  We present a resummation-improved prediction for $VH$ + 0 jets production at
the Large Hadron Collider. We focus on highly-boosted final states in the
presence of jet veto to suppress the $t{\bar t}$ background. In this case,
conventional fixed-order calculations are plagued by the existence of large
Sudakov logarithms $\alpha_s^n \log^m (p_T^{veto}/Q)$ for $Q\sim m_V + m_H$
which lead to unreliable predictions as well as large theoretical
uncertainties, and thus limit the accuracy when comparing experimental
measurements to the Standard Model. In this work, we show that the resummation
of Sudakov logarithms beyond the next-to-next-to-leading-log accuracy, combined
with the next-to-next-to-leading order calculation, reduces the scale
uncertainty and stabilizes the perturbative expansion in the region where the
vector bosons carry large transverse momentum. Our result improves the
precision with which Higgs properties can be determined from LHC measurements
using boosted Higgs techniques.
