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

We are grateful to Jose Santiago for sharing (and for instructing us on) matchmakereft, as well as for discussions and for comments on the manuscript. We are also enormously thankful to Renato Fonseca for the many enlightening discussions and for help with Sym2Int. MC would also like to thank Christopher Murphy for clarifying some calculations in ref. [30]. MC and ADC are supported by SRA under grant PID2019-106087GB-C21/C22 (10.13039/501100011033). MC is also supported by the Junta de Andalucia grants FQM 101, A-FQM-211-UGR18 and P18-FR-4314 (FEDER), as well as by the Spanish MINECO under the Ramon y Cajal programme. ADC is also supported by the Spanish MINECO under the FPI programme. GG acknowledges support by LIP (FCT, COMPETE2020Portugal2020, FEDER, POCI-01-0145-FEDER-007334) as well as by FCT under project CERN/FIS-PAR/0024/2019 and under the grant SFRH/BD/144244/2019.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 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.Sugar Research Australia PID2019-106087GB-C21/C22Junta de Andalucia FQM 101 A-FQM-211-UGR18 P18-FR-4314Spanish MINECO under the Ramon y Cajal programme Spanish MINECO under the FPI programmePortuguese Foundation for Science and Technology POCI-01-0145-FEDER-007334 Portuguese Foundation for Science and TechnologyEuropean Commission CERN/FIS-PAR/0024/2019 SFRH/BD/144244/201