Discrete symmetries and Efficient Counting of Operators

Abstract: We present DECO ("Discrete and Efficient Counting of Operators"), an implementation of the Hilbert Series to enumerate subleading operator bases for SMEFT-like EFTs with symmetry groups as typically found in flavour and BSM physics. DECO can accommodate EFTs with arbitrary numbers and combinations of the SM gauge groups, as well as the discrete groups S4, A4, and Zn, and U(1) groups with residual global charge (and these groups' most important representations). The program is highly modular and can easily be extended to additional groups and/or representations. We demonstrate the design cases for DECO by using it to cross-check subleading operator bases of EFTs in the literature, which allows us to identify a missing operator in a widely used model for the neutrino masses and discuss said operator's impact.