Decay of rho and a1 mesons on the lattice using distillation

TL;DR

This study uses lattice QCD with distillation to analyze rho and a1 meson resonances, extracting their masses, couplings, and scattering lengths, providing detailed resonance parameters from first-principles calculations.

Contribution

It introduces a lattice QCD approach employing distillation and variational analysis to accurately determine meson resonance properties and phase shifts.

Findings

Extracted rho meson mass as 792(7)(8) MeV

Determined a1(1260) resonance parameters with mass 1.44(4) GeV

Calculated rho-pi scattering lengths for different channels

Abstract

We extract the P-wave pi-pi phase shift for five values of pion relative momenta, which gives information on the rho resonance. The Breit-Wigner formula describes the pi-pi phase shift dependence nicely and we extract m(rho)=792(7)(8) MeV and the coupling g_{\rho\pi\pi}=5.13(20) at our mpi=266 MeV. We extract the P-wave scattering length a_{l=1}^{\pi\pi}=0.082(10)(3) fm^3 from the state with the lowest pion relative momenta. We also determine the S-wave rho-pi phase shift for two values of relative momenta, which provides parameters of the lowest axial resonance a1(1260). Using the Breit-Wigner fit we extract m(a1)=1.44(4) GeV and the coupling g_{a_1\rho\pi}=1.1(3) GeV. From the lowest state we also extract the rho-pi scattering length a_{l=0}^{\rho\pi}=0.23(12) fm for our mpi. The simulation is performed using one Nf=2 ensemble of gauge configurations with clover-improved Wilson quarks. The phase shifts are determined from the lowest two energy-levels, which are obtained by the variational analysis with a number of quark-antiquark and meson-meson interpolators. The correlation functions are calculated using the distillation method with the Laplacian Heaviside (LapH) smearing of quarks.