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

TL;DR

This paper presents the first ab initio lattice QCD calculation at physical quark masses of vector meson resonances, accurately determining their masses and widths from scattering amplitudes.

Contribution

It introduces a novel lattice QCD approach to compute vector meson resonances directly at physical quark masses, including systematic error analysis.

Findings

Determined the $ ho(770)$ resonance parameters: mass 796 MeV, width 192 MeV.

Determined the $K^*(892)$ resonance parameters: mass 893 MeV, width 51 MeV.

Validated the lattice QCD method for extracting resonance properties from finite-volume spectra.

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 $K^*(892)$, 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 L\"uscher 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 $M_\rho = 796(5)(50)~\mathrm{MeV}$, $\Gamma_\rho = 192(10)(31)~\mathrm{MeV}$, $M_{K^*} = 893(2)(54)~\mathrm{MeV}$ and $\Gamma_{K^*} = 51(2)(11)~\mathrm{MeV}$, 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.