# Scalar-involved three-point Green functions and their phenomenology

## TL;DR

This paper uses resonance chiral theory to analyze specific three-point Green functions involving scalar, axial-vector, and vector currents, ensuring consistency with QCD constraints and exploring scalar spectrum implications.

## Contribution

It constructs a Lagrangian for these Green functions that satisfies QCD asymptotic constraints and studies their phenomenological implications.

## Key findings

- Green functions satisfy QCD asymptotic constraints
- Implications for scalar meson spectrum in large-Nc limit
- Analysis of decay processes of scalar mesons

## Abstract

We analyse within the framework of resonance chiral theory the $\langle SA_\mu A_\nu \rangle$ and $\langle SV_\mu V_\nu \rangle$ 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.