The hadronic vacuum polarization with twisted boundary conditions

Understand

The leading-order hadronic contribution to the muon anomalous magnetic moment is given by a weighted integral over the subtracted hadronic vacuum polarization.

• This integral is dominated by euclidean momenta of order the muon mass, i.e., momenta not accessible on current lattice volumes with periodic boundary conditions.
• Twisted boundary conditions can in principle help in accessing momenta of any size even in a finite volume, but their use leads to a modification of the Ward-Takahashi identity that normally guarantees transversality of the vacuum polarization.
• As a result, the vacuum polarization contains a non-transversal, quadratically divergent term, which arises as an artifact of using twisted boundary conditions in a finite volume.