Abstract
A key ingredient in the evaluation of hadronic light-by-light (HLbL) scattering in the anomalous magnetic moment of the muon $(g-2)_\mu$ concerns short-distance constraints (SDCs) that follow from QCD by means of the operator product expansion. Here we concentrate on the most important such constraint, in the longitudinal amplitudes, and show that it can be implemented efficiently in terms of a Regge sum over excited pseudoscalar states, constrained by phenomenological input on masses, two-photon couplings, as well as SDCs on HLbL scattering and the pseudoscalar transition form factors (TFFs). Our estimate of the effect of the longitudinal SDCs on the HLbL contribution is: $\Delta a_\mu^\text{LSDC}=13(6)\times 10^{-11}$. This is significantly smaller than previous estimates, which mostly relied on an ad-hoc modification of the pseudoscalar poles and led to up to a $40\%$ increase with respect to the nominal pseudoscalar-pole contributions, when evaluated with modern input for the relevant TFFs. We also comment on the status of the transversal SDCs and, by matching to perturbative QCD, argue that the corresponding correction will be significantly smaller than its longitudinal counterpart.
Highlights
The precision of the Standard-Model (SM) prediction for the anomalous magnetic moment of the muon, aμ 1⁄4 ðg − 2Þμ=2, is limited by hadronic contributions
A key ingredient in the evaluation of hadronic light-by-light (HLBL) scattering in the anomalous magnetic moment of the muon ðg − 2Þμ concerns short-distance constraints that follow from QCD by means of the operator product expansion
Our estimate of the effect of the longitudinal short-distance constraints on the HLBL contribution is ΔaLμSDC 1⁄4 13ð6Þ × 10−11. This is significantly smaller than previous estimates, which mostly relied on an ad-hoc modification of the pseudoscalar poles and led to up to a 40% increase with respect to the nominal pseudoscalar-pole contributions, when evaluated with modern input for the relevant transition form factors
Summary
The precision of the Standard-Model (SM) prediction for the anomalous magnetic moment of the muon, aμ 1⁄4 ðg − 2Þμ=2, is limited by hadronic contributions. To HVP, the second-largest contribution to the uncertainty arises from hadronic light-by-light (HLBL) scattering While in this case progress in lattice QCD is promising [16,17,18], another key development in recent years concerns the phenomenological evaluation, i.e., the use of dispersion relations to remove the reliance on hadronic models, either directly for the required four-point function that defines the HLBL tensor [19,20,21,22,23,24], the Pauli form factor [25], or in terms of sum rules [26,27,28,29,30]. The model dependence can be further reduced by matching to the pQCD quark loop, which, in addition, allows one to gain some insights into the scale where hadronic and pQCD-based descriptions should meet
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