Higgs trilinear coupling in the standard model effective field theory at the high luminosity LHC and the FCC-ee

Motivated by the updated high luminosity (HL)-LHC projections for Higgs pair production from ATLAS and CMS and by the release of the FCC-ee feasibility study, we critically revisit the sensitivity of the global standard model effective field theory (SMEFT) analysis to deformations of the Higgs self-coupling modifier <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:msub><a:mi>κ</a:mi><a:mn>3</a:mn></a:msub></a:math>. To this end, we quantify the impact of SMEFT operators modifying double Higgs production at the LHC and single Higgs production, including loop corrections, at the FCC-ee, and include renormalization group evolution throughout. We demonstrate that significantly improving on the legacy HL-LHC constraints on <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:msub><c:mi>κ</c:mi><c:mn>3</c:mn></c:msub></c:math> at the FCC-ee is not possible without the <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:msqrt><e:mi>s</e:mi></e:msqrt><e:mo>=</e:mo><e:mn>365</e:mn><e:mtext> </e:mtext><e:mtext> </e:mtext><e:mi>GeV</e:mi></e:math> run; that individual and marginalized determinations are similar at the HL-LHC while differing by up to a factor 3 at the FCC-ee; and that quadratic EFT corrections cannot be neglected, especially at the (HL-)LHC. This finding fundamentally alters the picture compared to strategic planning often based on one-parameter projections. Overall, the combination of HL-LHC and FCC-ee data offers unique potential to pin down the Higgs self-coupling with <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"><g:mo>∼</g:mo><g:mn>15</g:mn><g:mo>%</g:mo></g:math> precision.