Scalar pion form factor in two-flavor lattice QCD

We calculate the scalar form factor of the pion using two dynamical flavors of nonperturbatively 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, Q²=0, and two nonvanishing Q², we obtain an estimate for the scalar radius ⟨r²⟩ₛ^π 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 ⟨r²⟩ₛ^π=0.635±0.016 fm² at the physical pion mass (statistical error only). This is in good agreement with the phenomenological estimate from ππ-scattering. The inclusion of the disconnected contribution is essential for achieving this level of agreement.