The electroweak chiral Lagrangian with a light Higgs – systematics & application

I consider the Standard Model as an effective field theory (EFT) at the electroweak scale $v$. At the scale $f\geq v$ I assume a new, strong interaction that breaks the electroweak symmetry dynamically. The Higgs boson arises as a composite pseudo-Nambu-Goldstone boson in these scenarios and is therefore naturally light $(m_{h}\sim v)$. Based on these assumptions and the value of $\xi=v^{2}/f^{2}$, I explain the systematics that governs the effective expansion:\\

For $\xi=\mathcal{O}(1)$ the effective theory is given by a loop expansion, equivalent to an expansion in chiral dimensions (similar to chiral perturbation theory). I will briefly discuss the operators that arise at next-to-leading order ($\mathcal{O}(f^{2} / \Lambda^{2})\simeq \mathcal{O}(1/16\pi^{2})$). On the other hand, in the decoupling limit where $\xi\rightarrow 0$, an expansion in canonical dimension is recovered. The case where $\xi$ is small but non-zero is of phenomenological interest. It leads to a double expansion in $\xi$ and $1/16\pi^{2}$, which captures the expected corrections of a strongly-interacting light Higgs to the Standard Model in a systematic way. \\

Further, I will apply the leading order chiral Lagrangian to current LHC Higgs data. I will show that this gives a QFT justification of the $\kappa$-framework, which is currently used as phenomenological signal-strength parametrization by the experiments at the LHC. I will also present a fit of the leading order chiral Lagrangian to the LHC Higgs data.