An Efficient On-shell Framework for EFT Matching

Abstract: We develop an on-shell framework for matching ultraviolet (UV) theories to low-energy effective field theories (EFTs) at loop level, based on the unitary cut method. By promoting unitarity double-cuts to $d=4-2\epsilon$ dimensions, the constructible integrands incorporate both branch-cut components and rational terms. The unconstructible parts, such as tadpoles and kinematically independent bubbles, are proved to be unnecessary for EFT matching. In this framework, all requisite loop amplitudes are constructed by sewing a pair of on-shell tree-level amplitudes. Consequently, the method eliminates complications from gauge fixing and ghost fields inherent in traditional loop calculations, while also avoiding supplementary efforts to construct rational terms and implement generalized unitarity cuts for master integral coefficient extraction required in conventional on-shell approaches. This yields a more efficient and systematic methodology. Furthermore, UV amplitudes are systematically matched to a complete set of on-shell amplitude bases via large mass expansion, bypassing concerns about operator redundancies or gauge invariance issues inherent in traditional matching methods. Therefore, this framework can be more easily implemented in programs.