Using lattice chiral effective theory to study <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mi>π</mml:mi> <mml:mi>π</mml:mi> </mml:math> scattering

We use lattice field theory to study the finite-volume energy spectrum of the <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:mi>π</a:mi> <a:mi>π</a:mi> </a:math> system in <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"> <c:mi>S</c:mi> <c:mi>U</c:mi> <c:mo stretchy="false">(</c:mo> <c:mn>2</c:mn> <c:mo stretchy="false">)</c:mo> </c:math> chiral effective field theory (ChEFT) at leading order in the chiral expansion. This finite-volume spectrum can be directly related to the (infinite-volume) <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"> <g:mi>π</g:mi> <g:mi>π</g:mi> </g:math> scattering phase shifts by Lüscher’s formula. We compare our results to the finite-volume spectrum obtained from lattice QCD by the RBC-UKQCD Collaboration. Our calculation and the lattice QCD calculation are both performed with the physical pion mass and the same lattice volume (as measured in physical units). However, we find significant differences between the two calculations in the isospin <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"> <i:mi>I</i:mi> <i:mo>=</i:mo> <i:mn>0</i:mn> </i:math> channel. In particular, there is a nearly stable <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"> <k:mi>σ</k:mi> </k:math> 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.