We study the pion-photon transition form factor (TFF) Fγ*γπ0 (Q2) 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 a2 and a4 in comparison with the 1σ and 2σ error regions of the data and the most recent lattice constraints on a2 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.
We consider the calculation of the pion-photon transition form factor F super(gamma*gammapi0)(Q super(2)) within light-cone sum rules focusing attention to the low-mid region of momenta. The central ...aim is to estimate the theoretical uncertainties which originate from a wide variety of sources related to (i) the relevance of next-to-next-to-leading order radiative corrections (ii) the influence of the twist-four and the twist-six term (iii) the sensitivity of the results on auxiliary parameters, like the Borel scale M super(2), (iv) the role of the phenomenological description of resonances, and (v) the significance of a small but finite virtuality of the quasireal photon. Predictions for F super(gamma*gammapi0)(Q super(2)) are presented which include all these uncertainties and found to comply within the margin of experimental error with the existing data in the Q super(2) range between 1 and 5GeV super(2), thus justifying the reliability of the applied calculational scheme. This provides a solid basis for confronting theoretical predictions with forthcoming data bearing small statistical errors.
We show that using renormalization-group summation to generate the QCD radiative corrections to the π − γ transition form factor, calculated with light-cone sum rules (LCSR), renders the strong ...coupling free of Landau singularities while preserving the QCD form-factor asymptotics. This enables a reliable applicability of the LCSR method to momenta well below 1 GeV2. This way, one can use the new preliminary BESIII data with unprecedented accuracy below 1.5 GeV2 to fine tune the prefactor of the twist-six contribution. Using a combined fit to all available data below 3.1 GeV2, we are able to determine all nonperturbative scale parameters and a few Gegenbauer coefficients entering the calculation of the form factor. Employing these ingredients, we determine a pion distribution amplitude with conformal coefficients (b2, b4) that agree at the 1 σ level with the data for Q2 ≤ 3.1 GeV2 and fulfill at the same time the lattice constraints on b2 at N3 LO together with the constraints from QCD sum rules with nonlocal condensates. The form-factor prediction calculated herewith reproduces the data below 1 GeV2 significantly better than analogous predictions based on a fixed-order power-series expansion in the strong coupling constant.
We consider the light cone 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.
The binding effects of quarks within hadrons are discussed in terms of the pion distribution amplitude over longitudinal momentum fractions. To understand the behavior of this quantity at different ...momentum scales, the concept of synchronization in complex systems has been employed. It is argued that at low momentum scales, the quarks get correlated by nonlocal quark/gluon condensates that cause an endpoint-suppressed, mainly bimodal structure of the pion distribution amplitude inferred from a sum-rule analysis. The mass generation mechanism, within the framework of Dyson–Schwinger equations, and evolution effects pull these two peaks back to the center to form at Q2→∞ the asymptotic distribution amplitude which represents the most synchronized q¯q state.
The pion-photon transition form factor is studied by employing two types of sum rules: light cone sum rules (LCSR) and anomaly sum rules (ASR). By comparing the predictions for the pion-photon ...transition form factor, obtained from these two approaches, the applicability limit of the LCSRs at low momenta is determined. Reciprocally, the ASR threshold dependence on the momentum was extracted using our LCSR-based method in combination with two different types of pion distribution amplitudes and found that at higher Q super(2) it approaches a constant.
Using QCD sum rules with nonlocal condensates, we show that the distribution amplitude of the longitudinally polarized ρ-meson may have a shorttailed platykurtic profile in close analogy to our ...recently proposed platykurtic distribution amplitude for the pion. Such a chimera distribution de facto amalgamates the broad unimodal profile of the distribution amplitude, obtained with a Dyson–Schwinger equations-based computational scheme, with the suppressed tails characterizing the bimodal distribution amplitudes derived from QCD sum rules with nonlocal condensates. We argue that pattern formation, emerging from the collective synchronization of coupled oscillators, can provide a single theoretical scaffolding to study unimodal and bimodal distribution amplitudes of light mesons without recourse to particular computational schemes and the reasons for them.
We provide an in-depth analysis of the
π
distribution amplitude in terms of two different Gegenbauer representations. Detailed predictions for the
π
-
γ
transition form factor are presented, obtained ...with light-cone sum rules. Various
π
distribution amplitudes are tested and the crucial role of their endpoint behavior in the form-factor analysis is discussed. Comparison with the data is given.
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