The scalar pion form factor in two-flavor lattice QCD

TL;DR

This study computes the scalar form factor of the pion in two-flavor lattice QCD, including disconnected contributions, and estimates the scalar radius consistent with phenomenological data.

Contribution

It provides a lattice QCD calculation of the pion's scalar form factor with disconnected contributions, using improved Wilson fermions and chiral perturbation theory for physical extrapolation.

Findings

Scalar radius of the pion: 0.635±0.016 fm²

Disconnection contributions are crucial for accurate results

Results agree with phenomenological estimates from scattering data

Abstract

We calculate the scalar form factor of the pion using two dynamical flavors of non-perturbatively $\mathcal{O}(a)$-improved Wilson fermions, including both the connected and the disconnected contribution to the relevant correlation functions. We employ the calculation of all-to-all propagators using stochastic sources and a generalized hopping parameter expansion. From the form factor data at vanishing momentum transfer, $Q^2=0$, and two non-vanishing $Q^2$ we obtain an estimate for the scalar radius $\left<r^2\right>^\pi_{_{\rm S}}$ of the pion at one value of the lattice spacing and for five different pion masses. Using Chiral Perturbation Theory at next-to-leading order, we find $\left<r^2\right>^\pi_{_{\rm S}}=0.635\pm0.016$ fm$^2$ at the physical pion mass (statistical error only). This is in good agreement with the phenomenological estimate from $\pi\pi$-scattering. The inclusion of the disconnected contribution is essential for achieving this level of agreement.