Light and strange vector resonances from lattice QCD at physical quark masses

Abstract

We present the first ab initio calculation at physical quark masses of scattering amplitudes describing the lightest pseudoscalar mesons interacting via the strong force in the vector channel. Using lattice quantum chromodynamics, we postdict the defining parameters for two short-lived resonances, the $\rho (770)$ and $K^{\ast }(892)$, which manifest as complex energy poles in $\pi \pi$ and $K\pi$ scattering amplitudes, respectively. The calculation proceeds by first computing the finite-volume energy spectrum of the two-hadron systems, and then determining the amplitudes from the energies using the Lüscher formalism. The error budget includes a data-driven systematic error, obtained by scanning possible fit ranges and fit models to extract the spectrum from Euclidean correlators, as well as the scattering amplitudes from the latter. The final results, obtained by analytically continuing multiple parameterizations into the complex energy plane, are $M_{\rho }=796(5)(50)\mathrm{MeV}$, ${\Gamma }_{\rho }=192(10)(31)\mathrm{MeV}$, $M_{K^{\ast }}=893(2)(54)\mathrm{MeV}$ and ${\Gamma }_{K^{\ast }}=51(2)(11)\mathrm{MeV}$, where the subscript indicates the resonance and $M$ and $\Gamma$ stand for the mass and width, respectively, and where the first bracket indicates the statistical and the second bracket the systematic uncertainty.

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