Abstract
The hadronic light-by-light contribution to the muon anomalous magnetic moment depends on an integration over three off-shell momenta squared ( {Q}_i^2 ) of the correlator of four electromagnetic currents and the fourth leg at zero momentum. We derive the short-distance expansion of this correlator in the limit where all three {Q}_i^2 are large and in the Euclidean domain in QCD. This is done via a systematic operator product expansion (OPE) in a background field which we construct. The leading order term in the expansion is the massless quark loop. We also compute the non-perturbative part of the next-to-leading contribution, which is suppressed by quark masses, and the chiral limit part of the next-to-next-to leading contributions to the OPE. We build a renormalisation program for the OPE. The numerical role of the higher-order contributions is estimated and found to be small.
Highlights
The Standard Model (SM) is the theoretical framework developed to describe particle physics at its most fundamental level, and is able to predict the anomalous magnetic moments of the leptons with a high number of significant digits
We focus on the hadronic light-by-light (HLbL) scattering contribution, represented by the diagram in figure 1
The leading asymptotic behaviour of the HLbL for the (g − 2)μ kinematics has been confirmed to be given by the massless quark loop contribution
Summary
The Standard Model (SM) is the theoretical framework developed to describe particle physics at its most fundamental level, and is able to predict the anomalous magnetic moments of the leptons with a high number of significant digits. [18, 19] has allowed for better control of the low-energy region In the latter approach one considers individual intermediate states, for which short-distance constraints such as those derived can be used, examples are refs. The. OPE of the HLbL tensor in this kinematics must be performed by taking into account that the static photon needs to be formulated as a soft degree of freedom. OPE of the HLbL tensor in this kinematics must be performed by taking into account that the static photon needs to be formulated as a soft degree of freedom Several intermediate derivations are relegated to the appendices as well as the full formulae
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