Abstract
We study two versions of lightcone sum rules to calculate the γ*γ → π0 transition form factor (TFF) within QCD. While the standard version is based on fixed-order perturbation theory by means of a power-series expansion in the strong coupling, the new method incorporates radiative corrections by renormalization-group summation and generates an expansion within a generalized fractional analytic perturbation theory involving only analytic couplings. Using this scheme, we determine the relative nonperturbative parameters and the first two Gegenbauer coefficients of the pion distribution amplitude (DA) to obtain TFF predictions in good agreement with the preliminary BESIII data, while the best-fit pion DA satisfies the most recent lattice constraints on the second moment of the pion DA at the three-loop level.
Highlights
In this paper we present our recent work on the calculation of the two-photon process γ∗(Q2)γ(q2 ∼ 0) → π0 which contains in the form of a convolution the distribution amplitude of the pion [1]—the simplest bound state in QCD
We present the key elements of this formalism and apply it to the recently released preliminary data of the BESIII Collaboration [10, 11], which extend the range of measurements of the π−γ transition form factor (TFF) to very low Q2 ≪ 1 GeV2 values with an unprecedented precision
Instead of a power series expansion in terms of the strong coupling, as in fixed-order perturbation theory (FOPT), on which the standard lightcone sum rules (LCSR) method is based, the new perturbation theory employs only analytic couplings amounting to an improved version of fractional analytic perturbation theory (FAPT) [4]
Summary
In this paper we present our recent work on the calculation of the two-photon process γ∗(Q2)γ(q2 ∼ 0) → π0 which contains in the form of a convolution the distribution amplitude of the pion [1]—the simplest bound state in QCD. We present the key elements of this formalism and apply it to the recently released preliminary data of the BESIII Collaboration [10, 11], which extend the range of measurements of the π−γ transition form factor (TFF) to very low Q2 ≪ 1 GeV2 values with an unprecedented precision At such momenta the conventional LCSR method, based on fixed-order perturbation theory (FOPT), cannot describe this transition process with sufficient accuracy, though it works very well at high Q2 [12, 13]. The full QCD calculation of the two-loop coefficient function of leading twist to the TFF γ∗γ → π0 was carried out analytically by two different groups using different methods and obtaining coinciding results [14, 15] This level of computational accuracy of the NNLO radiative correction is required by the expected precision of forthcoming data of the Belle II experiment.
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