We use lattice field theory to study the finite-volume energy spectrum of the ππ 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) ππ scattering phase shifts by L\"uscher'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 σ 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.
@article{arxiv.2510.15187,
title = {Using lattice chiral effective theory to study pi-pi scattering},
author = {Cameron Cianci and Luchang Jin and Joshua Swaim},
journal= {arXiv preprint arXiv:2510.15187},
year = {2026}
}