Matching HEFT and SMEFT in double and triple Higgs production from weak boson fusion

TL;DR

The paper develops an amplitude-based matching between HEFT and SMEFT by comparing tree-level predictions for $VV\to HH$, $VV\to HHH$, and $HH\to HH$ processes. It derives analytic relations that express 14 LO/NLO HEFT coefficients in terms of 6 SMEFT dim-6 Wilson coefficients, and identifies cross-consistency relations among the HEFT coefficients. The authors show that triple-Higgs production grows with energy in HEFT but is suppressed at leading order in dim-6 SMEFT, offering a potential experimental discriminator between the two EFTs. Gauge-invariance checks and high-energy analyses reinforce the robustness of the matching and highlight distinct phenomenological patterns in collider observables. Overall, the amplitude-level approach provides a practical framework to translate SMEFT constraints into HEFT signatures and vice versa, aiding collider-based tests of BSM Higgs physics.

Abstract

In this work we study the matching between the two most popular effective field theories for beyond standard model Higgs physics, SMEFT and HEFT. To perform this matching we follow the approach of identifying the corresponding scattering amplitudes for physical processes in both theories, instead of the most usual approach of relating the corresponding effective Lagrangians or effective actions. In this work we focus on the physical processes of double and triple Higgs production from weak boson fusion, in particular, $WW \to HH$, $ZZ \to HH$, $WW \to HHH$ and $ZZ \to HHH$ and complement them with the elastic scattering $HH \to HH$. We present here the analytical solution to this matching in terms of relations among the coefficients in both theories and comment on the most relevant phenomenological implications of such relations for collider physics.

Figures (3)

• Figure 1: Relevant effective vertices for double and triple Higgs production. The corresponding values of $\Gamma_{WWH}$, $\Gamma_{WWHH}$, $\Gamma_{ZZH}$, $\Gamma_{ZZHH}$, $\Gamma_{HHH}$ and $\Gamma_{HHHH}$ are given in Appendix \ref{['apHEFT']} for HEFT and in Appendix \ref{['apSMEFT']} for SMEFT. We use different colors in these BSM vertices to visually differentiate them more clearly. For comparison, the corresponding SM Feynman rules are also included in Appendix \ref{['apSM']}.
• Figure 2: Feynman diagrams for $WW\to HH$ scattering in the unitary gauge. The labels s, c, t and u refer to s-channel, c-channel, t-channel and u-channel respectively. The diagrams for $ZZ \to HH$ are similar but changing $W$ by $Z$.
• Figure 3: Feynman diagrams for $WW\to HHH$ scattering in the unitary gauge. These diagrams are numbered from 1 to 26. The diagrams for $ZZ \to HHH$ are similar but changing $W$ by $Z$.