Disentangling a dynamical Higgs
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 gauge-Higgs 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. ; We also acknowledge partial support of the European Union network FP7 ITN INVISIBLES (Marie Curie Actions, PITN-GA-2011-289442), of CiCYT through the project FPA2009-09017, of CAM through the project HEPHACOS P-ESP-00346, of the European Union FP7 ITN UNILHC (Marie Curie Actions, PITN-GA- 2009-237920), of MICINN through the grant BES-2010-037869, of the Spanish MINECO's "Centro de Excelencia Severo Ochoa" Programme under grant SEV-2012-0249, and of the Italian Ministero dell'Universit`a e della Ricerca Scientifica through the COFIN program (PRIN 2008) and the contract MRTN-CT-2006-035505. The work of I.B. is supported by an ESR contract of the European Union network FP7 ITN INVISIBLES mentioned above. The work of L.M. is supported by the Juan de la Cierva programme (JCI-2011-09244). The work of O.J.P.E. is supported in part by Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq) and by Funda¸c˜ao de Amparo `a Pesquisa do Estado de S˜ao Paulo (FAPESP), M.C.G-G and T.C are supported by USA-NSF grant PHY-09-6739, M.C.G-G is also supported by CUR Generalitat de Catalunya grant 2009SGR502 and together with J.G-F by MICINN FPA2010-20807 and consolider-ingenio 2010 program CSD-2008-0037. J.G-F is further supported by ME FPU grant AP2009-2546. I.B., J.G-F., M.C.G-G., B.G., L.M, and S.R. acknowledge CERN TH department and J.G-F. also acknowledges ITP Heidelberg for hospitality during part of this work. ; Peer reviewed