Sigma decomposition: the CP-odd Lagrangian

Journal of High Energy Physics 2016.4 (2016): 016 reproduced by permission of Scuola Internazionale Superiore di Studi Avanzati (SISSA)Artículo escrito por un elevado número de autores, sólo se referencian el que aparece en primer lugar, el nombre del grupo de colaboración, si le hubiera, y los autores pertenecientes a la UAMIn Alonso et al., JHEP 12 (2014) 034, the CP-even sector of the effective chiral Lagrangian for a generic composite Higgs model with a symmetric coset has been constructed, up to four momenta. In this paper, the CP-odd couplings are studied within the same context. If only the Standard Model bosonic sources of custodial symmetry breaking are considered, then at most six independent operators form a basis. One of them is the weak-θ term linked to non-perturbative sources of CP violation, while the others describe CP-odd perturbative couplings between the Standard Model gauge bosons and an Higgs-like scalar belonging to the Goldstone boson sector. The procedure is then applied to three distinct exemplifying frameworks: the original SU (5) /SO (5) Georgi-Kaplan model, the minimal custodial-preserving SO (5) /SO (4) model and the minimal SU (3) / (SU (2) × U (1)) model, which intrinsically breaks custodial symmetry. Moreover, the projection of the high-energy electroweak effective theory to the low-energy chiral effective Lagrangian for a dynamical Higgs is performed, uncovering strong relations between the operator coefficients and pinpointing the differences with the elementary Higgs scenarioThe work of I.M.H. is supported by an ESR contract of the European Union network FP7 ITN INVISIBLES (Marie Curie Actions, PITN-GA-2011-289442). L.M. acknowledges partial support of the European Union network FP7 ITN INVISIBLES, of CiCYT through the project FPA2012- 31880, of the Spanish MINECO’s “Centro de Excelencia Severo Ochoa” Programme under grant SEV-2012-0249, and by a grant from the Simons Foundation. S.R. acknowledges partial support of the European Union network FP7 ITN INVISIBLES and of the COFIN program PRIN 2010. This work was partially performed at the Aspen Center for Physics, which is supported by National Science Foundation grant PHY-106629