The scalar radius of the pion from Lattice QCD in the continuum limit

Abstract

We extend our study of the pion scalar radius in two-flavour lattice QCD to include two additional lattice spacings as well as lighter pion masses, enabling us to perform a combined chiral and continuum extrapolation. We find discretisation artefacts to be small for the radius, and confirm the importance of the disconnected diagrams in reproducing the correct chiral behaviour. Our final result for the scalar radius of the pion at the physical point is $\left\langle r^2\right\rangle^\pi_{\rm S}=0.600\pm0.052$ fm$^2$, corresponding to a value of $\overline{\ell}_4=4.54\pm0.30$ for the low-energy constant $\overline{\ell}_4$ of NLO chiral perturbation theory.