Towards the renormalisation of the Standard Model effective field theory to dimension eight: Bosonic interactions I
Mikael Chala, Guilherme Guedes, Maria Ramos, Jose Santiago
Abstract
We compute the one-loop renormalisation group running of the bosonic Standard Model effective operators to order v^4/\Lambda^4 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow> <mml:msup> <mml:mi>v</mml:mi> <mml:mn>4</mml:mn> </mml:msup> <mml:mi>/</mml:mi> <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" display="inline"> <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" display="inline"> <mml:mi>Λ</mml:mi> </mml:math> 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 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mi>S</mml:mi> </mml:math> and U <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mi>U</mml:mi> </mml:math> 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.