**Utilising optimised operators and distillation to extract scattering phase shifts**

*A. Woss, C. Thomas, on behalf of the Hadron Spectrum Collaboration*

in 34th annual International Symposium on Lattice Field Theory

Contribution: pdf

**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 \cite{Peardon:2009gh}. 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.