All-Order Helicity Selection Rules in Effective Field Theories
Luigi C. Bresciani · Nudzeim Selimovic
Using on-shell methods, we derive an all-order non-renormalization theorem for general four-dimensional effective field theories, relying on Poincaré invariance and unitarity. Each operator is assigned the weights , where and are the number of particles and total helicity of its minimal configuration. At loops, the mixing vanishes when and either or , in the absence of non-holomorphic Yukawa couplings. These zeros follow entirely from tree-level data and are scheme independent under finite renormalizations that preserve the operator-length selection rule. For operators of dimensions five through eight, we identify broad classes of previously unknown zeros at higher loop orders, with particular emphasis on two loops, where the theorem provides direct checks on current calculations, as in the Standard Model Effective Field Theory.