Connecting physical resonant amplitudes and lattice QCD

TL;DR

This paper extrapolates lattice QCD results to physical pion mass to determine the $ ho$-resonance properties, connecting lattice calculations with experimental scattering data.

Contribution

It introduces a method to relate lattice QCD finite volume spectra to physical scattering amplitudes using unitarized chiral perturbation theory and pion mass dependence.

Findings

Good agreement with experimental phase shifts up to 1.2 GeV

Resonance pole found at approximately 755 MeV

Demonstrates a pathway from lattice data to experimental observables

Abstract

We present a determination of the isovector, $P$-wave $\pi\pi$ scattering phase shift obtained by extrapolating recent lattice QCD results from the Hadron Spectrum Collaboration using $m_\pi =236$ MeV. The finite volume spectra are described using extensions of L\"uscher's method to determine the infinite volume Unitarized Chiral Perturbation Theory scattering amplitude. We exploit the pion mass dependence of this effective theory to obtain the scattering amplitude at $m_\pi= 140$ MeV. The scattering phase shift is found to be in good agreement with experiment up to center of mass energies of 1.2 GeV. The analytic continuation of the scattering amplitude to the complex plane yields a $\rho$-resonance pole at $E_\rho= \left[755(2)(1)(^{20}_{02})-\frac{i}{2}\,129(3)(1)(^{7}_{1})\right]~{\rm MeV}$. The techniques presented illustrate a possible pathway towards connecting lattice QCD observables of few-body, strongly interacting systems to experimentally accessible quantities.