Hadron–Hadron interactions from $$N_\mathrm{{f}}=2+1+1$$Nf=2+1+1 lattice QCD: the $$\rho \,$$ρ-resonance: Extended Twisted Mass Collaboration

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 Luscher 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.