Off-Shell Higgs Probe of Naturalness

Examining the Higgs sector at high energy scales through off-shell Higgs production can potentially shed light on the naturalness problem of the Higgs boson mass. We propose such a study at the LHC by utilizing a representative model with a new scalar field (S) coupled to the standard model Higgs doublet (H) in a form |S|^{2}|H|^{2}. In the process pp→h^{*}→ZZ, the dominant momentum-dependent part of the one-loop scalar singlet corrections, especially above the new threshold at 2m_{S}, leads to a measurable deviation in the differential distribution of the Z-pair invariant mass, in accordance with the quadratic divergence cancellation to the Higgs mass. We find that it is conceivable to probe such new physics at the 5σ level at the high-luminosity LHC, improving further with the upgraded 27 TeV LHC, without requiring the precise measurement of the Higgs boson total width. The discovery of such a Higgs portal could also have important implications for thermal dark matter as well as for electroweak baryogenesis.