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

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.