Journal of High Energy Physics 2016.6 (2016): 038 reproduced by permission of Scuola Internazionale Superiore di Studi Avanzati (SISSA)In the context of the minimal SO(5) linear σ-model, a complete renormalizable Lagrangian -including gauge bosons and fermions- is considered, with the symmetry softly broken to SO(4). The scalar sector describes both the electroweak Higgs doublet and the singlet σ. Varying the σ mass would allow to sweep from the regime of perturbative ultraviolet completion to the non-linear one assumed in models in which the Higgs particle is a low-energy remnant of some strong dynamics. We analyze the phenomenological implications and constraints from precision observables and LHC data. Furthermore, we derive the d ≤ 6 effective Lagrangian in the limit of heavy exotic fermionsThe authors (each identified by the first letter of her/his last name) acknowledge partial financial support by the European Union through the FP7 ITN INVISIBLES (PITN-GA-2011-289442) (FGKMRS), by the Horizon2020 RISE InvisiblesPlus 690575 (FGKMRS), by CiCYT through the project FPA2012-31880 (GS), and by the Spanish MINECO through the Centro de excelencia Severo Ochoa Program under grant SEV-2012-0249 (GMS). The work of K.K. is supported by an ESR contract of the European Union network FP7 ITN INVISIBLES mentioned above. The work of S.S. is supported through the grant BES-2013-066480 of the Spanish MICINN and she also received support during from the Spanish MICINN grant EEBB-I-15-10242. We would also like to thank the Kavli Institute for Theoretical Physics — Santa Barbara (GM) (National Science Foundation grant PHY11-25915), the Mainz Institute for Theoretical Physics (M), the Physics Department of the University of California San Diego (S), the Aspen Center for Physics (GM) (National Science Foundation grant PHY-1066293 and the Simons Foundation) and the Institute for Theoretical Physics IFT-UAM/CSIC (F) for hospitality and/or partial support during the completion of this wor

The one-loop renormalization of the action for a set Dirac fermions and a set of scalars spanning an arbitrary manifold coupled via Yukawa-like and gauge interactions is presented. The computation is performed with functional methods and in a geometric formalism that preserves at all stages the symmetries of the action. The result is then applied to Higgs effective field theory to obtain the renormalization group evolution. In the Standard Model limit of this EFT the RGE equations collapse into a smaller linearly independent set; this allows to probe the dynamics of the scalar discovered at LHC via de-correlations in the running of couplings.

Abstract:We consider the scalar sector of the effective non-linear electroweak Lagrangian with a light "Higgs" particle. For a leading order Lagrangian, the complete one-loop offshell renormalization procedure is performed, including the effects of a finite Higgs mass. This determines the complete set of independent chiral invariant scalar counterterms required for consistency; these include bosonic operators often disregarded. A novel general parametrization of the Goldstone boson matrix is proposed, which reduces to the various usual ones for specific values of its parameter. Furthermore, new counterterms involving the Higgs field which are apparently chiral non-invariant are identified in the perturbative analysis. A redefinition of the Goldstone boson fields which absorbs all chiral non-invariant counterterms is then explicitly determined. The physical results translate into renormalization group equations which may be useful when comparing future Higgs data at different energies.