Non-universal probes of composite Higgs models: new bounds and prospects for FCC-ee

A bstract We study the leading loop-level phenomenology of composite Higgs models via the effective field theory of a strongly interacting light Higgs and top quark (SILH+TQ). We systematically analyze the renormalization group evolution (RGE) of tree-generated operators in the SILH+TQ scenario, finding large mixings of flavor non-universal operators into those affecting electroweak precision observables. We show that these model-independent RG contributions are more important than typical estimates for finite parts. Flavor non-universal effects are completely captured by examining three options for the top mixing: fully composite $$ {q}_L^3 $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msubsup> <mml:mi>q</mml:mi> <mml:mi>L</mml:mi> <mml:mn>3</mml:mn> </mml:msubsup> </mml:math> , equal compositeness, and fully composite t R . In the most phenomenologically viable case of a fully composite t R , we show that the strongest bound on the natural parameter space comes from next-to-leading log running of the 4-top operator $$ {\mathcal{O}}_{tt}=\left({\overline{t}}_R{\gamma}_{\mu }{t}_R\right)\left({\overline{t}}_R{\gamma}^{\mu }{t}_R\right) $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>O</mml:mi> <mml:mi>tt</mml:mi> </mml:msub> <mml:mo>=</mml:mo> <mml:mfenced> <mml:mrow> <mml:msub> <mml:mover> <mml:mi>t</mml:mi> <mml:mo>¯</mml:mo> </mml:mover> <mml:mi>R</mml:mi> </mml:msub> <mml:msub> <mml:mi>γ</mml:mi> <mml:mi>μ</mml:mi> </mml:msub> <mml:msub> <mml:mi>t</mml:mi> <mml:mi>R</mml:mi> </mml:msub> </mml:mrow> </mml:mfenced> <mml:mfenced> <mml:mrow> <mml:msub> <mml:mover> <mml:mi>t</mml:mi> <mml:mo>¯</mml:mo> </mml:mover> <mml:mi>R</mml:mi> </mml:msub> <mml:msup> <mml:mi>γ</mml:mi> <mml:mi>μ</mml:mi> </mml:msup> <mml:msub> <mml:mi>t</mml:mi> <mml:mi>R</mml:mi> </mml:msub> </mml:mrow> </mml:mfenced> </mml:math> into the Peskin-Takeuchi T parameter. In general, we find that this 2-loop effect allows existing electroweak precision data to give better constraints on 4-top operators than high-energy probes from top production at the LHC. Independent of the top mixing, we find that a future tera- Z machine such as FCC-ee has the potential to probe composite Higgs models up to a scale of m ∗ ≳ 25 TeV, and test the naturalness of the electroweak scale at the ≲ 10 −4 level.