Hadron–Hadron interactions from $$N_\mathrm{{f}}=2+1+1$$ lattice QCD: the $$\rho \,$$-resonance
M. Werner, M. Ueding, C. Helmes, C. Jost, B. Knippschild, B. Kostrzewa, C. Liu, L. Liu, B. Metsch, M. Petschlies, C. Urbach
Abstract
Abstract We present a lattice QCD investigation of the $$\rho $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>ρ</mml:mi></mml:math> -meson with $$N_\mathrm{{f}}=2+1+1$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msub><mml:mi>N</mml:mi><mml:mi>f</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mn>2</mml:mn><mml:mo>+</mml:mo><mml:mn>1</mml:mn><mml:mo>+</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:math> 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 $$\rho $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>ρ</mml:mi></mml:math> -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 $$\rho $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>ρ</mml:mi></mml:math> -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.