Measuring the quartic Higgs self-coupling at a multi-TeV muon collider

TL;DR

This work analyzes the potential to measure the quartic Higgs self-coupling $\lambda_4$ at a future high-luminosity multi-TeV muon collider by studying triple-Higgs production via weak-boson fusion. Using Monte Carlo simulations, the cross section for $\mu^+ \mu^- \to HHH \nu\bar{\nu}$ is expressed as a polynomial in the deviations $\delta_3$ and $\delta_4$ from the SM couplings, with detailed coefficient tables across several energies and $M_{HHH}$ regions. The study finds that the collider could achieve significant sensitivity to $\delta_4$, particularly near threshold, and that central-jet acceptance at higher $\sqrt{s}$ improves the constraints when forward regions are limited by backgrounds. For representative scenarios (e.g., $\lambda_3=\lambda_{SM}$ at $14$ TeV with ${\cal L} \sim 33$ ab$^{-1}$), a ~50% 1σ precision on $\lambda_4$ appears feasible, indicating tens of percent accuracy is possible with such a machine. These results motivate more detailed phenomenological and detector studies to fully establish the physics potential of a muon collider for probing the Higgs potential.

Abstract

Measuring the shape of the Higgs boson potential is of paramount importance and will be a challenging task at current as well as future colliders. While the expectations for the measurement of the trilinear Higgs self-coupling are rather promising, an accurate measurement of the quartic self-coupling interaction is presently considered extremely challenging even at a future 100 TeV proton-proton collider. In this work we explore the sensitivity that a muon collider with a center of mass energy in the multi-TeV range, and luminosities of the order of 10^35cm^-2s^-1, as presently under discussion, might provide thanks to a rather large three Higgs-boson production and to a limited background. By performing a first and simple analysis, we find a clear indication that a muon collider could provide a determination of the quartic Higgs self-coupling that is significantly better than what is currently considered attainable at other future colliders.

Figures (18)

• Figure 1: Representative Feynman diagrams contributing to the process $\mu^+ \mu^- \to H H H \nu \overline{\nu}$ that do not involve self-couplings (top-left and bottom-right), involve the trilinear twice (top-right) and once (central), and the quartic (bottom-left) couplings. $s$-channel diagrams (bottom-right) contribute but become negligible at high energy (note that in this case $\nu=\nu_e,\nu_\mu,\nu_\tau$).
• Figure 2: Expected cross sections (left) and signal event numbers for a reference integrated luminosity of 100 ab$^{-1}$ (right) for $\mu^+ \mu^- \to H H H \nu \overline{\nu}$ versus the c.m. collision energy, for $M_{\bar{\nu}\nu}\gtrsim 150$GeV. Cross sections for different assumptions of the trilinear and quartic couplings are presented, as well as for the SM case, obtained by Whizard (left-hand side) and MadGraph5_aMC@NLO (right-hand side). Details on the scenarios are given in the text.
• Figure 3: Inclusive Higgs transverse momentum distributions (normalized) for the $\mu^+ \mu^- \to H H H \nu \overline{\nu}$ process, in the SM, at different collision energies. A technical cut of $M_{\bar{\nu}\nu}\gtrsim 150$ GeV is included. The plot on the right includes an upper cut of 1 TeV on the $HHH$ invariant mass.
• Figure 4: Inclusive Higgs rapidity distributions (normalized) for the $\mu^+ \mu^- \to H H H \nu \overline{\nu}$ process, in the SM, at different collision energies. A technical cut of $M_{\bar{\nu}\nu}\gtrsim 150$ GeV is included. The plot on the right includes an upper cut of 1 TeV on the $HHH$ invariant mass.
• Figure 5: Inclusive $\Delta R$ distributions (normalized) for the $\mu^+ \mu^- \to H H H \nu \overline{\nu}$ process, in the SM, at different collision energies. A technical cut of $M_{\bar{\nu}\nu}\gtrsim 150$ GeV is included. The plot on the right includes an upper cut of 1 TeV on the $HHH$ invariant mass.