The pattern of deviations from Standard Model predictions and couplings is different for theories of new physics based on a non-linear realization of the SU(2) L ×U(1) Y gauge symmetry breaking and those assuming a linear realization. We clarify this issue in a model-independent way via its effective Lagrangian formulation in the presence of a light Higgs particle, up to first order in the expansions: dimension-six operators for the linear expansion and four derivatives for the non-linear one. Complete sets of gauge and gaugeHiggs operators are considered, implementing the renormalization procedure and deriving the Feynman rules for the non-linear expansion. We establish the theoretical relation and the differences in physics impact between the two expansions. Promising discriminating signals include the decorrelation in the non-linear case of signals correlated in the linear one: some pure gauge versus gauge-Higgs couplings and also between couplings with the same number of Higgs legs. Furthermore, anomalous signals expected at first order in the non-linear realization may appear only at higher orders of the linear one, and vice versa. We analyze in detail the impact of both type of discriminating signals on LHC physics.

The effective Lagrangian expansion provides a framework to study effects of new physics at the electroweak scale. To make full use of LHC data in constraining higher-dimensional operators we need to include both the Higgs and the electroweak gauge sector in our study. We first present an analysis of the relevant di-boson production LHC results to update constraints on triple gauge boson couplings. Our bounds are several times stronger than those obtained from LEP data. Next, we show how in combination with Higgs measurements the triple gauge vertices lead to a significant improvement in the entire set of operators, including operators describing Higgs couplings.

We study the indirect effects of new physics on the phenomenology of the recently discovered "Higgs-like" particle. In a model independent framework these effects can be parametrized in terms of an effective Lagrangian at the electroweak scale. In a theory in which the SU (2)L × U (1)Y gauge symmetry is linearly realized they appear at lowest order as dimension-six operators, containing all the SM fields including the light scalar doublet, with unknown coefficients. We discuss the choice of operator basis which allows us to make better use of all the available data on the new state, triple gauge boson vertex and electroweak precision tests, to determine the coefficients of the new operators. We illustrate our present knowledge of those by performing a global fit to the existing data which allows simultaneous determination of the eight relevant parameters quantifying the Higgs couplings to gluons, electroweak gauge bosons, bottom quarks, and tau leptons. We find that for all scenarios considered the standard model predictions for each individual Higgs coupling and observable are within the corresponding 68% CL allowed range. We finish by commenting on the implications of the results for unitarity of processes at higher energies.Note added: The analysis has been updated with all the public data available by October 2013. Updates of this analysis are provided at the web site http://hep.if.usp.br/Higgs as well as new versions of this manuscript.

Based on Run I data we present a comprehensive analysis of Higgs couplings. For the first time this SFitter analysis includes independent tests of the Higgs-gluon and top Yukawa couplings, Higgs decays to invisible particles, and off-shell Higgs measurements. The observed Higgs boson is fully consistent with the Standard Model, both in terms of coupling modifications and effective field theory. Based only on Higgs total rates the results using both approaches are essentially equivalent, with the exception of strong correlations in the parameter space induced by effective operators. These correlations can be controlled through additional experimental input, namely kinematic distributions. Including kinematic distributions the typical Run I reach for weakly interacting new physics now reaches 300 to 500 GeV.

The recently announced Higgs discovery marks the dawn of the direct probing of the electroweak symmetry breaking sector. Sorting out the dynamics responsible for electroweak symmetry breaking now requires probing the Higgs interactions and searching for additional states connected to this sector. In this work we analyze the constraints on Higgs couplings to the standard model gauge bosons using the available data from Tevatron and LHC. We work in a model-independent framework expressing the departure of the Higgs couplings to gauge bosons by dimension-six operators. This allows for independent modifications of its couplings to gluons, photons and weak gauge bosons while still preserving the Standard Model (SM) gauge invariance. Our results indicate that best overall agreement with data is obtained if the cross section of Higgs production via gluon fusion is suppressed with respect to its SM value and the Higgs branching ratio into two photons is enhanced, while keeping the production and decays associated to couplings to weak gauge bosons close to their SM prediction.