Field reparametrization in SMEFT

摘要

Debate topic for effective field theory (EFT) is the choice of a "basis" for dim = 6 operators. Clearly all bases are equivalent as long as they are a "basis", containing a minimal set of operators after the use of equations of motion and respecting the SU(3) x SU(2) x U(1) gauge invariance. From a more formal point of view a basis is characterized by its closure with respect to renormalization. Equivalence of bases should always be understood as a statement for the S-matrix and not for the Lagrangian, as dictated by the equivalence theorem. Any phenomenological approach that misses one of these ingredients is still acceptable for a preliminar analysis, as long as it does not pretend to be an EFT. Here we revisit the equivalence theorem and its consequences for EFT when two sets of higher-dimensional operators are connected by a set of non-linear, non-invariant, field reparametrizations.