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 $pp\to h^{*}\to ZZ$, 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 $5\sigma$ 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.

Figure 1

Representative set of Feynman diagrams for the one-loop corrections to $gg\to ZZ$ production, in the SM augmented by a gauge singlet scalar.

Figure 2

Real (top) and imaginary (bottom) parts of the Higgs boson renormalized self-energy corrections ${\widehat{\mathrm{\Sigma }}}_h$, scaled by the propagator factor $p^2-{\mu }_h^2$, as a function of $m_{4\ell }$.

Figure 3

Four lepton invariant mass distribution for the loop-induced $gg\to 4\ell$ process at the 14 TeV LHC in the SM (black) and in the presence of an additional scalar gauge singlet (red), including the leading one-loop electroweak effects from the additional scalar singlet. We display the signal ratio between the scalar singlet model and the SM in the bottom panel.

Figure 4

$2\sigma$ (red) and $5\sigma$ (blue) sensitivity on the singlet-Higgs coupling ${\lambda }_S$ as a function of the singlet mass $m_S$ from the off-shell Higgs analysis at the 14 TeV LHC, with $\mathcal{L}=3{\mathrm{ab}}^{-1}$ (dashed) and at the 27 TeV LHC, with $\mathcal{L}=15{\mathrm{ab}}^{-1}$ (solid). The $q\overline{q}\to ZZ$ and $gg\to ZZ$ backgrounds are taken into account for this estimate. For comparison, we also show the reach from VBF production of Higgs above its threshold, assuming the high-luminosity LHC $2\sigma$ level bounds $\mathcal{B}\mathcal{R}(h\to \text{invisible})<20\%$ (green dotted) and 5% (green dashed).