  We present a basis of dimension-eight Green's functions involving Standard
Model (SM) bosonic fields, consisting of 86 new operators. Rather than using
algebraic identities and integration by parts, we prove the independence of
these interactions in momentum space, including a discussion on evanescent
bosonic operators. Our results pave the way for renormalising the SM effective
field theory (SMEFT), as well as for performing matching of ultraviolet models
onto the SMEFT, to higher order. To demonstrate the potential of our
construction, we have implemented our basis in matchmakereft and used it to
integrate out a heavy singlet scalar and a heavy quadruplet scalar up to one
loop. We provide the corresponding dimension-eight Wilson coefficients.
Likewise, we show how our results can be easily used to simplify cumbersome
redundant Lagrangians arising, for example, from integrating out heavy fields
using the path-integral approach to matching.
