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We study two versions of lightcone sum rules to calculate the $\gamma^*\gamma\rightarrow\pi^0$ 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., Comment: 8 pages, 3 figures. Work dedicated to the memory of Maxim Polyakov, a deeply admired colleague and friend of ours. Presented at Virtual Tribute to Quark Confinement and the Hadron Spectrum, August 2nd-6th, 2021

We show that using renormalization-group summation to generate the QCD radiative corrections to the $\pi-\gamma$ transition form factor, calculated with lightcone 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 GeV$^2$. This way, one can use the new preliminary BESIII data with unprecedented accuracy below 1.5 GeV$^2$ to fine tune the prefactor of the twist-six contribution. Using a combined fit to all available data below 3.1 GeV$^2$, 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 $(b_2,b_4)$ that agree at the $1\sigma$ level with the data for $Q^2 \leqslant 3.1$ GeV$^2$ and fulfill at the same time the lattice constraints on $b_2$ at N$^3$LO together with the constraints from QCD sum rules with nonlocal condensates.The form-factor prediction calculated herewith reproduces the data below 1 GeV$^2$ significantly better than analogous predictions based on a fixed-order power-series expansion in the strong coupling constant., Comment: 15 pages, 3 figures, 1 table, [v3] reformatted in two-column style, 15 pages; references added, typos corrected, [v4] minor corrections

We study the pion-photon transition form factor (TFF) $F^{\gamma*\gamma\pi^0}(Q^2)$ 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 $1\sigma$ and $2\sigma$ 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., Comment: 16 pages, 3 tables, 4 figures; derives partly from arXiv:1904.02631; text revised and expanded; more and updated figures; references added; discussion of new results. References added. V3 matches version accepted for publication in Physical Review D

We discuss the evaluation of the transition form factor (TFF) $F^{\gamma*\gamma\pi^0}(Q^2)$ by means of QCD theory and by state-space reconstruction from topological data analysis. We first calculate this quantity in terms of quark-gluon interactions using light cone sum rules (LCSRs). The spectral density includes radiative corrections in leading, next-to-leading, and next-to-next-to-leading-order of perturbative QCD. Besides, it takes into account the twist-four and twist-six terms. The hard-scattering part in the LCSR is convoluted with various pion distribution amplitudes with different morphologies in order to obtain a wide range of predictions for the form factor, including two-loop evolution which accounts for heavy-quark thresholds. We then use nonlinear time series analysis to extract information on the long-term $Q^2$ behavior of the measured scaled form factor in terms of state-space attractors embedded in $\mathbb{R}^3$. These are reconstructed by applying the Packard-Takens method of delays to appropriate samplings of the data obtained in the CLEO, \textit{BABAR}, and Belle single-tagged $e^+e^- \to e^+e^-\pi^0$ experiments. The corresponding lag plots show an aggregation of states around the value $Q^2F^{\gamma*\gamma\pi^0}(Q^2) \approx 0.165\pm 0.005$ GeV pertaining to the momentum interval $Q^2\in [9-11]$~GeV$^2$. We argue that this attractor portrait is a transient precursor of a distribution of states peaking closer to the asymptotic limit $Q^2F^{\gamma*\gamma\pi^0}(Q^2\to \infty)=\sqrt{2}f_\pi$~GeV. More data with a regular increment of 1~GeV$^2$ in the range between 10 and 25~GeV$^2$ would be sufficient to faithfully determine the terminal portrait of the attractor., Comment: 26 pages, 2 tables, 9 figures, uses two-column format. In V2, url's in [22] and [24] removed to resolve problem with format. V3 contains in Figs. 2, 3, 8, 9 comparison with preliminary BESIII data [48] and extended explanations in text

We highlight the progress, current status, and open challenges of QCD-driven physics, in theory and in experiment. We discuss how the strong interaction is intimately connected to a broad sweep of physical problems, in settings ranging from astrophysics and cosmology to strongly-coupled, complex systems in particle and condensed-matter physics, as well as to searches for physics beyond the Standard Model. We also discuss how success in describing the strong interaction impacts other fields, and, in turn, how such subjects can impact studies of the strong interaction. In the course of the work we offer a perspective on the many research streams which flow into and out of QCD, as well as a vision for future developments., Comment: 246 pp, around 128 figures; v2 adds material, references, and corrections suggested by readers of v1 -- to be submitted to EPJC

The new data on the $\gamma^*\gamma \to \pi^0$ transition form factor of the Belle Collaboration are analyzed in comparison with those of BaBar (including the older data of CELLO and CLEO) using an approach based on light-cone sum rules. Performing a 2-, and a 3-parametric fit to these data, we found that the Belle and the BaBar data have no overlap at the $1\sigma$ level. While the Belle data agree with our predictions, the Babar data are in conflict with them., Comment: 8 pages, 6 figures, Presented at Light-Cone 2012, July 08-13, 2012, Cracow, Poland

We perform a comparative theoretical study of the data at spacelike momentum transfer for the $\gamma^*\gamma\to\pi^0$ transition form factor, just reported by the Belle Collaboration, vs. those published before by BaBar, also including the older CLEO and CELLO data. Various implications for the structure of the $\pi^0$ distribution amplitude vis-\`a-vis those data are discussed and the existing theoretical predictions are classified into three distinct categories. We argue that the actual bifurcation of the data with antithetic trends is artificial and reason that the Belle data are the better option., Comment: v1: 5 pages, 1 table, 2 figures. v2: 1 figure added and discussed in text; references regrouped, added and/or updated. v3: matches version to be published in PRD

A state-of-the-art analysis of the pion-photon transition form factor is presented based on an improved theoretical calculation that includes the effect of a finite virtuality of the quasi-real photon in the method of light-cone sum rules. We carry out a detailed statistical analysis of the existing experimental data using this method and by employing pion distribution amplitudes with up to three Gegenbauer coefficients $a_2, a_4, a_6$. Allowing for an error range in the coefficient $a_6\approx 0$, the theoretical predictions for $\gamma^*\gamma\to\pi^0$ obtained with nonlocal QCD sum rules are found to be in good agreement with all data that support a scaling behavior of the transition form factor at higher $Q^2$, like those of the Belle Collaboration. The data on $\gamma^*\gamma\to\eta/\eta'$ from CLEO and \babar are also reproduced, while there is a strong conflict with the auxetic trend of the \babar data above 10 GeV$^2$. The broader implications of these findings are discussed., Comment: v4: 13 pages, 1 table, 8 figures. Paper body radically redesigned and extended to include Belle data. Contains statistical data analysis and photon small virtuality. Conclusions and references updated. V5 matches version to appear in Physical Review D

We present an extended analysis of the data for the pion-photon transition form factor from different experiments, CELLO, CLEO, and BaBar, and discuss various theoretical approaches which try to reason from them. We focus on the divergent behavior of the BaBar data for the pion and those for the $\eta(\eta')$ pseudoscalar mesons and comment on recently proposed explanations for this discrepancy. We argue that it is not possible at present to accommodate these data within the standard QCD framework self-consistently., Comment: 5 pages, 2 figures, talk presented by the second author at the International Workshop on e^+e^- collisions from phi to psi (PHIPSI11), Novosibirsk (Russia), Sept. 19--22, 2011

An analysis of all available data (CELLO, CLEO, \babar) in the range $[1\div 40]$ GeV$^2$ for the pion-photon transition form factor in terms of light-cone sum rules with next-to-leading-order accuracy is discussed, including twist-four contributions and next-to-next-to-leading order and twist-six corrections---the latter two via uncertainties. The antithetic trend between the \babar data for the $\gamma^*\gamma\pi^0$ and those for the $\gamma^*\gamma\eta(\eta')$ transition is pointed out, emphasizing the underlying antagonistic mechanisms: endpoint enhancement for the first and endpoint-suppression for the second---each associated with pseudoscalar meson distribution amplitudes with distinct endpoint characteristics., Comment: 6 pages, 3 figures; needs style files svglov2.clo, svjour2.cls (supplied). Presented at LIGHTCONE 2011, 23 - 27 May, 2011, Dallas, USA. Accepted for publication in Few-Body Systems. In v2 name of second author in [28] corrected. V3 is final version, published online 23. Sep 2011

A global fit to the data from different collaborations (CELLO, CLEO, BaBar) on the pion-photon transition form factor is carried out using light-cone sum rules. The analysis includes the next-to-leading QCD radiative corrections and the twist-four contributions, while the main next-to-next-to-leading term and the twist-six contribution are taken into account in the form of theoretical uncertainties. We use the information extracted from the data to investigate the pivotal characteristics of the pion distribution amplitude. This is done by dividing the data into two sets: one containing all data up to 9 GeV$^2$, whereas the other incorporates also the high-$Q^2$ tail of the BaBar data. We find that it is not possible to accommodate into the fit these BaBar data points with the same accuracy and conclude that it is difficult to explain these data in the standard scheme of OCD., Comment: 8pages, 6 Figures, 2 Tables. Talk presented by the second and third authors at the 5th joint International HADRON STRUCTURE '11 Conference, Tatranska Strba (Slovak Republic),June 27--July 1, 2011.v2 minor corrections, 3 references are added

We discuss the possibility of quantum entanglement for pairs of charged particles produced in high-energy $pp$-collisions at the LHC. Using a framework of interacting Wilson lines, we calculate 2-D and 1-D two-particle angular correlation functions in terms of the differences of the pseudorapidities and azimuthal angles of the produced particles. The calculated near-side angular correlation shows a localized maximum around $\Delta\phi \approx 0$, though it is less pronounced compared to the peak observed by the CMS Collaboration. We argue that this soft correlation is universal and insensitive to the specific properties of the matter (quark-gluon plasma, QCD vacuum, etc.) used to describe hadronic states---though such properties can be included to further improve the results., Comment: v1: 4 pages, 1 figure (eps file embedded in text); v2: 9 pages, 6 eps figures, significantly revised and extended, new results on 2-D and 1-D correlations presented, references updated and added; v3: matches the version accepted for publication in Int. J. Mod. Phys. A; v4: minor corrections, matches the final version in Int. J. Mod. Phys. A

We discuss the status of the pion distribution amplitude (DA) in connection with QCD sum rules and experimental data on the $\gamma^*\gamma^\to \pi^0$ transition form factor. Contents: (a) Pion DA in generalized QCD Sum Rules (SRs); (b) Light Cone Sum Rules (LCSR) analysis of the CLEO data for the $\gamma^*\gamma\to\pi^{0}$ transition form factor; (c) Recent lattice QCD data for the pion DA; (d) BaBar data---a challenge for QCD?, Comment: 6 pages, 3 figures, talk delivered by the first author at the International Meeting "Excited QCD'', January 31--February 5, 2010, Tatranska Lomnica (Slovakia)

The transition pion-photon form factor is studied within the framework of Light-Cone QCD Sum Rules. The spectral density for the next-to-leading order corrections is calculated for any Gegenbauer harmonic. At the level of the next-to-next-to-leading (NNLO) radiative corrections, only that part of the hard-scattering amplitude is included that is proportional to the $\beta$-function, taking into account the leading zeroth-order harmonic. The relative size of the NNLO contribution in the prediction for the form factor $F^{\gamma^{*}\gamma\pi}(Q^2)$ has been analyzed, making use of the BLM scale-setting procedure. In addition, predictions for the form factor $F^{\gamma^{*}\rho\pi}$ are obtained that turn out to be sensitive to the endpoint behavior of the pion distribution amplitude, thus providing in connection with experimental data an additional adjudicator for the pion distribution amplitude. In a note added, we comment on the preliminary high-$Q^2$ BaBar data on $F^{\gamma^{*}\gamma\pi}$ arguing that the significant growth of the form factor between 10 and 40 GeV$^2$ cannot be explained in terms of higher-order perturbative corrections at the NNLO., Comment: 36 pages, 8 figures, 1 table. v2 new entry in Table I with reference added and replaced Fig. 6. v3 extended discussion of BaBar data (added 1 figure and references). v4 double reference removed; matches version published in Nucl. Phys. B. v5 corrected Ref. [62]; v6 corrects several errors (all boldfaced) and extended acknowledgments