Abstract
We accomplish the complete two-loop computation of the leading-twist contribution to the photon-pion transition form factor γγ^{*}→π^{0} by applying the hard-collinear factorization theorem together with modern multiloop techniques. The resulting predictions for the form factor indicate that the two-loop perturbative correction is numerically important. We also demonstrate that our results will play a key role in disentangling various models of the twist-two pion distribution amplitude thanks to the envisaged precision at Belle II.
Highlights
We demonstrate that our results will play a key role in disentangling various models of the twist-two pion distribution amplitude thanks to the envisaged precision at Belle II
The double-virtual photon-to-pion form factor has been demonstrated to be an indispensable ingredient for determining the hadronic light-by-light (HLBL) scattering contribution to the anomalous magnetic moment of the muon in the dispersive framework [19]
The comprehensive data-driven strategy of determining the pion-pole contribution to the HLBL scattering further illustrates that the yielding hadronic uncertainties of ðg − 2Þμ can be reduced substantially with the improved determination of the single virtual photon-pion form factor [20,21]
Summary
We accomplish the complete two-loop computation of the leading-twist contribution to the photon-pion transition form factor γγà → π0 by applying the hard-collinear factorization theorem together with modern multiloop techniques. The collinear QCD dynamics dictating the TFF at large momentum transfer is encapsulated in the universal lightcone distribution amplitude (DA), which is undoubtedly of decisive importance for the model-independent description of semi- and nonleptonic B-meson decays, such as B → πl−νl, B → πlþl−, and B → ππ, on the basis of QCD factorization demanding the detailed information on the very pion DA as the fundamental nonperturbative input [22,23,24,25]. The lattice QCD technique has been applied to address the photon-pion form factor at low photon virtualities with very encouraging predictions [26,27].
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