# Hadron-Hadron Interactions from $N_f=2+1+1$ Lattice QCD: The $\rho$-resonance

## TL;DR

This study uses lattice QCD with multiple ensembles to analyze the rho meson, determining its mass and width, and extrapolating to the physical point with results consistent with experiments within uncertainties.

## Contribution

First lattice QCD calculation of the rho meson using Nf=2+1+1 flavors across multiple lattice spacings and pion masses, providing detailed phase shift analysis and extrapolation.

## Key findings

- Rho meson mass agrees with experimental value at the physical point.
- Decay width differs by about two standard deviations from experimental data.
- Lattice artefacts are not detectable within statistical uncertainties.

## Abstract

We present an investigation of the Rho-meson from Nf=2+1+1 flavour lattice QCD. The calculation is performed based on gauge configuration ensembles produced by the ETM collaboration with three lattice spacing values and pion masses ranging from 230 MeV to 500 MeV. Applying the L\"uscher method phase shift curves are determined for all ensembles separately. Assuming a Breit-Wigner form, the Rho-meson mass and width are determined by a fit to these phase shift curves. Mass and width combined are then extrapolated to the chiral limit, while lattice artefacts are not detectable within our statistical uncertainties. For the Rho-meson mass extrapolated to the physical point we find good agreement with experiment. The corresponding decay width differs by about two standard deviations from the experimental value.