We present a lattice calculation of the electromagnetic form factor of the pion obtained using the tree-level Symanzik improved gauge action with two flavors of dynamical twisted Wilson quarks. The simulated pion masses range approximately from 260 to 580 MeV, and the lattice box sizes are chosen in order to guarantee that $M_{\pi }L\gtrsim 4$. Accurate results for the form factor are obtained using all-to-all quark propagators evaluated by a stochastic procedure. The momentum dependence of the pion form factor is investigated up to values of the squared four-momentum transfer $Q^2\simeq 0.8{\mathrm{GeV}}^2$ and, thanks to the use of twisted boundary conditions, down to $Q^2\simeq 0.05{\mathrm{GeV}}^2$. Volume and discretization effects on the form factor appear to be within the statistical errors. Our results for the pion mass, decay constant and form factor are analyzed using (continuum) chiral perturbation theory at next-to-next-to-leading order. The extrapolated value of the pion charge radius is $⟨r^2{⟩}^{\mathrm{phys}}=0.456\pm {0.030}_{\mathrm{stat}}\pm {0.024}_{\mathrm{syst}}$ in nice agreement with the experimental result. The extrapolated values of the pion form factor agree very well with the experimental data up to $Q^2\simeq 0.8{\mathrm{GeV}}^2$ within uncertainties which become competitive with the experimental errors for $Q^2\gtrsim 0.3{\mathrm{GeV}}^2$. The relevant low-energy constants appearing in the chiral expansion of the pion form factor are extracted from our lattice data, which come essentially from a single lattice spacing, adding the experimental value of the pion scalar radius in the fitting procedure. Our findings are in nice agreement with the available results of chiral perturbation theory analyses of $\pi -\pi$ scattering data as well as with other analyses of our collaboration.

• Received 21 December 2008

DOI:https://doi.org/10.1103/PhysRevD.79.074506