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

TL;DR

This study uses lattice QCD with physical quark masses to accurately determine the resonance parameters of the $ ho(770)$ and $K^*(892)$ particles by analyzing scattering amplitudes and complex pole positions, including comprehensive uncertainties.

Contribution

It introduces a novel two-step formalism for extracting resonance parameters from lattice QCD data, incorporating systematic uncertainty estimation and complex pole analysis.

Findings

Precise resonance mass and width values with statistical and systematic errors.

Extension of lattice QCD analysis methods to include complex pole extraction.

Quantitative uncertainty assessment for resonance parameters.

Abstract

We present our study of the $\rho(770)$ and $K^*(892)$ 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 L\"uscher 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 $M_{K^{*}} = 893(2)(8)(54)(2)~\mathrm{MeV}$ and $\Gamma_{K^{*}} = 51(2)(11)(3)(0)~\mathrm{MeV}$ for the $K^*(892)$ 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.