Search

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 discuss cross-link relations between the $��$ and $��$-meson channels emerging from two different descriptions of the QCD vacuum: Instanton physics and QCD sum rules with nonlocal condensates (NLC). We derive in both schemes an intriguing linear relation between the $��$ and the $��^\|$-meson distribution amplitudes in terms of their conformal coefficients and work out the specific impact of the scalar NLC in these two channels. Using a simple model with Gaussian decay of the scalar NLC, we are able to relate it to the moments of the pion non-singlet parton distribution function measurable in experiment -- a highly nontrivial result. The implications for the pion and the $��^\|$-meson DAs entailed by the obtained cross-link relations are outlined in terms of two generic scenarios., 9 pages, 1 table, 4 figures. V2 matches published version

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 consider the lightcone sum-rule (LCSR) description of the pion-photon transition form factor in combination with the renormalization group of QCD. The emerging scheme represents a certain version of Fractional Analytic Perturbation Theory and significantly extends the applicability domain of perturbation theory towards lower momenta $Q^2\lesssim 1$ GeV$^2$. We show that the predictions calculated herewith agree very well with the released preliminary data of the BESIII experiment, which have very small errors just in this region, while the agreement with other data at higher $Q^2$ is compatible with the LCSR predictions obtained recently by one of us using fixed-order perturbation theory., 8 pages, 1 figure, talk presented at the "XXIV International Workshop on High Energy Physics and Quantum Field Theory" (22 - 29 September 2019, Sochi, Russia). A number of misprints are corrected

A survey is presented on the current status of 3D nucleon tomography. Several research frontiers are addressed that dominate modern physics from theory to current and future experiments. We have now a much more detailed spatial image of the nucleon thanks to various theoretical concepts and methods to describe its charge distribution and spin decomposition which are highlighted here. The progress of lattice computations of these quantities is reported and the prospects of what we can come to expect in the near future are discussed. Multi-dimensional maps of the nucleon's partonic structure appear now within reach of forthcoming experiments., Based on the Plenary Round Table at XII Quark Confinement and the Hadron Spectrum, 29 August - 3 September, 2016, Thessaloniki, Greece, 32 pages, 1 Table 17 Figures (embedded as pdf). arXiv admin note: text overlap with arXiv:1208.1244

We consider the pion-photon transition form factor at low to intermediate spacelike momenta within the theoretical framework of light-cone sum rules. We derive predictions which take into account all currently known contributions stemming from QCD perturbation theory up to the next-to-next-to-leading order (NNLO) and by including all twist terms up to order six. In order to enable a more detailed comparison with forthcoming high-precision data, we also estimate the main systematic theoretical uncertainties, stemming from various sources, and discuss their influence on the calculations --- in particular the dominant one related to the still uncalculated part of the NNLO contribution. The analysis addresses, in broad terms, also the role of the twist-two pion distribution amplitude derived with different approaches., Comment: 10 pages, 3 figures, Based on the talk given at the XIIth International Conference "Quark Confinement and the Hadronic Spectrum" (Thessaloniki, Greece, 28 August - 4 September 2016)

Using QCD sum rules with nonlocal condensates, we show that the distribution amplitude of the longitudinally polarized $��$-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., 13 pages, 4 figures. In v2 a typo in Eq. (12) corrected. V3 contains clarifications in text; typos corrected; Table expanded; new references included and discussed; conclusions unchanged; matches version to be published in Nucl. Phys. A. V4: typos in AdS/QCD entries in Table I and in text, bottom of page 5, corrected. In v6 typo in expression for gauge link below Eq. (1) corrected

An outstanding goal of physics is to find solutions that describe hadrons in the theory of strong interactions, Quantum Chromodynamics (QCD). For this goal, the light-front Hamiltonian formulation of QCD (LFQCD) is a complementary approach to the well-established lattice gauge method. LFQCD offers access to the hadrons' nonperturbative quark and gluon amplitudes, which are directly testable in experiments at existing and future facilities. We present an overview of the promises and challenges of LFQCD in the context of unsolved issues in QCD that require broadened and accelerated investigation. We identify specific goals of this approach and address its quantifiable uncertainties., White Paper of International Light Cone Advisory Committee

This report attempts to capture the essential workings of gauge links (Wilson lines) inside gauge-invariant formulations of parton distribution functions in QCD and gain some deeper insight into their key (renormalization) properties. We show, in particular, that the one-loop anomalous dimension of the Cherednikov-Stefanis quark TMD PDF is in the lightcone gauge $A^+=0$, combined with the Mandelstam--Leibbrandt pole prescription, the same as that obtained in the special covariant gauge $a=-3$, leaving no uncanceled rapidity singularities., 8 pages, 2 figures. Presented at Light-Cone 2012, July 08-13, 2012, Cracow, Poland. Dedicated to the memory of Walter Gloeckle, teacher, friend, and colleague. V2 has a couple of minor corrections. V3 matches version accepted for publication in Acta Physica Polonica B

The new data on the $��^*��\to ��^0$ 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 $1��$ level. While the Belle data agree with our predictions, the Babar data are in conflict with them., 8 pages, 6 figures, Presented at Light-Cone 2012, July 08-13, 2012, Cracow, Poland

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

A generalized idea of gauge invariance, that embodies into the Wilson lines the spin-dependent Pauli term $\sim F^{\mu\nu}[\gamma_\mu, \gamma_\nu]$, is applied to set up a new framework for the operator definition of transverse-momentum-dependent parton densities (TMDs). We show that such a treatment of gauge invariance is justified, since it does not change the leading-twist behavior of the TMDs, albeit it contributes to their twist-three properties, in particular, to their anomalous dimensions. We discuss other consequences of this generalization and its possible applications to lattice simulations of the TMDs., Comment: 5 pages, 2 figures. Invited talk given at the XIX International Workshop on Deep Inelastic Scattering (DIS 2011), 11 - 15 Apr 2011, Thomas Jefferson National Accelerator Facility, Newport News (VA)

We discuss the possibility of non-minimal gauge invariance of transverse-momentum-dependent parton densities (TMDs) that allows direct access to the spin degrees of freedom of fermion fields entering the operator definition of (quark) TMDs. This is achieved via enhanced Wilson lines that are supplied with the spin-dependent Pauli term $\sim F^{\mu\nu}[\gamma_\mu, \gamma_\nu]$, thus providing an appropriate tool for the "microscopic" investigation of the spin and color structure of TMDs. We show that this generalization leaves the leading-twist TMD properties unchanged but modifies those of twist three by contributing to their anomalous dimensions. We also comment on Collins' recent criticism of our approach., Comment: 4 pages. Presented at the XIV Workshop on High Energy Spin Physics, 20-24 Sept 2011, Dubna, Russia

We discuss the end-point behavior of the pion distribution amplitude (DA) and calculate its slope using QCD sum rules with nonlocal condensates. This is done in terms of the standard derivative and also with the help of an "integral derivative", recently obtained by us. Our approach favors a value of the slope of the order (or less) of the asymptotic DA and is in clear disagreement with flat-type pion DAs., 13 pages, 5 figures, 3 tables, invited talk given by the second author at "QUARKS-2010, 16th International Seminar on High Energy Physics", Kolomna, Russia, 6-12 June, 2010. v2 An important reference is added with a corresponding insertion in the text. v3 minor typos corrected

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)

We summarize the renormalization-group properties of transverse-momentum dependent (TMD) parton distribution functions (PDF)s arguing that in the light-cone gauge the overlapping ultraviolet and rapidity divergences cannot be solely controlled by (dimensional) regularization, but necessitate their renormalization. In doing so, we show that at the one-loop order this additional divergence entails an anomalous dimension which can be attributed to a cusp in the gauge contour at light-cone infinity. Then, we present a recent analysis of TMD PDFs which incorporates in the gauge links the Pauli term $\sim F^{\mu\nu}[\gamma_\mu,\gamma_\nu]$. This generalized treatment of gauge invariance is shown to be justified, in the sense that it does not modify the behavior of the leading-twist contribution, though it contributes to the anomalous dimension of that of twist-three. An important consequence of the inclusion of the spin-dependent Pauli term is the appearance of a constant phase---the same for the leading twist-two and subleading distribution functions---that ensues from the interaction of the Pauli term in the transverse gauge link with the gauge field accompanying the fermion. Remarkably, this phase has opposite sign for the Drell-Yan process as compared to the semi-inclusive DIS., Comment: 10 pages, 2 figures embedded as eps files. Invited plenary talk presented by the first author at the "Lightcone Conference 2010", June 14-18, 2010, Valencia, Spain. Needs PoS.cls and PoSlogo.ps (included)

We discuss duality in ``two-photon''-like processes in the scalar $\varphi^3_E$ model and also in the process $\gamma^*\gamma\to\pi\pi$ in QCD. Duality implies the equivalence between two distinct nonperturbative mechanisms. These two mechanisms, one involving a twist-3 Generalized Distribution Amplitude, the other employing a leading-twist Transition Distribution Amplitude, are associated with different regimes of factorization. In the kinematical region, where the two mechanisms overlap, duality is observed for the scalar $\varphi^3_E$ model, while in the QCD case the appearance of duality turns out to be sensitive to the particular nonperturbative model applied and can, therefore, be used as a tool for selecting the most appropriate one., Comment: 6 pages, 3 figures. Talk given at Conference PHOTON-09, DESY, Hamburg, May 11-15, 2009

We present results of a calculation of the electromagnetic pion form factor within the framework of QCD Sum Rules with nonlocal condensates, using a perturbative spectral density which includes $O(\alpha_s)$ contributions., Comment: 7 pages, 2 figures, talk presented by the first author at the International Meeting "Excited QCD", February 8--14, 2009, Zakopane (Poland), typos and references corrected

Different approaches to define transverse-momentum dependent parton distribution functions are considered from the point of view of their renormalization-group properties. The associated one-loop anomalous dimensions of these quantities are presented and compared to each other. We give arguments in favor of the "pure light-like" definition, and the use of the light-cone gauge., Comment: 4 pages. Talk presented by the first author at Workshop on the International Workshop "Transverse Partonic Structure of Hadrons", 21-26 Jun 2009, Erevan, Armenia

We use light-cone QCD sum rules to calculate the pion-photon transition form factor, taking into account radiative corrections up to the next-to-next-to-leading order of perturbation theory. We compare the obtained predictions with all available experimental data from the CELLO, CLEO, and the BaBar Collaborations. We point out that the BaBar data are incompatible with the convolution scheme of QCD, on which our predictions are based, and can possibly be explained only with a violation of the factorization theorem. We pull together recent theoretical results and comment on their significance., 10 pages, 4 figures, 3 tables. Presented by the first author at Workshop "Recent Advances in Perturbative QCD and Hadronic Physics", 20--25 July 2009, ECT*, Trento (Italy), in Honor of Prof. Anatoly Efremov's 75th Birthday. v2 wrong reference tag removed. v3 Fig. 4 and Ref. [27] corrected

We present some recently obtained results on transverse-momentum dependent parton distribution functions (TMD PDFs), the latter being important ingredients for the description of semi-inclusive hadronic processes. Special attention is payed to the renormalization group (RG) properties of these objects. In particular, their leading-order anomalous dimension is calculated in the light-cone gauge. It is shown that the RG properties can be used to reveal, in the most economic way, the general structure of the gauge links entering the operator definition of TMD PDFs., 7 pages, 1 figure. Talk presented at XIX International Baldin Seminar on High Energy Physics Problems "Relativistic Nuclear Physics and Quantum Chromodynamics", Dubna, Russia, 29 Sept - 4 Oct 2008

We find that in "two-photon"-like processes in the scalar $\varphi^3_E$ model and also in hadron-pair production arising from the collisions of a real (transversely polarized) and a highly virtual, longitudinally polarized, photon in QCD, there is duality between two distinct nonperturbative mechanisms. These two mechanisms, one involving a twist-3 Generalized Distribution Amplitude, the other employing a leading-twist Transition Distribution Amplitude, are associated with different regimes of factorization. In the kinematical region, where the two mechanisms overlap, duality is observed for the scalar $\varphi^3_E$ model, while in the QCD case the appearance of duality turns out to be sensitive to the particular nonperturbative model applied and can, therefore, be used as a tool for selecting the most appropriate one., Comment: Talk presented at XIX International Baldin Seminar on High Energy Physics Problems "Relativistic Nuclear Physics and Quantum Chromodynamics", Dubna, Russia, September 29 to October 4, 2008

We describe the present status of the pion distribution amplitude (DA) as it originates from several sources: (i) a nonperturbative approach based on QCD sum rules with nonlocal condensates, (ii) an $O(\alpha_s)$ QCD analysis of the CLEO data on F^{\gamma\gamma^*\pi}(Q^2) with asymptotic and renormalon models for higher twists, and (iii) recent high-precision lattice QCD calculations of the second moment of the pion DA. We show predictions for the pion electromagnetic form factor, obtained in analytic QCD perturbation theory, and compare it with the JLab data on F_{\pi}(Q^2). We also discuss in this context an improved model for nonlocal condensates in QCD and show its consequences for the pion DA and the \gamma\gamma^*\to\pi transition form factor. We include a brief analysis of meson-induced massive lepton (muon) Drell--Yan production for the process \pi^{-}N\to\mu^{+}\mu^{-}X, considering both an unpolarized nucleon target and longitudinally polarized protons., Comment: Invited plenary talk presented by the first author at ``Hadron Structure '07'' International Conference, Modra-Harm{\'o}nia, Slovakia, Sept. 2--7, 2007. 14 pages, 10 figures

We discuss recent developments in the understanding of gauge-invariant transverse-momentum dependent (TMD) parton-distribution functions (PDF). We compute the leading-order $\overline{\text{MS}\vphantom{^1}}$-scheme anomalous dimension of such a quantity in the light-cone gauge and show that it receives a contribution that can be associated with a cusp obstruction at transverse light-cone infinity. This anomalous dimension is intimately related to expectation values composed of fields and eikonal factors along a cusped contour and is absent in covariant gauges. The implications of these findings are addressed and a modified definition of TMD PDFs is proposed., Comment: 7 pages, 2 figures. Invited talk presented by the first author at International Workshop "Hadron Structure and QCD" (HSQCD'2008), June 30 - July 4, 2008, Gatchina, Russia (hsqcd.cls supplied)

A theoretical framework is presented to treat hadronic observables within analytic perturbative QCD beyond the leading order of the coupling and for more than one single large momentum scale. The approach generalizes and extends the pioneering work of Shirkov and Solovtsov on an analytic strong running coupling. Some applications to hadronic observables at the partonic level are also discussed., Comment: 16 pages, 1 table, 3 figures with 7 eps files embedded; needs ils2008.sty (supplied). Invited contribution in memory of I. L. Solovtsov at Seminar in Bogoliubov Laboratory of Theoretical Physics, JINR, 141980 Dubna, Russia, Jan. 17, 2008. v2: Equations (11) and (34) corrected. Figure 3 replaced

The renormalization properties of unintegrated (transverse-momentum dependent) parton distribution functions (TMD PDF's) are used for analyzing their completely gauge-invariant definition. To this end, the UV anomalous dimension is calculated at the one-loop order in the light-cone gauge and a consistent treatment of the extra singularities, which produce undesirable contributions in the anomalous dimensions, is given. The generalized definition of a TMD PDF, based on the renormalization procedure for the Wilson exponentials with obstructions, is proposed. The reduction of the re-defined TMD PDF to the integrated PDF's, as well as their probabilistic interpretation, are discussed., Comment: 7 pages, 2 figures. Talk presented by the first author at 15th International Seminar on High Energy Physics QUARKS-2008, Sergiev Posad, Russia, 23-29 May, 2008. v2: typo in the Eq. (20) corrected

We discuss the renormalization of gauge-invariant transverse-momentum dependent (TMD), i.e., unintegrated, parton distribution functions (PDFs) and carry out the calculation of their anomalous dimension at one loop. We show that in the light-cone gauge, TMD PDFs contain UV divergences that may be attributed to the renormalization effect on a cusp-like junction point of the gauge contours at infinity. In order to eliminate the anomalous dimension ensuing from this cusp, we propose to use in the definition of the TMD PDFs, a soft counter term in terms of a path-ordered phase factor along a particular cusped contour extending to transverse light-cone infinity and comprising light-like and transverse segments. We argue that this additional factor is analogous to the "intrinsic" Coulomb phase factor found before in QED., Comment: 9 pages, 5 figures, invited plenary talk given by the first author at XIII International Conference on Selected Problems of Modern Theoretical Physics, Dubna, Russia, June 23-27, 2008

This paper is the write-up version of the theory summary talk given at the HSQCD 2008 Workshop in Gatchina, Russia. Recent theoretical developments and results are summarized focusing on works that point out new perspectives, ranging from perturbative QCD, DGLAP and ERBL evolution, polarized and unpolarized parton distribution functions, small-x physics to nonperturbative QCD, lattice simulations, quark-gluon matter, hadron spectroscopy, and predictions for the LHC., Comment: v1: 23 pages; uses hsqcd.cls (included). Theory Summary talk of International Workshop "Hadron Structure and QCD" (HSQCD'2008), June 30 - July 4, 2008, Gatchina, Russia; v2: one reference added

We study the phenomenon of duality in hard exclusive reactions to which QCD factorization applies. Considering "two-photon"-like processes in the scalar $��^3_E$ model and also hadron-pair production from the collisions of a real (transversely polarized) and a highly virtual, longitudinally polarized, photon in QCD, we identify two regimes of factorization each of them associated with a distinct nonperturbative mechanism. One mechanism involves twist-3 Generalized Distribution Amplitudes, whereas the other one employs leading-twist Transition Distribution Amplitudes. In the case of the scalar $��^3_E$ model, we find duality in that kinematical region where the two mechanisms overlap. In the QCD case, the appearance of duality is sensitive to the particular nonperturbative model applied and can, therefore, be used as an additional adjudicator., 14 pages, 8 figures. Substantial changes in the text, 4 figures added, 1 removed; no changes in conclusions

We present a detailed analysis of meson-induced massive lepton (muon) Drell--Yan production for the process $��^{-}N\to��^{+}��^{-}X$, considering both an unpolarized nucleon target and longitudinally polarized protons. Using a QCD framework, we focus on the angular distribution of $��^+$, which is sensitive to the shape of the pion distribution amplitude, the goal being to test corresponding results against available experimental data. Predictions are made, employing various pion distribution amplitudes, for the azimuthal angle dependence of the $��^{+}$ distribution in the polarized case, relevant for the planned COMPASS experiment. QCD evolution is given particular attention in both considered cases., V1: 18 pages, 10 figures (48 eps files), 2 tables. V2: one wrong reference removed, missing reference in text inserted; matches version to appear in Phys. Rev. D

A range of issues pertaining to the use of Wilson lines in integrated and transverse-momentum dependent (TMD) parton distribution functions (PDF) is discussed. The relation between gauge invariance and the renormalization properties of the Wilson-line integrals is given particular attention. Using an anomalous-dimensions based analysis in the light-cone gauge, a generalized definition of the TMD PDFs is proposed, which employs a cusped Wilson line, and contains an intrinsic "Coulomb-like" phase., Comment: 5 pages, 2 figures, Invited talk presented by the first author at the XII Advanced Research Workshop on High Energy Spin Physics (DSPIN-07), September 3-7, 2007, Dubna, Russia

Different ``analytization'' procedures for the factorized pion form factor are discussed in comparison with the standard QCD perturbation theory at NLO. It is argued that demanding the analyticity of the exclusive amplitude as a \emph{whole}, entails insensitivity of the results on all scheme and scale-setting parameters, including the factorization scale. This enables us to develop an approach of optimized perturbation theory within the MS-bar scheme and to generalize the Analytic Perturbation Theory to non-integer (fractional) powers of the strong running coupling in the complex Q^2 plane, Comment: 7 pages, 1 figure, 1 table, needs hsqcd.cls. Invited plenary talk presented by the first author at Hadron Structure and QCD: from Low to High Energies, St. Petersburg, Russia, 20-24 September 2005

I elaborate on the implementation of analyticity of hadronic quantities at the amplitude level and show that it amounts to the extension of Analytic Perturbation Theory of Shirkov and Solovtsov to non-integer (fractional) powers of the strong running coupling. I give evidence that at the NLO of the factorized pion's electromagnetic form factor this framework diminishes the uncertainty due to the renormalization-scheme choice and nearly removes the dependence on both the renormalization and the factorization scale. I supplement this discussion by considering effects caused by retaining transverse momenta that give rise to Sudakov factors., Invited talk at the XI Workshop on High Energy Spin Physics, Dubna, Russia, September 27 - October 1, 2005; 5 pages, 3 figures as eps files embedded, needs wrapfig

A pion distribution amplitude, derived from nonlocal QCD sum rules, has been employed to calculate $F_{\gamma^*\gamma\to\pi}(Q^2)$ using light-cone sum rules, and $F_{\pi}(Q^2)$ in NLO QCD perturbation theory. Predictions are presented for both observables and found to be in good agreement with the corresponding data. Calculating the hard pion form factor by Analytic Perturbation Theory to two-loop order, it is shown that the renormalization-scheme and scale-setting dependencies are diminished., Comment: 9 pages, 4 figures consisting of 6 eps files. Needs hsqcd.cls. Invited plenary talk presented by the first author at Hadron Structure and QCD: from Low to High Energies, St. Petersburg, Repino, Russia, 18-22 May 2004

We present an investigation of the pion's electromagnetic form factor F_{\pi}(Q^2) in the spacelike region utilizing two new ingredients: (i) a double-humped, endpoint-suppressed pion distribution amplitude derived before via QCD sum rules with nonlocal condensates--found to comply at the 1\sigma level with the CLEO data on the $\pi\gamma$ transition--and (ii) analytic perturbation theory at the level of parton amplitudes for hadronic reactions. The computation of F_{\pi}(Q^2) within this approach is performed at NLO of QCD perturbation theory (standard and analytic), including the evolution of the pion distribution amplitude at the same order. We consider the NLO corrections to the form factor in the \bar{MS} scheme with various renormalization scale settings and also in the \alpha_V-scheme. We find that using standard perturbation theory, the size of the NLO corrections is quite sensitive to the adopted renormalization scheme and scale setting. The main results of our analysis are the following: (i) Replacing the QCD coupling and its powers by their analytic images, both dependencies are diminished and the predictions for the pion form factor are quasi scheme and scale-setting independent. (ii) The magnitude of the factorized pion form factor, calculated with the aforementioned pion distribution amplitude, is only slightly larger than the result obtained with the asymptotic one in all considered schemes. (iii) Including the soft pion form factor via local duality and ensuring the Ward identity at Q^2=0, we present predictions that are in remarkably good agreement with the existing experimental data both in trend and magnitude., Comment: RevTex, 51 pages, 17 figures as 19 EPS files, embedded. Fig. 16(b) modified to show hard and soft form factors separately, Table I expanded; some references added. No changes of content. Paper to appear in PRD

We analyze power-suppressed contributions to singlet pseudoscalar $��$ and $��^{\prime}$ meson transition form factors. These corrections stem from endpoint singularities and help improve the agreement between QCD theory and the experimental data, in particular, at low-momentum transfers. Using the CLEO data, we extract information on the profile of the $��_1$ and $��_8$ distribution amplitudes in the $SU(3)_{F}$ octet-singlet basis employing both the one-angle and the two-angle mixing schemes. In the former scheme, we find good agreement with the CLEO data, while in the second case, our approach requires non-asymptotic profiles for these mesons., 19 pages, 6 figures consisting of 9 eps files. Needs here.sty. Typo in $beta_1$ corrected. Invited plenary talk presented by the first author at Second Symposium on Threshold Meson Production in pp and pd Interactions. Extended COSY-11 collaboration meeting. Collegium Maius, Cracow, Poland, May 31-June 3, 2004

We discuss the status of the pion distribution amplitude (DA) from analyzing the CLEO experimental data in the context of QCD sum-rule techniques and QCD perturbation theory at the NLO accuracy. The constraints extracted this way for the Gegenbauer coefficients a_2 and a_4 exclude \Phi_{CZ} at the 4\sigma level, while \Phi_{asy} is outside the 3\sigma error ellipse. These data provide strong support for the type of endpoint-suppressed, double-humped pion DA we derived via QCD sum rules with nonlocal condensates and favor a value of the vacuum quark virtuality \lambda_q^2 \simeq 0.4 GeV^2. This pion DA is in agreement with the E791 data, though these experimental results should be viewed carefully and further confirmation is necessary for a more accurate judging of pion DAs from them., Comment: 6 pages, 4 figures, cernrep class. Talk presented at the LC03 Workshop "Hadrons and beyond"

In the context of QCD sum rules with non-local condensates we present a pion distribution amplitude, which is double-humped with its end-points x\to(0,1) strongly suppressed, and show that it matches the CLEO experimental data on the pion-photon transition at the 1\sigma level accuracy, being also in compliance with the CELLO data. We also include some comments on the nucleon distribution amplitude and the nucleon evolution equation., Comment: Invited contribution to the Festschrift in honor of Prof. Anatoly Efremov's 70th birthday; 8 pages, 4 figures as eps-files (wrapfig.sty needed)

Using QCD perturbation theory in NLO and light-cone QCD sum rules, we extract from the CLEO experimental data on the F^{\gamma^*\gamma\pi}(Q^{2} transition form factor constraints on the Gegenbauer coefficients a_2 and a_4, as well as on the inverse moment _{\pi} of the pion distribution amplitude. We show that both the asymptotic and the Chernyak--Zhitnitsky pion distribution amplitudes are excluded at the 3\sigma- and 4\sigma-level, respectively, while the data confirms the end-point suppressed shape of the pion DA we previously obtained with QCD sum rules and nonlocal condensates. These findings are also supported by the data of the Fermilab E791 experiment on diffractive dijet production., Comment: 9 pages, 7 figures. Talk given at NAPP2003, Dubrovnik, May 26--31, 2003; misprints fixed

We compute power-suppressed corrections to the ����and ��^{\prime}��transition form factors Q^2F_{��(��^{\prime})��}(Q^2) arising from the end point regions x \to 0,1 by employing the infrared-renormalon approach. The contribution to the form factors from the quark and gluon content of the ��,��^{\prime} mesons is taken into account using for the ��-��^{\prime} mixing the SU_f(3) singlet ��_1 and octet ��_8 basis. The theoretical predictions obtained this way are compared with the corresponding CLEO data and restrictions on the input parameters (Gegenbauer coefficients) B_2^q(��_1), B_2^g(��_1), and B_2^q(��_8) in the distribution amplitudes for the ��_1,��_8 states with one nonasymptotic term are deduced. Comparison is made with the results from QCD perturbation theory., 25 pages, RevTeX4 used. 9 figures as EPS files. Text significantly changed to include variation of theoretical parameters. Figures modified. Corrected typo in equation (34) and trivial mistake in $\beta_1$-coefficient. References added. Conclusions unchanged

I present a unifying scheme for hadronic functions that comprises logarithmic corrections due to gluon emission in perturbative QCD, as well as power-behaved corrections of nonperturbative origin. The latter are derived by demanding that perturbatively resummed partonic observables should be analytic in the whole $Q^2$-plane if they are to be related to physical observables measured in experiments. I also show phenomenological consequences of this approach. The focus is on the electromagnetic pion form factor to illustrate both effects, Sudakov logarithms and power corrections in leading order of $\Lambda_{\rm{QCD}}^2/Q^2$. The same approach applied to the inclusive Drell-Yan cross section enables us to perform an absolutely normalized calculation of the leading power correction in $b^2\Lambda_{\rm{QCD}}^2$ (b being the impact parameter), which after exponentiation, gives rise to a nonperturbative Sudakov-type contribution that provides enhancement rather than suppression, hence partly counteracting the perturbative Sudakov suppression., Comment: 14 pages; 2 figures containing 3 EPS files; RevTex style; to appear by Springer Verlag as Lecture Notes in Physics. V2: The following equations have been corrected: second line of (26), (34), (39), (44), (45); values of a_0, a_1, a_2 below (40) corrected; Conclusions unchanged. See also hep-ph/0101031

By remaining strictly within the confines of QCD, i.e., {\it without} invoking the parton model or any other exogenous element, we identify and resum perturbatively to leading order, along with a correction term, enhanced radiative gluon contributions to the Drell-Yan type ($q\bar{q}$ pair annihilation) and deep-inelastic-scattering type ($eq\to eq+X$) cross-sections. The key feature of the adopted approach is the recasting of QCD in terms of a space-time mode of description, which employs a path-integral formulation of field theories, as originally implied in works of Fock, Feynman and Schwinger., 29 pages; 3 figures as EPS files; some minor typos corrected; RevTex style; submitted to Phys. Rev. D

Employing the standard hard-scattering approach (HSA) in conjunction with the running-coupling (RC) method, the latter joined with the infrared-renormalon calculus, we compute power-suppressed corrections $\sim 1/Q^{2n}, n=1, 2,...$ to the massless $��^{\prime}$ meson - virtual gluon transition form factor (FF) $Q^2F_{��^{\prime}g^{*}g^{*}}(Q^2,��)$. Contributions to the form factor from the quark and gluon components of the $��^{\prime}$ meson are taken into account. Analytic expressions for the FF's $F_{��^{\prime}gg^{*}}(Q^2,��=\pm 1)$ and $F_{��^{\prime}g^{*}g^{*}}(Q^2,��=0)$ are also presented, as well as Borel transforms $B[Q^{2}F_{��^{\prime}g^{*}g^{*}}](u)$ and resummed expressions. It is shown that except for $��=\pm 1, 0$, the Borel transform contains an infinite number of infrared renormalon poles. It is demonstrated that in the explored range of the total gluon virtuality $1 \rm {GeV}^{2} \leq Q^2 \leq 25 \rm {GeV}^{2}$, power corrections found with the RC method considerably enhance the FF $F_{��^{\prime}g^{*}g^{*}}(Q^{2}, ��)$ relative to results obtained only in the context of the standard HSA with a ``frozen'' coupling., 38 pages, RevTeX4 used. 18 figures as PS/EPS files. Discussion extended; some typos corrected; change of renormalization scale to 1 GeV. Main results unchanged. Matches version to be published in Eur. Phys. J. C

Using QCD sum rules with nonlocal condensates the twist-2 pion distribution amplitude is determined by means of its moments and their confidence intervals, including also radiative corrections. An admissible set of pion distribution amplitudes is constructed in the a_2, a_4 plane of the Gegenbauer polynomial expansion coefficients. The determined a_2, a_4 region strongly overlaps with that extracted from the CLEO data by Schmedding and Yakovlev. Comparisons are given with results from Fermilab experiment E791 and recent lattice calculations., Comment: 4 pages in moriond style; 1 photo and 2 figures unite 7 EPS files; to appear in Proc. of XXXIVth Rencontres de Moriond "QCD and High Energy Hadronic Interactions", March 17 to 24, 2001, Les Arcs, Savoie, France

We develop and discuss in technical detail an infrared-finite factorization and optimized renormalization scheme for calculating exclusive processes, which enables the inclusion of transverse degrees of freedom without entailing suppression of calculated observables, like form factors. This is achieved by employing an analytic, i.e., infrared stable, running strong coupling $��_{\rm s}(Q^{2})$ which removes the Landau singularity at $Q^{2}=��_{\rm QCD}^{2}$ by a minimum power-behaved correction. The ensuing contributions to the cusp anomalous dimension - related to the Sudakov form factor - and to the quark anomalous dimension - which controls evolution - lead to an enhancement at high $Q^{2}$ of the hard part of exclusive amplitudes, calculated in perturbative QCD, while simultaneously improving its scaling behavior. The phenomenological implications of this framework are analyzed by applying it to the pion's electromagnetic form factor, including the NLO contribution to the hard-scattering amplitude, and also to the pion-photon transition at LO. For the pion wave function, an improved ansatz of the Brodsky-Huang-Lepage type is employed, which includes an effective (constituent-like) quark mass, $m_{\rm q}=0.33$ GeV. Predictions for both form factors are presented and compared to the experimental data, applying Brodsky-Lepage-Mackenzie commensurate scale setting. We find that the perturbative hart part prevails at momentum transfers above about 20 GeV ${}^{2}$, while at lower $Q^{2}$-values the pion form factor is dominated by Feynman-type contributions. The theoretical prediction for the $��^{*}��\to ��^{0}$ form factor indicates that the true pion distribution amplitude may be somewhat broader than the asymptotic one., 41 pages in RevTeX; 10 figures (2 added) as PS files; Table 1 slightly changed; expanded discussion of BHL ansatz; misprints corrected; some clarifications and references added; results unchanged. Matches version to appear in Eur.Phys.J.C

We develop and discuss an infrared-finite factorization and optimized renormalization scheme for calculating exclusive processes which enables the inclusion of transverse degrees of freedom without entailing suppression of calculated observables, like form factors. This is achieved by employing an analytic, i.e., infrared stable, effective coupling $\alpha_{s}(Q^{2})$ which removes the Landau singularity at $Q^{2}=\Lambda_{\rm QCD}^{2}$ by a power-behaved correction. The ensuing contributions to the cusp anomalous dimension, related to the Sudakov form factor, and to the quark anomalous dimension, which controls evolution, lead to enhancement of the hard part of exclusive amplitudes, calculated in perturbative QCD. The phenomenological implications of this framework are analyzed by applying it to the pion's electromagnetic form factor and the pion-photon transition., Comment: 23 pages, RevTeX is used. Four figures in PS files

Sudakov-type form factors for quark vertex functions in QCD are discussed using a worldline approach., 7 pages, RevTeX is used. No figures

We point out some serious problems in the investigation of Kundu et al. which claims agreement with the existing data of the proton form factor, calculated without taking into account the intrinsic k_{perp}-dependence of the proton wave function., 3 pages, RevTeX is used, no figures

We dedicate this document to the memory of Mikhail Polikarpov, who passed away in July 2013. Misha worked with us for decades as a convener of the “Confinement” section of the Quark Confinement and Hadron Spectrum Series. He guided and expanded the scientific discussion of that topic, inspiring and under taking new research avenues. From its initial conception, he supported the enterprise of this document and organized Sect. 8, writing the part on confinement himself. He attracted the XIth Conference on Quark Confinement and the Hadron Spectrum to St. Petersburg (September 8-12, 2014; see http://phys.spbu.ru/confxi.html). His warm and kind personality, his high sense of humor, his ideas in physics, and his special energy in imagining and realizing new projects will be always a loss and an example for us. We also miss four other physicists who made lasting contributions to the field of strong interactions: Dmitri Diakonov, Nikolai Uraltsev, Pierre van Baal, and Kenneth Wilson. We remember Misha, Dima, Ken, Kolya, and Pierre with fondness and gratitude. In addition, S.G. would like to dedicate her work on this document to the memory of her mother and mentor, Gladys Strom Gardner. The authors thank Mikko Laine for collaboration during initial stages of the project. In addition, Véronique Bernard, Alex Bondar, Geoffrey T. Bodwin, Davide Caffarri, Gilberto Colangelo, Lance Dixon, Gernot Eichmann, Christoph Hanhart, Ulrich Heinz, Aleksi Kurkela, Vittorio Lubicz, Alexander Milov, Bachir Moussallam, Antonio Pineda, Brad Plaster, Massimiliano Procura, Joan Soto, Reinhard Stock, Ruth Van de Water, Ubirajara van Kolck, Julia Velkovska, and Richard Williams provided helpful correspondance and contributions during the preparation of this review. Finally, the Editors thank Małgorzata Janik for maintaining document and bibliography updates and for coordinating an editorial team of Jeremi Niedziela and Anna Zaborowska., 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., The authors appreciate and acknowledge support for work on this document provided, in part or in whole, by • U.S. Department of Energy, Office of Science, Offices of Nuclear and High-Energy physics, under contracts #DE-FG02-05ER41375 and #DE-FG02-91ER40628 (M. Alford and K. Schwenzer) • the EU I3HP project EPOS “Exciting Physics of Strong Interactions” (WP4 of HadronPhysics3) (R. Alkofer) • U.S. Department of Energy grant no. DE-SC0007984, (P. Arnold) • Deutsche Forschungsgemeinschaft DFG EClust 153 “Origin and Structure of the Universe” (N. Brambilla, L. Fabbietti, B. Ketzer, A. Vairo) • Deutsche Forschungsgemeinschaft DFG grants BR 4058/2-1 and BR 4058/1-1; work supported in part by DFG and NSFC (CRC 110) (N. Brambilla, A. Vairo) • U.S. Department of Energy (T. Cohen) • Istituto Nazionale di Fisica Nucleare (INFN) of Italy (P. Di Nezza) • the Ministry of Education and Science of the Russian Federation; the Russian Foundation for Basic Research under grants 12-02-01032 and 12-02-01296 and the German Research Foundation (DFG) under grant HA 1457/9-1. (S. Eidelman) • Bundesministerium für Bildung und Forschung BMBF Grant No. 05P12WOGHH; Helmholtz Young Investigator University Group, VHNG-330 (L. Fabbietti) • Swiss National Science Foundation (SNF) under the Sinergia grant number CRSII2 141847 1 (X. Garcia i Tormo) • U.S. Department of Energy Office of Nuclear Physics under contract DE-FG02-96ER40989 (S. Gardner) • DOE Contract No. DE-AC05-06OR23177 under which JSA operates the Thomas Jefferson National Accelerator Facility, and by the National Science Foundation through grants PHY-0855789 and PHY-1307413 (J. Goity) • Austrian Science Foundation FWF under project No. P20016-N16 (R. Höllwieser) • Polish National Science Centre reaserch grant UMO-2012/05/N/ST2/ 02757 (M. A. Janik) • European Union in the framework of European Social Fund through the Warsaw University of Technology Development Programme (M. A. Janik) • U.S. Department of Energy, Office of Nuclear Physics, under grant DE-FG02-89ER40531 (D. Keane) • Bundesministerium für Bildung und Forschung BMBF Grant No. 05P12WOCC1 (B. Ketzer) • European Union program “Thales” ESF/NSRF 2007-2013 (E. Kiritsis) • European Union (European Social Fund, ESF) and Greek national funds through the Operational Program “Education and Lifelong Learning” of the National Strategic Reference Framework (NSRF) under “Funding of proposals that have received a positive evaluation in the 3rd and 4th Call of ERC Grant Schemes” (E. Kiritsis) • European Union’s Seventh Framework Programme under grant agreements (FP7-REGPOT-2012-2013-1) No. 316165, and PIF-GA-2011- 300984 and by the European Commission under the ERC Advanced Grant BSMOXFORD 228169 (E. Kiritsis) • Fermilab is operated by Fermi Research Alliance, LLC, under Contract No. DE-AC02-07CH11359 with the U.S. Department of Energy (A. S. Kronfeld) • U.S. Department of Energy Office of Nuclear Physics under contract DE-FG02-97ER4014 (H.-W. Lin) • Spanish grant FPA2011-27853-C02-01 (Felipe J. Llanes-Estrada) • Center for Computational Sciences as part of the Rhineland-Palatinate Research Initiative (H. B. Meyer) • the DFG grant ME 3622/2-1 (H. B. Meyer) • the European Research Council under the European Community’s Seventh Framework Programme (FP7/2007-2013) / ERC grant agreement No. 210223 (A. Mischke) • Netherlands Organisation for Scientific Research (project number 680-47-232) (A. Mischke) • Dutch Foundation for Fundamental Research (project number 10PR2884) (A. Mischke) • the Russian Foundation for Basic Research (grant 14-02-01220) (R. Mizuk) • U.S. Department of Energy by Lawrence Berkeley National Laboratory, Nuclear Science Division, under Contract No. DE-AC02- 05CH11231 (G. Odyniec) • Spanish Government and EU funds for regional development grants FPA2011-23778 and CSD2007-00042 (A. Pich) • Generalitat Valenciana grant PrometeoII/2013/007 (A. Pich) • the European Research Council under the European Community’s Seventh Framework Programme (FP7/2007-2013) / ERC grant agreement No. 291377 (R. Pittau) • Spanish grant FPA2011-22398 (R. Pittau) •U. S. Department of Energy under contract No. DE-AC02-98CH10886 and the National Science Foundation under grant Nos. PHY-0969739 and -1316617 (J.-W. Qiu) • Italian MIUR under project 2010YJ2NYW and INFN under specific initiative QNP (G. Ricciardi) • The European Research Council grant HotLHC ERC-2011-StG279579; by Ministerio de Ciencia e Innovacion of Spain (FPA2009- 11951) and by Xunta de Galicia. (C. A. Salgado) • the EU I3HP project “Study of Strongly Interacting Matter” (acronym HadronPhysics3), Grant Agreement No. 283286 (H. Sazdjian) • Austrian Science Foundation FWF under project No. P23536-N16 (A. Schmitt) •NSF PHY-0969490 and Indiana University Center for Spacetime Symmetries (W. M. Snow) • Lawrence Livermore National Laboratory is operated by Lawrence Livermore National Security, LLC, for the U.S. Department of Energy, National Nuclear Security Administration, under Contract DE-AC52- 07NA27344. The work is also supported in part by the US DOE JET topical collaboration. (R. Vogt) • Academy of Finland, grant # 266185 (A. Vuorinen)