Higgs couplings at high scales

We study the off-shell production of the Higgs boson at the LHC to probe Higgs physics at higher energy scales utilizing the process $gg\to h^{*}\to ZZ$. We focus on the energy scale dependence of the off-shell Higgs propagation, and of the top quark Yukawa coupling, $y_t(Q^2)$. Extending our recent study [D. Goncalves, T. Han, and S. Mukhopadhyay, Phys. Rev. Lett. 120, 111801 (2018).], we first discuss threshold effects in the Higgs propagator due to the existence of new states, such as a gauge singlet scalar portal, and a possible continuum of states in a conformal limit, both of which would be difficult to discover in other traditional searches. We then examine the modification of $y_t(Q^2)$ from its Standard Model (SM) prediction in terms of the renormalization group running of the top Yukawa, which could be significant in the presence of large flat extra dimensions. Finally, we explore possible strongly coupled new physics in the top-Higgs sector that can lead to the appearance of a nonlocal $Q^2$-dependent form factor in the effective top-Higgs vertex. We find that considerable deviations compared to the SM prediction in the invariant mass distribution of the $Z$-boson pair can be conceivable, and may be probed at the $2\sigma$ level at the high-luminosity 14 TeV HL-LHC for a new physics scale up to $\mathcal{O}(1\mathrm{TeV})$, and at the upgraded 27 TeV HE-LHC for a scale up to $\mathcal{O}(3\mathrm{TeV})$. For a few favorable scenarios, $5\sigma$ level observation may be possible at the HE-LHC for a scale of about $\mathcal{O}(1\mathrm{TeV})$.

Figure 1

Representative set of Feynman diagrams for $gg\to ZZ$ production in the SM involving the Higgs boson (left) and the SM fermion box diagram (right).

Figure 2

Four-lepton invariant mass distribution for the $gg\to 4\ell$ process in the full SM (red), the triangle component ${\sigma }_{tt}$ (black dashed), the box component ${\sigma }_{cc}$ (black solid), and the interference between them ${\sigma }_{tc}$ (black dotted), for the LHC at 14 TeV (left) and 27 TeV (right).

Figure 3

Representative set of Feynman diagrams for the one-loop corrections to $gg\to ZZ$ production from the singlet scalar sector.

Figure 4

Real (left) and imaginary (right) 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 5

Four-lepton invariant mass distribution for the $gg\to 4\ell$ process at the 14 TeV (left) and 27 TeV LHC (center) in the SM (black) and in the presence of an additional gauge singlet scalar (red), including the one-loop EW effects from the singlet scalar sector. We show the signal ratio between the scalar singlet model and the SM in the bottom panels. Right: $2\sigma$ (red) and $5\sigma$ (blue) sensitivities on the singlet-Higgs coupling ${\lambda }_S$ at the scale $m_h^2$ as a function of the singlet scalar 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). For comparison, we also show the reach from the weak-boson fusion production of the Higgs above its threshold, assuming the high-luminosity LHC $2\sigma$ confidence level projections of $\mathcal{B}\mathcal{R}(h\to \text{invisible})<20\%$ (green dotted) and 5% (green dashed).

Figure 6

Real (left) and imaginary (right) components for the amplitude ratio between the $s$-channel quantum critical Higgs ${\mathcal{M}}_{h,\mathrm{QCH}}$ and SM ${\mathcal{M}}_{h,\mathrm{SM}}$ as a function of $m_{4\ell }$. We present two BSM scenarios $\mu =400\mathrm{GeV}$ (red) and $\mu =700\mathrm{GeV}$ (green), assuming $\mathrm{\Delta }=1.3$.

Figure 7

Four-lepton invariant mass distribution for the $gg\to 4\ell$ process at the 14 TeV (left) and 27 TeV LHC (center) for the SM (black) and quantum critical Higgs with $\mathrm{\Delta }=1.3$ and $\mu =400\mathrm{GeV}$ (red) and $\mu =700\mathrm{GeV}$ (green). We show the signal ratio between the QCH model and the SM in the bottom panels. Right: $5\sigma$ (blue) and $2\sigma$ (red) bounds on the conformal symmetry breaking scale $\mu$. We show results for the 14 TeV LHC (dashed) and the 27 TeV HE-LHC (solid), assuming $\mathrm{\Delta }=1.1$.

Figure 8

LO RGE running of top Yukawa $y_t$ as a function of the energy scale $\mu$, in the SM (black solid), the MSSM (green long-dashed), a model with one extra dimension (blue dot-dashed) and one with two extra dimensions (red short-dashed). In the MSSM case the common mass of the sparticles is taken to be 500 GeV. In the extra-dimensional scenarios (with inverse radius $1/R=500\mathrm{GeV}$) only the SM gauge fields are assumed to propagate in the bulk, while the matter fields are confined to the brane.

Figure 9

Four-lepton invariant mass distribution for the $gg\to 4\ell$ process at the 14 TeV (left) and 27 TeV LHC (center) for the SM (black), and the 5D (red solid) and 6D (red dashed) extra-dimensional models, including the respective RGE evolution for $y_t$, at the $\sqrt{s}=14\mathrm{TeV}$ LHC (left) and the 27 TeV HE-LHC (center), with the inverse radius $1/R=500\mathrm{GeV}$. We show the signal ratio between the extra-dimensional model and the SM in the bottom panels. Right: $2\sigma$ (red) and $5\sigma$ (blue) bounds on the 6D model scale $1/R$ at the HE-LHC.

Figure 10

Top: Four-lepton invariant mass distribution for the $gg\to 4\ell$ process at the 14 TeV (upper left) and 27 TeV LHC (upper right) in the SM (black) and in the presence of a form factor in the Higgs-top coupling for a strong interaction scale $\mathrm{\Lambda }=1.5\mathrm{TeV}$ (red). We show the signal ratio between the form factor model and the SM in the bottom panels. Bottom: $5\sigma$ (blue) and $2\sigma$ (red) bounds on the scale $\mathrm{\Lambda }$, for two different form factor scenarios with $n=2$ (dashed) and $n=3$ (solid), at the 14 TeV (left) and 27 TeV (right) LHC.