Connected and Leading Disconnected Hadronic Light-by-Light Contribution to the Muon Anomalous Magnetic Moment with a Physical Pion Mass

We report a lattice QCD calculation of the hadronic light-by-light contribution to the muon anomalous magnetic moment at a physical pion mass. The calculation includes the connected diagrams and the leading, quark-line-disconnected diagrams. We incorporate algorithmic improvements developed in our previous work. The calculation was performed on the $48^3\times 96$ ensemble generated with a physical pion mass and a 5.5 fm spatial extent by the RBC and UKQCD Collaborations using the chiral, domain wall fermion formulation. We find $a_{\mu }^{\mathrm{HLbL}}=5.35(1.35)\times {10}^{-10}$, where the error is statistical only. The finite-volume and finite lattice-spacing errors could be quite large and are the subject of ongoing research. The omitted disconnected graphs, while expected to give a correction of order 10%, also need to be computed.

Figure 1

Left: the HVP diagram. Right: the HLbL diagram. The muon and photon lines are shown explicitly while the quark loops and exchanged gluons of QCD are represented by the shaded circles.

Figure 2

Connected hadronic light-by-light diagrams. There are four additional diagrams resulting from further permutations of the photon vertices on the muon line.

Figure 3

Leading-order disconnected diagram, which is nonzero in the SU(3) limit. There are additional diagrams that can be obtained from permutation of the photon vertices on the muon line.

Figure 4

Disconnected diagrams of order $m_s-m_l$. There are additional diagrams that can be obtained from permutation of the photon vertices on the muon line.

Figure 5

Disconnected diagrams of order $(m_s-m_l{)}^2$ and higher. There are additional diagrams that can be obtained from permutation of the photon vertices on the muon line.

Figure 6

Histograms of the contribution to $F_2$ from different separations $|r|$. The $i$th bin includes the contribution from the region where $i-1<|r|\le i$. The sum of all bins gives the final result for $F_2$. Left: the cHLbL contribution where $r=x-y$. Right: the dHLbL contribution where $r=z-y$.