Using lattice chiral effective theory to study pi-pi scattering

Abstract

We use lattice field theory to study the finite-volume energy spectrum of the $\pi \pi$ system in $SU(2)$ chiral effective field theory (ChEFT) at leading order in the chiral expansion. \hl{This finite-volume spectrum can be directly related to the (infinite-volume) $\pi \pi$ scattering phase shifts by Lüscher's formula.} We compare our results to the finite-volume spectrum obtained from lattice QCD \hl{by the RBC-UKQCD collaboration}. Our calculation and the lattice QCD calculation are both performed with the physical pion mass and the same \sout{physical volume}\hl{lattice volume (as measured in physical units)}. However, we find significant differences between the two calculations in the isospin $I=0$ channel. In particular, there is a nearly stable $\sigma$ resonance in our lattice ChEFT calculation, which is absent in the lattice QCD calculation. This likely indicates that ChEFT does not converge well with a naive lattice regularization.