From QCD to Physical Resonances

TL;DR

This paper presents a novel method combining lattice QCD data and chiral perturbation theory to extrapolate scattering amplitudes to physical quark masses, successfully identifying the rho resonance pole.

Contribution

It introduces a new approach integrating lattice QCD results with unitarized chiral perturbation theory for resonance analysis at physical quark masses.

Findings

Agreement with experimental phase shifts up to 1.2 GeV

Successful extrapolation of scattering amplitude to physical masses

Precise determination of the rho resonance pole

Abstract

In this talk, we present the first chiral extrapolation of a resonant scattering amplitude obtained from lattice QCD. Finite-volume spectra, determined by the Hadron Spectrum Collaboration at $m_\pi = 236$ MeV, for the isotriplet $\pi\pi$ channel are analyzed using the L\"uscher method to determine the infinite-volume scattering amplitude. Unitarized Chiral Perturbation Theory is then used to extrapolate the scattering amplitude to the physical light quark masses. The viability of this procedure is demonstrated by its agreement with the experimentally determined scattering phase shift up to center-of-mass energies of 1.2 GeV. Finally, we analytically continue the amplitude to the complex plane to obtain the $\rho$-pole at $\left[755(2)(1)\left({}^{20}_{02}\right) - \frac{i}{2} 129(3)(1)\left({}^7_1\right)\right]$ MeV.