Unitarity Bounds and Basis Transformations in SMEFT: An Analysis of Warsaw and SILH Bases

Abstract: The equivalence between the Warsaw and SILH bases in Standard Model Effective Field Theory is well established, with transformation rules connecting the two via equations of motion and field redefinitions. This study presents an explicit calculation of the analytical unitarity bounds-defined as the marginal limit of the parameter space-for dimension-six operators within both the Warsaw and SILH bases. We employ a coupled channel analysis to scrutinize scattering processes involving vector bosons and fermions. We conduct a comprehensive investigation into the transformation of unitarity bounds under changes in the operator basis. Our findings demonstrate that the transformation rules, as implicated by the equivalence theorem, can be directly applied to convert unitarity bounds from one basis to another, provided that the operators involved in the transformation rules do not belong to the same subset defined by a block in the coupled channel matrix.