Hadronic production of $W$ and $Z$ bosons at large transverse momentum

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, ${\alpha }_s^m{\ln }^m(p_T^2\mathrm{/}{Q}^2)$, 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 $5\mathrm{\%}$ 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.