A Green's basis for the bosonic SMEFT to dimension 8

Abstract

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 dimensioneight 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.

One-loop Matching of the Type-II Seesaw Model onto the Standard Model Effective Field Theory

“…Then, the generated operators from SuperTracer can be further converted into the independent operators in the Warsaw basis of the SMEFT [5]. However, in order to cross-check our results via diagrammatic approach, we first convert these operators into those in Green's basis [33,42,83] by utilizing the algebraic, Fierz identities and integration by parts. Finally, with the help of the EOMs of fields, we can obtain the relevant operators in the Warsaw basis from those in the Green's basis.…”

Towards the renormalisation of the Standard Model effective field theory to dimension eight: bosonic interactions II

“…We carry renormalisation by computing the divergences of the operators in the basis of independent Green's functions of Ref. [10], which extends the basis of independent physical operators of Ref. [8].…”

“…The former operators can be projected onto the latter using the relations derived through the equations of motion in Ref. [10]. This procedure ensures that only off-shell 1-particle irreducible (1PI) Feynman diagrams have to be considered in the calculation.…”

Neutrino seesaw models at one-loop matching: Discrimination by effective operator

“…The result of functional matching can be practically complicated. With identities from the Lorentz and the gauge groups, as well as integration by part, it can be turned into the Green's basis [53,[61][62][63], which is the simplest complete off-shell basis. However, for process where all particles are on-shell, the Green's basis would be over-complete and would inherit redundancy from EOM, meaning that two or more operators in the Green's basis can be related through EOM.…”