Abstract
We consider the lightcone sum-rule description of the pion-photon transition form factor, based on dispersion relations, in combination with the renormalization group of QCD, in terms of the formal solution of the Efremov-Radyushkin-Brodsky-Lepage evolution equation, and show that the emerging scheme amounts to a certain version of Fractional Analytic Perturbation Theory (FAPT). In order to ensure the correct asymptotic behavior of the considered physical quantity, this modified FAPT version has to be supplemented by process-specific boundary conditions---in contrast to the standard one. However, it provides the advantage of significantly improving the inclusion of radiative corrections in the low-momentum regime of QCD perturbation theory using renormalization-group summation.
Highlights
The description of hard exclusive hadronic processes in QCD is difficult because it must account for typical nonperturbative phenomena like the hadron binding dynamics and/or long-distance effects pertaining to soft contributions that cannot be assessed by means of perturbative quantum chromodynamics.Consider for example the pion-photon transition form factor for two highly virtual photons describing the reaction γÃð−Q2ÞγÃð−q2Þ → π0 by assuming that Q2, q2 ≫ m2ρ
We develop an extended version of fractional analytic perturbation theory (FAPT)—originally developed in [43,44,45] with recourse to [46]—by augmenting this perturbation theory with a new analytic charge In that amends the conflict between the FAPT analytic couplings at Q2 1⁄4 0 and the asymptotic behavior of the transition form factor (TFF) following from QCD
In this work we considered the π0γÃγ TFF and proposed an approach, which combines the method of light cone sum rules (LCSRs) based on dispersion relations, with the renormalization-group summation expressed in terms of the formal solution of the ERBL evolution equation
Summary
The description of hard exclusive hadronic processes in QCD is difficult because it must account for typical nonperturbative phenomena like the hadron binding dynamics and/or long-distance effects pertaining to soft contributions that cannot be assessed by means of perturbative quantum chromodynamics (pQCD). A useful calculational scheme to implement a consistent factorization of short-distance dynamics, amenable to QCD perturbation theory via hard-gluon exchanges, from longdistance phenomena, encoded in nonperturbative hadron distribution amplitudes based on the light cone operator product expansion, is provided by light cone sum rules (LCSRs) [1,2]. In this scheme, correlation function (1) can be cast in the form of a dispersion relation in terms of the large photon virtuality Q2 to obtain a LCSR. VI, while some important technical issues are treated in three Appendices
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