Jet angular correlation in vector-boson fusion processes at hadron colliders

Higgs boson and massive-graviton productions in association with two jets via vector-boson fusion (VBF) processes and their decays into a vector-boson pair at hadron colliders are studied. They include scalar and tensor boson production processes via weak-boson fusion in quark-quark collisions, gluon fusion in quark-quark (qq), quark-gluon (qg) and gluon-gluon (gg) collisions, as well as their decays into a pair of weak bosons or virtual gluons which subsequently decay into l (l) over bar, q (q) over bar or gg. We give the helicity amplitudes explicitly for all the VBF subprocesses, and show that the VBF amplitudes dominate the exact matrix elements not only for the weak-boson fusion processes but also for all the gluon fusion processes when appropriate selection cuts are applied, such as a large rapidity separation between two jets and a slicing cut for the transverse momenta of the jets. We also show that our off-shell vector-boson current amplitudes reduce to the standard quark and gluon splitting amplitudes with appropriate gluon-polarization phases in the collinear limit. Nontrivial azimuthal angle correlations of the jets in the production and in the decay of massive spin-0 and -2 bosons are manifestly expressed as the quantum interference among different helicity states of the intermediate vector-bosons. Those correlations reflect the spin and the CP nature of the Higgs bosons and the massive gravitons.