Abstract
We study the pion-photon transition form factor (TFF) ${F}^{\ensuremath{\gamma}*\ensuremath{\gamma}{\ensuremath{\pi}}^{0}}({Q}^{2})$ using a state-of-the art implementation of light cone sum rules (LCSRs) within fixed-order QCD perturbation theory. The spectral density in the dispersion relation includes all currently known radiative corrections up to the next-to-next-to-leading-order (NNLO) and all twist contributions up to order six. Predictions for the TFF are obtained for various pion distribution amplitudes (DAs) of twist two, including two-loop evolution which accounts for heavy-quark mass thresholds. The influence of the main theoretical uncertainties is quantified in order to enable a more realistic comparison with the data. The characteristics of various pion DAs are analyzed in terms of the conformal coefficients ${a}_{2}$ and ${a}_{4}$ in comparison with the $1\ensuremath{\sigma}$ and $2\ensuremath{\sigma}$ error regions of the data and the most recent lattice constraints on ${a}_{2}$ with NLO and NNLO accuracy. Our results provide more stringent bounds on the variation of the pion DA and illuminate the corresponding asymptotic behavior of the calculated TFF.
Highlights
In this work we consider the pion-photon transition form factor FγÃγÃπ0 ðq21; q22Þ for the process γÃðq21ÞγÃðq22Þ → π0 with q21 1⁄4 −Q2 and q22 1⁄4 −q2 assuming Q2 ≫ q2 and adopting a single-tagged experimental setup
In this work we carried out a comprehensive analysis of the pion-photon transition form factor in QCD using the method of light cone sum rules (LCSRs) within fixed-order perturbation theory (FOPT) to NNLO and twist-six accuracy
The presented predictions for this exclusive observable are of considerable interest for two different reasons: (i) they provide a handle on the involved pion distribution amplitude and (ii) they represent a powerful tool to study the onset of scaling at high Q2 in present-days experiments
Summary
In this work we consider the pion-photon transition form factor FγÃγÃπ0 ðq; q22Þ for the process γÃðq21ÞγÃðq22Þ → π0 with q21 1⁄4 −Q2 and q22 1⁄4 −q2 assuming Q2 ≫ q2 and adopting a single-tagged experimental setup. A reliable theoretical scheme able to include the other two nonperturbative ingredients, together with perturbative radiative corrections and nonperturbative higher-twist contributions, is the method of light-cone sum rules (LCSRs) [1,2] in combination with fixed-order perturbation theory (FOPT) within QCD This scheme provides computational techniques which can be used in connection with various pion DAs and is useful for the analysis of the experimental data [3,4] that are eventually indicating discrepant observations applying to the same phenomenon; see [5,6] for a detailed comparison of various theoretical approaches and a classification scheme of the predictions. The analogous values for the platykurtic (pk) DA [17] are given
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