Abstract
We have studied the P → γ⋆ γ⋆ form factor in Resonance Chiral Theory, with P = π0; η, η', to compute the contribution of the pseudoscalar pole to the hadronic light-by-light piece of the anomalous magnetic moment of the muon. In this work we allow the leading U(3) chiral symmetry breaking terms, obtaining the most general expression for the form factor of order O(m2P). The parameters of the Effective Field Theory are obtained by means of short distance constraints on the form factor and matching with the expected behavior from QCD. Those parameters that cannot be fixed in this way are fitted to experimental determinations of the form factor within the spacelike momentum region of the virtual photon. Chiral symmetry relations among the transition form factors for π0, η and η' allow for a simultaneous fit to experimental data for the three mesons. This shows an inconsistency between the BaBar π0 data and the rest of the experimental inputs. Thus, we find a total pseudoscalar pole contribution of aP,HLbLη = (8:47 ± 0:16) · 10-10 for our best fit (neglecting the BaBar π0 data). Also, a preliminary rough estimate of the impact of NLO in 1=NC corrections and higher vector multiplets (asym) enlarges the uncertainty up to aP,HLbLη = (8:47 ± 0:16stat ± 0:09NC +0:5 -0:0asym).
Highlights
Nowadays, the anomalous magnetic moment of the muon, aμ, has been predicted to an outstanding precision of O (α/π)5 for purely electromagnetic effects[1] and to two loops1 precision in electroweak corrections[2]
An interesting point is that the experimental error is orders of magnitude larger than those estimated for aQμ ED and aEμW, the uncertainty of the hadronic contributions is of the same order of the experimental error[2]
If one is to assume the Standard Model (SM) is all that is needed to understand this difference, there is something about the SM that is not understood; if the assumption is that the difference stems from Beyond Standard Model (BSM) effects, the SM must be further improved to reduce the uncertainties in order to have a more controlled SM background for the search of BSM effects
Summary
The anomalous magnetic moment of the muon, aμ, has been predicted to an outstanding precision of O (α/π) for purely electromagnetic effects (aQμ ED)[1] and to two loops precision in electroweak corrections (aEμW)[2]. The remaining hadronic piece, aμHLbL depends on γγ → γγ scattering, which involves strong interactions (HLbL), as shown in the right-hand-side diagram of Fig. 1 The latter cannot be obtained in the same manner as aμHVP, and so, has to be obtained either numerically or in a model dependent way. We focus on the pseudoscalar pole contribution to the HLbL piece, aμP,HLbL, which in order to be fully described needs only the Transition Form Factor (TFF), FPγ γ (q2, p2). As it has been shown in ref [9], this TFF gives most of its contribution to aμ at Euclidian squared photon momenta. Its complete expression before imposing such constraints can be found therein
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