Phase shifts in I=2 {\pi}{\pi}-scattering from two lattice approaches

TL;DR

This study compares two lattice QCD approaches, Luscher's finite volume method and the HAL QCD potential method, to determine the phase shift in I=2 ππ scattering, highlighting their systematic uncertainties and consistency.

Contribution

It is the first direct comparison of Luscher's and HAL QCD methods for I=2 ππ scattering phase shifts on the lattice, including systematic uncertainty analysis.

Findings

Both methods yield consistent phase shift results.

The potential method allows phase shift calculation at arbitrary energies.

Systematic uncertainties differ between the two approaches.

Abstract

We present a lattice QCD study of the phase shift of $I{=}2$ $\pi\pi$ scattering on the basis of two different approaches: the standard finite volume approach by Luscher and the recently introduced HAL QCD potential method. Quenched QCD simulations are performed on lattices with extents $N_s{=}16,24,32,48$ and $N_t{=}128$ as well as lattice spacing $a{\sim}0.115\,\mathrm{fm}$ and a pion mass of $m_\pi{\sim}940\,\mathrm{MeV}$. The phase shift and the scattering length are calculated in these two methods. In the potential method, the error is dominated by the systematic uncertainty associated with the violation of rotational symmetry due to finite lattice spacing. In Luscher's approach, such systematic uncertainty is difficult to be evaluated and thus is not included in this work. A systematic uncertainty attributed to the quenched approximation, however, is not evaluated in both methods. In case of the potential method, the phase shift can be calculated for arbitrary energies below the inelastic threshold. The energy dependence of the phase shift is also obtained from Luscher's method using different volumes and/or nonrest-frame extension of it. The results are found to agree well with the potential method.