Towards the renormalisation of the Standard Model effective field theory to dimension eight: bosonic interactions II
Supratim Das Bakshi, M. Chala, Álvaro Díaz-Carmona, Guilherme Guedes
Abstract
Abstract We calculate the renormalisation group running of the bosonic Standard Model (SM) effective operators at one loop and to order $$v^4/\Lambda ^4$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msup> <mml:mi>v</mml:mi> <mml:mn>4</mml:mn> </mml:msup> <mml:mo>/</mml:mo> <mml:msup> <mml:mi>Λ</mml:mi> <mml:mn>4</mml:mn> </mml:msup> </mml:mrow> </mml:math> , with $$v\sim 246$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>v</mml:mi> <mml:mo>∼</mml:mo> <mml:mn>246</mml:mn> </mml:mrow> </mml:math> GeV being the electroweak scale and $$\Lambda$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>Λ</mml:mi> </mml:math> the unknown new physics threshold. We focus on contributions driven by one dimension-eight term and SM couplings, thus extending (and completing) the effort initiated in Chala et al. (SciPost Phys 11:065, 2021). arXiv:2106.05291 , in which quantum corrections from pairs of dimension-six interactions were considered. We highlight some interesting consequences, including the renormalisation of loop-induced interactions by tree-level generated terms and, more importantly, the validity of positivity bounds on different operators inducing anomalous gauge quartic couplings.