Massless-Massive Amplitude Correspondence I: Helicity-chirality Matching and On-shell Higgsing

TL;DR

The paper develops a massless–massive amplitude correspondence by organizing massive states into Minimal Helicity-Chirality (MHC) amplitudes and expanding in the chirality-flip parameter $m\eta$. It introduces an on-shell Higgsing procedure that maps leading MHC amplitudes to massless helicity structures and generates subleading terms via Higgs insertions, recasting on-shell Higgsing as a transversality flip. The approach provides explicit leading and subleading 3-point matches for the Standard Model sectors ($FFS$, $FFV$, $VVS$, $VVV$) and clarifies the role of conserved currents and Goldstone modes in the massless limit, enabling a covariant, UV-to-IR unification of amplitudes. The framework yields a systematic, scalable program to construct higher-point massive amplitudes from massless seeds, with clear gauge–Yukawa unification constraints and potential extensions to EFTs and symmetry-broken theories. Overall, it offers a constructive, on-shell route to bridge unbroken and broken phases of gauge theories through a unified MHC/Higgsing formalism.

Abstract

In this work, the massless-massive correspondence for the on-shell scattering amplitudes is constructed so the massive amplitudes could inherit advantageous techniques developed in the massless calculation. This correspondence is established by matching massless amplitudes to Minimal Helicity-Chirality (MHC) amplitudes, which arise from an expansion of massive spin-spinor amplitudes in terms of the chirality-flip $mη$ order by order. The primary MHC amplitude deforms into a massless amplitude of the same helicity; if a vector boson is involved, it may instead vanish due to the associated conserved current. In cases where the primary amplitude vanishes, the leading contributions originate from descendant MHC amplitudes, each corresponding to a distinct massless amplitude in the ultraviolet theory containing either a transverse gauge boson or a Goldstone boson. We propose a systematic amplitude deformation procedure for three-point massless-massive matching based on helicity-chirality unification and the scaling properties of $mη$. Sub-leading MHC amplitudes are matched to massless amplitudes with additional on-shell Higgs splitting, a process known as on-shell Higgsing. In this work, we extend and reinterpret on-shell Higgsing as a transversality flip between different MHC states, and obtain all the 3-point massless-massive matching results in the spontaneous broken standard model.

Figures (5)

• Figure 1: Unifying massless $FFS$ and $FFV$ amplitudes into a single massive term, realizing the IR unification, which also validates the $SU(2)$ little group covariance.
• Figure 2: The complete top-down matching for the $FFS$ amplitude.
• Figure 3: The complete top-down matching for the $FFV$ amplitude.
• Figure 4: The complete top-down matching for the massive $VVS$ amplitude with typical helicity category $(-1,0,0)$ and $(0,0,0)$ .
• Figure 5: The top-down matching from 3-pt and 4-pt massless amplitudes to the massive $VVV$ amplitude.