Abstract
We present results for single pseudoscalar meson pole contributions and pion box contributions to the hadronic light-by-light (LBL) correction of the muon's anomalous magnetic moment. We follow the recently developed dispersive approach to LBL, where these contributions are evaluated with intermediate mesons on-shell. However, the space-like electromagnetic and transition form factors are not determined from analytic continuation of time-like data, but directly calculated within the functional approach to QCD using Dyson-Schwinger and Bethe-Salpeter equations. This strategy allows for a systematic comparison with a strictly dispersive treatment and also with recent results from lattice QCD. Within error bars, we obtain excellent agreement for the pion electromagnetic and transition form factor and the resulting contributions to LBL. In addition, we present results for the η and η′ pole contributions and discuss the dynamical effects in the η−η′ mixing due to the strange quarks. Our result for the total pseudoscalar pole contributions is aμPS-pole=91.6(1.9)×10−11 and for the pion-box contribution we obtain aμπ−box=−16.3(2)(4)×10−11.
Highlights
The anomalous magnetic moment aμ = (g −2)μ of the muon is currently under intense scrutiny from both theory and experiment
With all ingredients described in the previous section put together, numerical results for transition form factor (TFF) in the functional approach have been discussed in a number of works, see
In this work we have presented a calculation of the pseudoscalar pole and pion box contributions to hadronic light-by-light scattering based on a functional approach to QCD via Dyson-Schwinger and Bethe-Salpeter equations
Summary
2)μ of the muon is currently under intense scrutiny from both theory and experiment. With a persistent discrepancy of about 3–4 standard deviations between the theoretical. As summarised e.g. in [33], it does extremely well in the pseudoscalar meson sector and very reasonably in the vector meson channels This includes observables such as masses, form factors, charge radii and transition form factors which are all highly relevant for the calculation of aμ. Given this quality, it is plausible to make use of functional methods as a complementary tool to lattice QCD and dispersive approaches. In this work we use previously obtained results for the pion electromagnetic form factor (EMFF) and the pion two-photon transition form factor (TFF) in the DSE/BSE framework to determine the dispersive pion box and pion pole contributions to hadronic LBL. We use a Euclidean notation throughout this work; see e.g. Appendix A of Ref. [33] for conventions
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