  The phenomenology of Standard Model and New Physics at hadron colliders
depends critically on results from global QCD analysis for parton distribution
functions (PDFs). The accuracy of the standard next-to-leading-order (NLO)
global analysis, nominally a few percent, is generally well matched to the
expected experimental precision. However, serious questions have been raised
recently about the stability of the NLO analysis with respect to certain
inputs, including the choice of kinematic cuts on the data sets and the
parametrization of the gluon distribution. In this paper, we investigate this
stability issue systematically within the CTEQ framework. We find that both the
PDFs and their physical predictions are stable, well within the few percent
level. Further, we have applied the Lagrange Multiplier method to explore the
stability of the predicted cross sections for W production at the Tevatron and
the LHC, since W production is often proposed as a standard candle for these
colliders. We find the NLO predictions on sigma_W to be stable well within
their previously-estimated uncertainty ranges.
