An Indirect Model-Dependent Probe of the Higgs Self-Coupling

TL;DR

The paper proposes a model-dependent indirect approach to bound the Higgs self-coupling below the di-Higgs threshold by exploiting NLO corrections to the Higgs-strahlung process $e^+e^-\to hZ$. It derives a full one-loop EW correction that depends linearly on the self-coupling modification parameter $\delta_h$ and analyzes multiple realistic scenarios: (i) a single-parameter $\delta_h$ modification yielding about a $|\delta_h|\lesssim 28\%$ sensitivity at $\sqrt{s}=240$ GeV, (ii) combined $\delta_h$ and $\delta_Z$ leading to ellipse constraints when measurements are performed at different energies, (iii) the decoupling-limit 2HDM where $\delta_h$-driven NLO effects can dominate LO $hZZ$ modifications, and (iv) generic EFT contexts where cancellations between operators limit model-independence. The method provides complementary information to direct di-Higgs measurements and offers a concrete pathway to probing the Higgs potential in well-motivated theories such as 2HDMs, though it remains sensitive to assumptions about cancellations among new physics contributions.

Abstract

The Higgs associated production cross section at an $e^+ e^-$ collider is indirectly sensitive to the Higgs self-coupling, $h^3$, at next-to-leading order (NLO). Utilizing this, a new indirect method is proposed for constraining deviations in the self-coupling below the di-Higgs production threshold in certain models. Although this indirect constraint is model-dependent, making it valid only under specific assumptions, meaningful indirect constraints on the self-coupling may be realized. Specific realistic scenarios where the indirect constraint applies are discussed and in particular it is shown that in the well-motivated class of two Higgs-doublet models there exist regions of parameter space in which the NLO effects from a modified self-coupling dominate over the LO modifications, demonstrating a concrete scenario in which large modifications of the Higgs self-coupling may be indirectly constrained using the proposed method. Other models, such as strongly coupled scenarios, are also discussed. The indirect method would give valuable constraints on deviations in the Higgs self-coupling, and would be complementary to the direct measurements possible with di-Higgs production at other colliders, providing precious additional information in the effort to unravel the properties of the Higgs boson.

Figures (4)

• Figure 1: NLO vertex corrections to the associated production cross section which depend on the Higgs self-coupling. These terms lead to a linear dependence on modifications of the self-coupling $\delta_h$.
• Figure 2: Corrections to $\sigma (e^+ e^- \to hZ)$, for a given variation in the self-coupling, $\delta_h$, as a function of the CM energy from $220$ to $500$ GeV.
• Figure 3: Indirect $1\sigma$ constraints possible in $\delta_Z - \delta_h$ parameter space by combining associated production cross section measurements of $0.4\%$ ($1\%$-estimated) precision at $\sqrt{s} = 240$ GeV, ($350$ GeV) in solid black. For large values of $|\delta_h|$ this ellipse can only be considered qualitatively as the calculation is only valid to lowest order in $\delta_h$. The different scales should be noted. Direct constraints possible at the high luminosity LHC and 1 TeV ILC (with LU denoting luminosity upgrade) are also shown for comparison. This plot only applies to the specific model discussed in Sec. \ref{['sec:twocoup']} and if energy-dependent $hZZ$ couplings were allowed then such a constraint could not be determined.
• Figure 4: Contours of the ratio of NLO modifications to $\sigma (e^+ e^- \to h Z)$ from a modified Higgs self-coupling relative to the LO modifications due to the modified $hZZ$ vertex in a 2HDM as a function of the parameters $\beta$ and $m_{A}$. In the gray region the LO modifications dominate and in the white region the NLO corrections involving the self-coupling dominate. Loops of additional heavy scalars are not included and are estimated to be subdominant. The LO $hZZ$ coupling modification is set to a constant value of $0.1\%$, such that the region above the dashed line corresponds to deviations greater than the expected experimental sensitivity. For fixed $\delta$ and large $m_{A}$ we have $\delta \sim \overline{\lambda} v^2 / 2 m_A^2$Englert:2014uua, where $\overline{\lambda}$ is a combination of dimensionless couplings and mixing angles in the Higgs sector, thus large $m_A$ and $\delta^2 = 0.1 \%$ large requires almost non-perturbative couplings. This does not, however, alter the ratio of the magnitude of effects from the NLO self-coupling modification relative to the LO $hZZ$ modifications, and large or non-perturbative couplings are not required for the self-coupling modification to dominate.