  We extend our previous work [1] on calculating non-global logarithms in $e^+
e^-$ annihilation to Higgs/vector boson production in association with a single
hard jet at hadron colliders. We analytically compute non-global coefficients
in the jet mass distribution up to four loops using the anti-k$_t$ jet
algorithm. Our calculations are performed in the eikonal approximation,
assuming strong energy ordering for the emitted gluons, thus capturing only the
leading logarithms of the distribution. We compare our analytical results with
the all-orders large-N$_c$ numerical solution. In general, the gross features
of the non-global logarithm distribution observed in the $e^+ e^-$ case remain
valid for the V/H+jet processes.
