Physical-mass calculation of $\rho (770)$ and $K^{\ast }(892)$ resonance parameters via $\pi \pi$ and $K\pi$ scattering amplitudes from lattice QCD

Abstract

We present our study of the $\rho (770)$ and $K^{\ast }(892)$ resonances from lattice quantum chromodynamics (QCD) employing domain-wall fermions at physical quark masses. We determine the finite-volume energy spectrum in various momentum frames and obtain phase-shift parameterizations via the Lüscher formalism, and as a final step the complex resonance poles of the $\pi \pi$ and $K\pi$ elastic scattering amplitudes via an analytical continuation of the models. By sampling a large number of representative sets of underlying energy-level fits, we also assign a systematic uncertainty to our final results. This is a significant extension to data-driven analysis methods that have been used in lattice QCD to date, due to the two-step nature of the formalism. Our final pole positions, $M+i\Gamma /2$, with all statistical and systematic errors exposed, are $M_{K^{\ast }}=893(2)(8)(54)(2)\mathrm{MeV}$ and ${\Gamma }_{K^{\ast }}=51(2)(11)(3)(0)\mathrm{MeV}$ for the $K^{\ast }(892)$ resonance and $M_{\rho }=796(5)(15)(48)(2)\mathrm{MeV}$ and ${\Gamma }_{\rho }=192(10)(28)(12)(0)\mathrm{MeV}$ for the $\rho (770)$ resonance. The four differently grouped sources of uncertainties are, in the order of occurrence: statistical, data-driven systematic, an estimation of systematic effects beyond our computation (dominated by the fact that we employ a single lattice spacing), and the error from the scale-setting uncertainty on our ensemble.

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