Abstract
We calculate the phase shift for the I = 1 ππ scattering in 2+1 flavor lattice QCD at mπ = 410 MeV, using all-to-all propagators with the LapH smearing. We first investigate the sink operator independence of the I = 2 ππ scattering phase shift to estimate the systematics in the LapH smearing scheme in the HAL QCD method at mπ = 870 MeV. The difference in the scattering phase shift in this channel between the conventional point sink scheme and the smeared sink scheme is reasonably small as long as the next-toleading analysis is employed in the smeared sink scheme with larger smearing levels. We then extract the I = 1 ππ potential with the smeared sink operator, whose scattering phase shift shows a resonant behavior (ρ resonance). We also examine the pole of the S-matrix corresponding to the ρ resonance in the complex energy plane.
Highlights
IntroductionAn alternative way to investigate unstable particles is the HAL QCD method [17,18,19], in which scattering phase shifts are calculated from corresponding potentials
The understanding of hadron spectra including unstable particles from the first principle is one of the important goals in lattice QCD
(2) The next-toleading (NLO) analysis is needed for the smeared sink scheme to reproduce the scattering phase shift consistent with the one in the point sink scheme
Summary
An alternative way to investigate unstable particles is the HAL QCD method [17,18,19], in which scattering phase shifts are calculated from corresponding potentials. (1) The point sink operator scheme, the standard of the HAL QCD potential method, is a good scheme in the sense that the leading order (LO) analysis gives the correct scattering phase shift. This is the first time to observe the conventional resonance like ρ in the HAL QCD potential method. We determine the mass and decay width of the ρ resonance from the pole of the S-matrix in the complex plane
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