Utilising optimised operators and distillation to extract scattering phase shifts

TL;DR

This paper investigates how the choice of distillation smearing affects the accuracy of energy spectra and scattering phase shifts in lattice QCD, focusing on the $ ho$ resonance in $$ scattering.

Contribution

It introduces optimized operators and compares distillation spaces of different ranks to improve extraction of scattering parameters in lattice QCD.

Findings

Higher distillation ranks improve spectral accuracy.

Optimized operators enhance phase shift extraction.

Results are demonstrated on an anisotropic lattice with physical pion mass.

Abstract

In this investigation, we examine how the precision of energy spectra and scattering phase shifts, extracted in lattice QCD, depend upon the degree of distillation type smearing. We use the variational method to extract energy spectra for the isospin-1, $J^{PC}=1^{--}$ channel and use the L\"{u}scher method to compute scattering amplitudes, relevant for the $\rho$ resonance, in $\pi\pi$ elastic scattering. Optimised interpolating operators for a single ground state pion are constructed and these are used to construct two pion operators. Calculations are performed on an anisotropic lattice with a pion mass of $m_\pi=236$ MeV. We provide a comprehensive comparison of energy spectra and scattering phase shifts across distillation spaces of varying rank.