Higgs Couplings at a Future Wakefield Collider

Technical Summary: Higgs Couplings at a Future Wakefield Collider

Problem Statement
The paper addresses the physics potential of a proposed 10 TeV linear plasma wakefield collider (WFC) for measuring Higgs boson couplings. While WFC technology offers a compact path to the energy frontier (requiring facilities of order kilometers rather than hundreds), it faces specific technological hurdles: the difficulty of accelerating high-quality positron beams and the challenge of preserving flat-beam geometries in plasma stages. These challenges lead to significant beam-beam interactions (beamstrahlung and pair production), which smear the luminosity spectrum across a broad range of center-of-mass energies ($\sqrt{s}$) rather than providing a monochromatic beam. The central question is whether these spectral smearing effects, combined with the potential necessity of abandoning flat beams or positron beams entirely, would degrade the precision of Higgs coupling measurements to a point where the WFC is uncompetitive with other future collider proposals (e.g., FCC, muon colliders, or photon colliders).

Methodology
The authors perform a comparative analysis of Higgs coupling sensitivities across several 10 TeV collider configurations, assuming a geometric integrated luminosity of 10 ab$^{-1}$. The study utilizes the following framework:

• Collider Configurations: The analysis compares $e^+e^-$ and $e^-e^-$ collisions with both round and flat beam geometries, as well as a $\gamma\gamma$ collider generated via Compton back-scattering off $e^-$ beams. A mono-energetic "MuC" (muon collider) benchmark is included for comparison.
• Theoretical Framework: Higgs couplings are parameterized using the $\kappa$-framework within a restricted leading-order Higgs Effective Field Theory (HEFT). The study focuses on deviations in the Higgs couplings to electroweak bosons ($\kappa_W, \kappa_Z$), the Higgs self-coupling ($\kappa_3$), and the quartic gauge-Higgs couplings ($\kappa_{W^2}, \kappa_{Z^2}$).
• Event Generation and Simulation: Signal and background processes are generated using MadGraph5_aMC@NLO. The dominant production channels considered are Vector Boson Fusion (VBF) ($WBF$ and $ZBF$) and photon fusion. The analysis focuses on the $h \to b\bar{b}$ decay channel for single Higgs and $hh \to b\bar{b}b\bar{b}$ for double Higgs.
• Luminosity Spectra: Crucially, the study incorporates detailed luminosity spectra ($d\mathcal{L}/d\sqrt{s}$) simulated with WarpX and CAIN for the various WFC configurations. These spectra account for beamstrahlung effects, which spread the collision energy.
• Analysis Strategy: Events are reweighted to account for the specific luminosity spectra of each collider and the dependence of cross-sections on the Lagrangian parameters. A Poisson log-likelihood analysis is performed to extract 68% confidence level (CL) contours on the coupling parameters. The analysis includes event categorization based on tagging (untagged, electron-tagged, and jet-tagged) to separate $WBF$ and $ZBF$ contributions.

Key Contributions

1. Quantification of Beamstrahlung Impact: The paper demonstrates that the broad luminosity spectra resulting from beam-beam interactions do not inherently impede high-precision Higgs measurements, provided the spectra can be measured or calculated with sufficient accuracy. In fact, the broad energy scan can enhance sensitivity for certain processes (like VBF) compared to mono-energetic collisions.
2. Alternative Configurations: The study rigorously evaluates alternatives to the standard $e^+e^-$ WFC. It finds that $e^-e^-$ and $\gamma\gamma$ configurations, which bypass the positron acceleration challenge, remain viable for precision physics.
3. Flat vs. Round Beams: The analysis challenges the assumption that flat beams are strictly necessary for precision. It finds that for the same geometric luminosity, round beams often yield higher total effective luminosity across the full center-of-mass range relevant for Higgs production, offering no significant disadvantage in coupling sensitivity compared to flat beams.
4. Benchmarking: The work provides a direct sensitivity comparison between WFC options and other future collider concepts, including the FCC-ee/hh, CLIC, and the XFEL Compton Collider (XCC).

Results

• Single Higgs Sensitivity: $e^+e^-$ colliders achieve the best precision on $\Delta\kappa_W$ and $\Delta\kappa_Z$ due to higher $WBF$ rates. However, if the luminosity of $e^+e^-$ colliders is reduced by a factor of $\sim10$ (reflecting positron acceleration difficulties), their advantage diminishes significantly. Round beams generally perform as well as or better than flat beams in this context.
• Double Higgs Sensitivity: The sensitivity to the Higgs self-coupling ($\Delta\kappa_3$) and quartic couplings ($\Delta\kappa_{V^2}$) is driven primarily by the untagged event category and the high-mass tail of the spectrum.
• $\gamma\gamma$ Collider Performance: A 10 ab$^{-1}$ dataset at a $\gamma\gamma$ collider yields qualitatively similar sensitivity to a 10 ab$^{-1}$ muon collider and is comparable to a 1 ab$^{-1}$ dataset at an $e^+e^-$ wakefield collider. This suggests that a $\gamma\gamma$ WFC could serve as a powerful alternative if positron acceleration remains a bottleneck.
• Comparison to Other Machines: The projected sensitivities of the WFC configurations are competitive with other future proposals. Specifically, a 10 TeV WFC is expected to improve upon the precision delivered by lower-energy Higgs factories like the LCF or the $\gamma\gamma$ XCC. However, the paper notes that direct comparisons with the FCC or muon colliders require careful interpretation due to differences in systematic uncertainty assumptions and detector modeling maturity.

Significance and Claims
The authors claim that a 10 TeV wakefield collider represents a "paradigm shift" capable of merging high-precision "factory" capabilities with energy-frontier discovery potential. The primary significance of this work is the validation that the specific technological challenges of wakefield acceleration (positron difficulty and beamstrahlung) do not preclude the machine from being a competitive instrument for precision Higgs physics.

The paper modestly concludes that while a WFC would be capable of a competitive Higgs precision program, its ultimate performance is heavily dependent on the achievable luminosity and the ability to control systematic uncertainties related to the luminosity spectrum. It posits that if positron acceleration remains a bottleneck, alternative configurations like $\gamma\gamma$ or $e^-e^-$ colliders offer a robust path forward, maintaining sensitivity comparable to other leading future collider concepts. The work serves as an input to the R&D program for future wakefield accelerators, suggesting that insisting on mono-energetic or flat beams may not be strictly necessary for physics goals, provided the luminosity spectra are well-characterized.