Revisiting Vh( b(b)over-bar) at the LHC and FCC-hh

Diboson production processes provide good targets for precision measurements at present and future hadron colliders. We consider V h production, focusing on the h -> b (b) over bar decay channel, whose sizeable cross section makes it accessible at the LHC. We perform an improved analysis by combining the 0-, 1- and 2-lepton channels with a scale-invariant b-tagging algorithm that allows us to exploit events with either a boosted Higgs via mass-drop tagging or resolved b-jets. This strategy gives sensitivity to 4 dimension-6 SMEFT operators that modify the W and Z couplings to quarks and is competitive with the bounds obtained from global fits. The benefit of the h -> b (b) over bar decay channel is the fact that it is the only V h channel accessible at the LHC Run 3 and HL-LHC, while at FCC-hh it is competitive with the effectively background-free h -> gamma gamma channel assuming <= 5% systematic uncertainty. Combining the boosted and resolved categories yields a 17% improvement on the most strongly bounded Wilson coefficient at the LHC Run 3 with respect to the boosted category alone (and a 7% improvement at FCC-hh). We also show that, at FCC-hh, a binning in the rapidity of the V h system can significantly reduce correlations between some EFT operators. The bounds we obtain translate to a lower bound on the new physics scale of 5, 8, and 20 TeV at the LHC Run 3, HL-LHC, and FCC-hh respectively, assuming new-physics couplings of order unity. Finally, we assess the impact of the V h production channel on anomalous triple gauge coupling measurements, comparing with their determination at lepton colliders.