Abstract: We are entering the era of the precision test of the Standard Model (SM), the Standard Model effective field theory (SMEFT) provides a systematic way to parameterize the deviation from the SM. We develop a generic algorithm for enumerating the effective operators in the SMEFT for a given dimension, which can in principle be extended to any massless Lorentz invariant quantum field theory with gauge symmetry. We use the Young Tabluea Method and the operator-amplitude correspondence to eliminate the redundancy in the Lorentz and gauge structures, and use the symmetric group technique to resolve the flavor relation redundancy in the presence of repeated fields. We implemented the whole algorithm in a Mathematica package--ABC4EFT (Amplitude Basis Calculator for EFT)
