Abstract
We evaluate axial vector transition form factors in holographic QCD models that have been shown to reproduce well recent experimental and theoretical results for the pion transition form factor. Comparing with L3 data on $f_1\to\gamma\gamma^*$ we find remarkable agreement regarding the shape of single-virtual form factors. In the double-virtual case, the holographic results differ strongly from a simple dipole form, and this has an important impact on the corresponding estimate of the axial vector contribution to the anomalous magnetic moment of the muon $a_\mu$ through hadronic light-by-light scattering. We demonstrate that hard-wall models satisfy the Melnikov-Vainshtein short-distance constraint for the latter, if and only if the infinite tower of axial vector states is included. The results for $a_\mu$, however, are strongly dominated by the first few resonances. Numerically, these results turn out to be surprisingly large: (2.9 - 4.1)$\times 10^{-10}$ in the hard-wall models, 57-58% of which are due to the longitudinal contribution, which is the one responsible for the Melnikov-Vainshtein short-distance constraint. Rescaling the holographic result to obtain an optimal fit of L3 data, but then matching only 52% of the asymptotic constraint, the result is reduced to $2.2(5)\times 10^{-10}$, which is still significantly larger than most previous phenomenological estimates of the axial vector exchange contribution.
Highlights
AND SUMMARYPresently, there is a discrepancy between the measured and the predicted values of the anomalous magnetic moment of the muon [1] of the order of [2,3,4] aeμxp :− atμheory ≃ 26 × 10−10, above 3 standard deviations with currently estimated errors
In view of the upcoming new experiment at FERMILAB [5], much effort is being put into reducing the theoretical uncertainty of the Standard Model prediction, which is dominated by hadronic effects [2,3,4,6,7,8,9,10], while QED [17] and electroweak effects [18,19] appear under control
In Ref. [21], we have recently revisited the predictions of chiral holographic QCD models [22,23,24,25,26]. While these models are certainly only a crude approximation to real QCD, we found that the bottom-up holographic models introduced in [27,28,29] agree remarkably well with new recent low-energy data [10] for π → γγà as well as with the results of the dispersive approach for double-virtual pion transition form factors (TFF) [9], leading to a result [21] for aπμ0 ≃ 5.9ð2Þ × 10−10 which is close to the new evaluations in [9,10,13]
Summary
There is a discrepancy between the measured and the predicted values of the anomalous magnetic moment of the muon [1] of the order of [2,3,4] aeμxp :− atμheory ≃ 26 × 10−10, above 3 standard deviations with currently estimated errors. We find that the predicted Q2 dependence of the single-virtual TFF agrees perfectly with the data, when the parameters of the holographic models are fixed to reproduce fπ and mρ (as was done in our study of the pion TFF [21]) With the latter, the hard-wall model of Ref. 58% and 57% of these results (1.7–2.3 × 10−10) arise from the longitudinal part of the axial vector meson propagator that is responsible for the MV-SDC This is comparable to (albeit smaller than) the extra contribution obtained originally in the MV model [30], ΔaPμS;MV 1⁄4 2.35 × 10−10, where one structure function is artificially kept fixed to its on-shell value. Since in real QCD, away from the chiral large-Nc limit, both excited pseudoscalar mesons and axial vector mesons contribute, we consider a datadriven adjustment of the holographic results, which are used as a mere, albeit sophisticated phenomenological model for the axial vector TFF and the resulting contribution for aμ, and which could be combined with models for excited pseudoscalar mesons along the lines of Ref. [34]
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