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

TL;DR

This study uses lattice QCD to accurately determine the pion's scalar radius, accounting for lattice spacing and pion mass effects, confirming the significance of disconnected diagrams and providing a precise physical value.

Contribution

It extends previous lattice QCD analyses by including additional lattice spacings and lighter pion masses, enabling a combined chiral and continuum extrapolation for the pion scalar radius.

Findings

Discretisation artefacts are small for the radius.

Disconnected diagrams are crucial for correct chiral behaviour.

Final scalar radius value at physical point: 0.600±0.052 fm².

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.