Scalar-involved three-point Green functions and their phenomenology

Abstract

We analyse within the framework of resonance chiral theory the $⟨S{A}_{\mu }{A}_{\nu }⟩$ and $⟨S{V}_{\mu }{V}_{\nu }⟩$ three-point Green functions, where $S$, $A_{\mu }$ and $V_{\mu }$ are short for scalar, axial-vector and vector $SU(3)$ hadronic currents. We construct the necessary Lagrangian such that the Green functions fulfill the asymptotic constraints, at large momenta, imposed by QCD at leading order. We study the implications of our results on the spectrum of scalars in the large-$N_C$ limit, and analyse their decays.

Comments: 30 pages, 5 figures. v2: Typos in Eqs. (B.4) and (B.6) of the appendices in the published version are corrected