# Hadronic coupling constants of $g_{\sigma\pi\pi}$ in lattice QCD

## TL;DR

This study calculates the hadronic decay coupling constant $g_{\sigma\pi\pi}$ in lattice QCD using three-point functions and the moving-wall source technique, providing a numerical estimate on a MILC gauge ensemble.

## Contribution

First lattice QCD calculation of $g_{\sigma\pi\pi}$ using three-point functions with the moving-wall source technique.

## Key findings

- Estimated $g_{\sigma\pi\pi}=2.71(42)$ GeV on MILC fine lattice.
- Demonstrated effectiveness of the moving-wall source technique for three-point function calculations.
- Provided a numerical value for the $\sigma$ decay coupling constant in lattice QCD.

## Abstract

We investigate the coupling constant $g_{\sigma\pi\pi}$ for the hadronic decay $\sigma\to\pi\pi$ only using the relevant three-point function, which is evaluated by the moving-wall source technique with a pretty good noise-to-signal ratio. This simulation is carried out on a $40^3\times96$ MILC gauge configuration with $N_f=2+1$ flavor of the "Asqtad" improved staggered dynamical sea quarks at the lattice spacing $a \approx 0.09$ fm. Our estimated value for this given MILC fine lattice gauge ensemble $g_{\sigma\pi\pi}=2.71(42)$ GeV.