# Lattice QCD Calculation of Flavor Singlet Matrix Elements and N-N Scattering Lengths

## TL;DR

This paper presents lattice QCD calculations of flavor singlet matrix elements, including meson mass differences, sigma terms, and proton axial vectors, along with exploratory nucleon-nucleon scattering length analysis.

## Contribution

It introduces a gauge-fixing-free wall source method for flavor singlet matrix elements and provides initial N-N scattering length results with phenomenological insights.

## Key findings

- Mass difference between η' and pseudoscalar octet mesons quantified.
- Proton sigma term and axial vector matrix elements estimated.
- Initial N-N scattering lengths discussed with phenomenological context.

## Abstract

We report on our recent study of flavor singlet matrix elements calculated with the wall source method without gauge fixing. Results are presented for the mass difference between $\eta^{\prime}$ and pseudoscalar octet mesons, the $\pi$-N $\sigma$ term and the proton axial vector matrix elements. An exploratory calculation of the N-N scattering lengths is also discussed including a phenomenological study with one-boson exchange potentials.