Hadron\u2013Hadron interactions from N_mathrm{{f}}=2+1+1 lattice QCD: the rho ,-resonance

M Werner,C Liu,L Liu,M Petschlies,C Helmes,C Jost,B Metsch,B Knippschild,B Kostrzewa,C Urbach,M Ueding

doi:10.1140/epja/s10050-020-00057-4

Abstract

We present a lattice QCD investigation of the rho -meson with N_mathrm{{f}}=2+1+1 dynamical quark flavours for the first time. 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 to 500 MeV. Applying the Lüscher 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.

Highlights

The ρ-meson represents together with thefamous σ meson ( f0(500)) one of the most prominent meson resonances in the standard model
While the two linear fits certainly provide a good description of the data for Mρ and gρππ separately, we decided to quote the results from the combined fit as our final result
We have presented an investigation of the ρ-meson properties using lattice QCD with Nf = 2 + 1 + 1 Wilson twisted mass quarks at maximal twist

Summary

Introduction

The ρ-meson represents together with the (in-)famous σ meson ( f0(500)) one of the most prominent meson resonances in the standard model. The ρ, being the lightest vector meson, plays a fundamental role in many processes within the context of vector meson dominance; for a review see Ref. QCD: interaction properties can only be computed using the famous Lüscher method [4,5,6]. Infinite volume scattering properties can be extracted from finite volume energy shifts. In the the Lüscher method has been developed further in many directions, for a review see Ref. For this paper most relevant is the derivation of the formalism in moving frames [14,15,16], which allows one to map out the phase shift at many different scattering momenta, without the need to study different volumes

Methods

Results

Discussion

Conclusion