In our previous work, Blum et al. [Phys. Rev. Lett. 118, 022005 (2017)], the connected and leading disconnected hadronic light-by-light contributions to the muon anomalous magnetic moment ($g-2$) have been computed using lattice QCD ensembles corresponding to physical pion mass generated by the RBC/UKQCD Collaboration. However, the calculation is expected to suffer from a significant finite-volume error that scales like $1/L^2$ where $L$ is the spatial size of the lattice. In this paper, we demonstrate that this problem is cured by treating the muon and photons in infinite-volume, continuum QED, resulting in a weighting function that is precomputed and saved with affordable cost and sufficient accuracy. We present numerical results for the case when the quark loop is replaced by a muon loop, finding the expected exponential approach to the infinite volume limit and consistency with the known analytic result. We have implemented an improved weighting function which reduces both discretization and finite-volume effects arising from the hadronic part of the amplitude.

• Received 21 May 2017

DOI:https://doi.org/10.1103/PhysRevD.96.034515