Renormalization and non-renormalization of scalar EFTs at higher orders

A bstract We renormalize massless scalar effective field theories (EFTs) to higher loop orders and in the EFT expansion. To facilitate calculations with R* renormalization method, we construct suitable operator bases using Hilbert series related ideas commutative algebra conformal representation theory, including their novel application off-shell correlation functions. obtain new results ranging from full one at mass dimension twelve five loops six. explore structure of anomalous matrix an emphasis on its zeros, investigate effects orthonormal operators. For real scalar, zeros can be explained by a ‘non-renormalization’ rule recently derived Bern et al. complex find two selection rules for mixing n - ( ? 2)-field operators, maximal number fields fixed dimension. The first appears only when is primary, valid loop. second more generic bases, three loops. Finally, comment how may used provide systematic enumeration class evanescent operators that appear particular EFT.