Sigma decomposition: the CP-odd Lagrangian

In 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 scenario.