  We introduce a modified factorization formalism in quantum chromodynamics for
hadronic production of $W$ and $Z$ bosons at large transverse momentum $p_T$.
When $p_T$ is much larger than the invariant mass $Q$ of the vector boson, this
new factorization formalism systematically resums the large fragmentation
logarithms, $\alpha_s^m\ln^m(p_T^2/Q^2)$, to all orders in the strong coupling
$\alpha_s$. Using our modified factorization formalism, we calculate the
next-to-leading order (NLO) predictions for $W$ and $Z$ boson production at
high $p_T$ at the CERN Large Hadron Collider and at a future 100 TeV
proton-proton collider. Our NLO results are about $5\%$ larger in
normalization, and they show improved convergence and moderate reduction of the
scale variation compared to the NLO predictions derived in a conventional
fixed-order perturbative expansion.
