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

Understand

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.