Enumerating the operators of an effective field theory

Abstract

Until recently little was known about the high-dimensional operators of the standard model effective field theory (SMEFT). However, in the past few years the number of these operators has been counted up to mass dimension 15 using techniques involving the Hilbert series. In this work I will show how to perform the same counting with a different method. This alternative approach makes it possible to cross-check results (it confirms the SMEFT numbers), but it also provides some more information on the operators beyond just counting their number. The considerations made here apply equally well to any other model besides SMEFT and, with this purpose in mind, they were implemented in a computer code.