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Signs, Spin, SMEFT: Sum Rules at Dimension Six

We place theoretical constraints on the leading deviations to four-fermion standard model interactions. Invoking S-matrix analyticity and partial wave unitarity, we develop new dispersion relations that yield either spin-dependent sum rules on dimension-six fermionic operators or information about the amplitude's behavior at large momentum. The pattern of SMEFT inequalities we find for theories obeying certain large-momentum constraints enables a diagnosis of properties of emerging new physics. These relations form a bridge between new physics searches: discovery of flavor-violating $τ$ decays at Belle II would motivate the search for flavor-conserving new physics below 25 TeV, as the results would provide definitive information about the UV.