Fitting Higgs Data with Nonlinear Effective Theory

In a recent paper we showed that the electroweak chiral Lagrangian at leading order is equivalent to the conventional $\kappa$ formalism used by ATLAS and CMS to test Higgs anomalous couplings. Here we apply this fact to fit the latest Higgs data. The new aspect of our analysis is a systematic interpretation of the fit parameters within an EFT. Concentrating on the processes of Higgs production and decay that have been measured so far, six parameters turn out to be relevant: $c_V$, $c_t$, $c_b$, $c_\tau$, $c_{\gamma\gamma}$, $c_{gg}$. A global Bayesian fit is then performed with the result: $c_{V} = 0.98 \pm 0.09$, $c_{t} = 1.34 \pm 0.19$, $c_{b} = 0.78 \pm 0.18$, $c_{\tau} = 0.92 \pm 0.14$, $c_{\gamma\gamma} = -0.24 \pm 0.37$, $c_{gg} = -0.30 \pm 0.17$. Additionally, we show how this leading-order parametrization can be generalized to next-to-leading order, thus improving the $\kappa$ formalism systematically. The differences with a linear EFT analysis including operators of dimension six are also discussed. One of the main conclusions of our analysis is that since the conventional $\kappa$ formalism can be properly justified within a QFT framework, it should continue to play a central role in analyzing and interpreting Higgs data.