  Weak gravitational lensing has been used extensively in the past decade to
constrain the masses of galaxy clusters, and is the most promising
observational technique for providing the mass calibration necessary for
precision cosmology with clusters. There are several challenges in estimating
cluster masses, particularly (a) the sensitivity to astrophysical effects and
observational systematics that modify the signal relative to the theoretical
expectations, and (b) biases that can arise due to assumptions in the mass
estimation method, such as the assumed radial profile of the cluster. All of
these challenges are more problematic in the inner regions of the cluster,
suggesting that their influence would ideally be suppressed for the purpose of
mass estimation. However, at any given radius the differential surface density
measured by lensing is sensitive to all mass within that radius, and the
corrupted signal from the inner parts is spread out to all scales. We develop a
new statistic that is ideal for estimation of cluster masses because it
completely eliminates mass contributions below a chosen scale (which we suggest
should be about 20 per cent of the virial radius), and thus reduces sensitivity
to systematic and astrophysical effects. We use simulated and analytical
profiles to quantify systematic biases on the estimated masses for several
standard methods of mass estimation, finding that these can lead to significant
mass biases that range from ten to over fifty per cent. The mass uncertainties
when using our new statistic are reduced by up to a factor of ten relative to
the standard methods, while only moderately increasing the statistical errors.
This new method of mass estimation will enable a higher level of precision in
future science work with weak lensing mass estimates for galaxy clusters.
