On the renormalization of the electroweak chiral Lagrangian with a Higgs

Journal of High Energy Physics 2015.3 (2015): 043 reproduced by permission of Scuola Internazionale Superiore di Studi Avanzati (SISSA)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 off-shell 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 energiesWe acknowledge illuminating conversations with Ilaria Brivio, Ferruccio Feruglio, Howard Georgi, María José Herrero, Luca Merlo, Pilar Hernández and Stefano Rigolin. We also acknowledge partial support of the European Union network FP7 ITN INVISIBLES (Marie Curie Actions, PITN-GA-2011-289442), of MICINN, through the project FPA2012-31880, and of the Spanish MINECO’s “Centro de Excelencia Severo Ochoa” Programme under grant SEV-2012-0249. The work of K.K. and P.M. 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 of MICINN. K.K. acknowledges IFT-UAM/CSIC for hospitality during the initial stages of this wor