Examining the Higgs boson potential at lepton and hadron colliders: a comparative analysis

TL;DR

The paper assesses how well the Higgs self-coupling $λ$ and the Higgs potential $V(η_H)$ can be reconstructed at future hadron and lepton colliders across $120~\text{GeV}<m_H<200~\text{GeV}$. It shows that hadron colliders face severe backgrounds in the low-mass region, limiting $λ$ sensitivity there, while 0.5–1 TeV $e^+e^-$ colliders provide competitive precision for $m_H\lesssim 140$ GeV; for $m_H>150$ GeV, higher-energy facilities (CLIC, VLHC) are required to achieve meaningful constraints. The analysis highlights strong complementarity between collider types: to map the Higgs potential robustly, one needs a coordinated program spanning hadron, linear, and multi-TeV colliders. The results quantify how different final states (e.g., $pp\to HH\to 4b$, $pp\to bb\tau\tau$, $ZHH$, $HH\nu\bar{ν}$) contribute to constraints on $λ$ and illustrate the practical challenges of measuring the Higgs self-coupling across the explored mass range.

Abstract

We investigate inclusive Standard Model Higgs boson pair production at lepton and hadron colliders for Higgs boson masses in the range 120 GeV < m_H < 200 GeV. For m_H < 140 GeV we find that hadron colliders have a very limited capability to determine the Higgs boson self-coupling, λ, due to an overwhelming background. We also find that, in this mass range, supersymmetric Higgs boson pairs may be observable at the LHC, but a measurement of the self coupling will not be possible. For m_H > 140 GeV we examine ZHH and HH nu bar-nu production at a future e+e- linear collider with center of mass energy in the range of sqrt{s}=0.5 - 1 TeV, and find that this is likely to be equally difficult. Combining our results with those of previous literature, which has demonstrated the capability of hadron and lepton machines to determine λin either the high or the low mass regions, we establish a very strong complementarity of these machines.

Figures (10)

• Figure 1: Distribution of the visible invariant mass, $m_{vis}$, in $pp\to 4b$, after all kinematic cuts (Eqs. (\ref{['eq:cuts1']}) -- (\ref{['eq:cuts3']})), for the QCD continuum background (solid) and the SM signal for $m_H=120$ GeV (dashed) at the LHC. The dotted and dot-dashed lines show the signal cross section for $\lambda_{HHH}=\lambda/\lambda_{SM}=0$ and $\lambda_{HHH}=2$, respectively.
• Figure 2: Distribution of the visible invariant mass, $m_{vis}$, after all kinematic cuts, in $pp\to b\bar{b}\tau_\ell\tau_h$ for the SM signal with $m_H=120$ GeV (solid), the QCD continuum background (dashed) and the $t\bar{t}$ background (a) at the LHC, and (b) at the VLHC. $\tau_\ell$ ($\tau_h$) indicates that the $\tau$ lepton decays leptonically (hadronically).
• Figure 3: The total $e^+e^-\to ZHH$ cross section times branching ratio for $\sqrt{s}=500$ GeV (solid lines) and $\sqrt{s}=1$ TeV (dashed lines) for various final states.
• Figure 4: The $e^+e^-\to HH\nu\bar{\nu}$ cross section times branching ratio for $\sqrt{s}=500$ GeV (solid lines), $\sqrt{s}=800$ GeV (dashed lines) and $\sqrt{s}=1$ TeV (dotted lines) for various final states. The curves for $HH\to 4b$ also contain the efficiency for tagging four $b$-quarks.
• Figure 5: Estimated $1\sigma$ limits achievable for $\Delta\lambda_{HHH}=(\lambda-\lambda_{SM})/\lambda_{SM}$ in $e^+e^-\to ZHH$, $Z\to\ell\ell,\, jj$, $HH\to b+$ jets ($\ell=e,\,\mu$) for $\sqrt{s}=500$ GeV (solid lines), $\sqrt{s}=800$ GeV (dashed lines), and $\sqrt{s}=1$ TeV (dotted lines) and an integrated luminosity of 1 ab$^{-1}$. The allowed region is between the two lines of equal texture.