35$ % lower) compared
to WL masses. For massive clusters, \textit{Chandra}'s calibration may thus be
more accurate. The opposite appears to be true at the low mass end. We observe
the mass bias to increase with cluster mass, but presence of Eddington bias
precludes firm conclusions at this stage. Nevertheless, the systematic
\textit{Chandra} -- \textit{XMM-Newton} difference is important because {\em
Planck}'s detections of massive clusters via the Sunyaev-Zeldovich (SZ) effect
are calibrated via {\em XMM-Newton} observations. The number of detected SZ
clusters are inconsistent with {\em Planck}'s cosmological measurements of the
primary Cosmic Microwave Background (CMB). Given the \textit{Planck} cluster
masses, if an (unlikely) uncorrected $\sim 20$ % calibration bias existed, this
tension would be eased, but not resolved.
