Abstract
In this work we study the axial contributions to the hadronic light-by-light piece of the muon anomalous magnetic moment using the framework of resonance chiral theory. As a result, we obtain $a_{\mu}^{\textrm{HLbL};A} = \left(0.8^{+3.5}_{-0.1}\right)\cdot 10^{-11}$, that might suggest a smaller value than most recent calculations, underlining the need of future work along this direction. In particular, we find that our results depend critically on the asymptotic behavior of the form factors, and as such, emphasizes the relevance of future experiments for large photon virtualities. In addition, we present general results regarding the involved axial form factors description, comprehensively examining (and relating) the current approaches, that shall be of general interest.
Highlights
Melnikov and Vainshtein [45] derived operator product expansion (OPE) constraints on the hadronic lightby-light (HLbL) tensor and built a model where these were saturated by dropping the momentum dependence of the singly-virtual transition form factors, which increases the axial contributions to aμ
Several appendices complete our discussion: Appendix A collects several useful relations derived from Schouten identity; Appendix B includes four other basis for the axial transition form factors, briefly commenting about short-distance constraints; Appendix D summarizes the treatment of Uð3Þ flavor breaking corrections in RχT and discusses the determination of the model parameters using short-distance QCD constraints and phenomenological information from LEP; Appendix C shows in detail the estimate of higher orders in RχT; Appendix F summarizes the implications of the OPE for the axial transition form factors
We have studied the axial-vector contributions to the hadronic light-by-light piece of the muon anomalous magnetic moment, aHμ LbL;A
Summary
The anomalous magnetic moment of a charged lepton l, al 1⁄4 ðgl − 2Þ=2 is nonvanishing because of quantum radiative corrections, and has played a key role since its first measurement showing its nonvanishing value [1,2] for l 1⁄4 e, confirmed immediately after with the famous Schwinger computation of al 1⁄4 α=ð2πÞ þ Oðα2Þ [3] Over the years, it has been (and it still is) one of the most stringent tests of the whole Standard Model, thanks to the increasing accuracy of its determination over time (l 1⁄4 e, μ) and the improved theoretical computations with reduced uncertainties that became available. The ones in size, but with similar errors, are the axial-vector contributions, whose study and evaluation is the aim of this paper
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