Towards the renormalisation of the Standard Model effective field theory to dimension eight: Bosonic interactions I Rodríguez Chala, Mikael Guedes, Guilherme Ramos, María Santiago Pérez, José We would like to thank Jorge de Blas for useful discussions. MC and JS are supported by the Ministry of Science and Innovation under grant number FPA2016-78220-C3-1/3-P (FEDER), SRA under grant PID2019-106087GB-C21/C22 (10.13039/501100011033), and by the Junta de Andalucia grants FQM 101, A-FQM-211-UGR18 and P18-FR-4314 (FEDER). MC is also supported by the Spanish MINECO under the Ramon y Cajal programme. GG and MR acknowledge support by LIP (FCT, COMPETE2020-Portugal2020, FEDER, POCI-01-0145-FEDER007334) as well as by FCT under project CERN/FIS-PAR/0024/2019. GG is also supported by FCT under the grant SFRH/BD/144244/2019. MR is also supported by Fundacao para a Ciencia e Tecnologia (FCT) under the grant PD/BD/142773/2018. We compute the one-loop renormalisation group running of the bosonic Standard Model effective operators to order v(4)/Lambda(4), with v similar to 246 GeV being the electroweak scale and Lambda the unknown new physics threshold. We concentrate on the effects triggered by pairs of the leading dimension-six interactions, namely those that can arise at tree level in weakly-coupled ultraviolet completions of the Standard Model. We highlight some interesting consequences, including the interplay between positivity bounds and the form of the anomalous dimensions; the non-renormalisation of the S and U parameters; or the importance of radiative corrections to the Higgs potential for the electroweak phase transition. As a byproduct of this work, we provide a complete Green basis of operators involving only the Higgs and derivatives at dimension-eight, comprising 13 redundant interactions. 2021-11-08T13:20:19Z 2021-11-08T13:20:19Z 2021-09-21 journal article Chala, M... [et al.]. Towards the renormalisation of the Standard Model effective field theory to dimension eight: Bosonic interactions I. SciPost Phys. 11, 065 (2021). [https://doi.org/10.21468/SciPostPhys.11.3.065] http://hdl.handle.net/10481/71375 10.21468/SciPostPhys.11.3.065 eng http://creativecommons.org/licenses/by/3.0/es/ open access Atribución 3.0 España SciPost