We perform a non-perturbative lattice calculation of the P-wave pion-pion scattering phase in the ρ-meson decay channel using two flavors of maximally twisted mass fermions at pion masses ranging from 480 MeV to 290 MeV. Making use of finite-size methods, we evaluate the pion-pion scattering phase in the center-of-mass frame and two moving frames. Applying an effective range formula, we find a good description of our results for the scattering phase as a function of the energy covering the resonance region. This allows us to extract the ρ-meson mass and decay width and to study their quark mass dependence.

Using a quantum mechanical model, the exact energy eigenstates for two-particle two-channel scattering are studied in a cubic box with periodic boundary conditions in all three directions. A relation between the exact energy eigenvalue in the box and the two-channel S-matrix elements in the continuum is obtained. This result can be viewed as a generalization of the well-known Lüscher's formula which establishes a similar relation in elastic scattering.

We present a reliable nonperturbative calculation of the QCD correction, at leading order in the electromagnetic coupling, to the anomalous magnetic moment of the electron, muon, and tau leptons using two-flavor lattice QCD. We use multiple lattice spacings, multiple volumes, and a broad range of quark masses to control the continuum, infinite-volume, and chiral limits. We examine the impact of the commonly ignored disconnected diagrams and introduce a modification to the previously used method that results in a well-controlled lattice calculation. We obtain 1.513(43)×10(-12), 5.72(16)×10(-8), and 2.650(54)×10(-6) for the leading-order two-flavor QCD correction to the anomalous magnetic moment of the electron, muon, and tau, respectively, each accurate to better than 3%.