We present a formula that allows one to calculate the pion form factor in the timelike region $2m_{\pi }\le \sqrt{s}\le 4m_{\pi }$ in lattice QCD. The form factor quantifies the contribution of two-pion states to the vacuum polarization. It must be known very accurately in order to reduce the theoretical uncertainty on the anomalous magnetic moment of the muon. At the same time, the formula constitutes a rare example where, in a restricted kinematic regime, the spectral function of a conserved current can be determined from Euclidean observables without an explicit analytic continuation.

• Received 15 May 2011

DOI:https://doi.org/10.1103/PhysRevLett.107.072002