arXiv subjects

A. P. Bakulev

Publications and source records attributed to A. P. Bakulev.

At least 37 records · Page 2Linked to original sources

arXiv2006

Fractional Analytic Perturbation Theory in QCD and Exclusive Reactions

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

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arXiv2005

QCD Analytic Perturbation Theory. From integer powers to any power of the running coupling

We propose a new generalized version of the QCD Analytic Perturbation Theory of Shirkov and Solovtsov for the computation of higher-order corrections in inclusive and exclusive processes. We construct non-power series expansions for the analytic images of the running coupling and its powers for any fractional (real) power and complete the linear space of these solutions by constructing the index derivative. Using the Laplace transformation in conjunction with dispersion relations, we are able to derive at the one-loop order closed-form expressions for the analytic images in terms of the Lerch function. At the two-loop order we provide approximate analytic images of products of powers of the running coupling and logarithms--typical in higher-order perturbative calculations and when including evolution effects. Moreover, we supply explicit expressions for the two-loop analytic coupling and the analytic images of its powers in terms of one-loop quantities that can strongly simplify two-loop calculations. We also show how to resum powers of the running coupling while maintaining analyticity, a procedure that captures the generic features of Sudakov resummation. The algorithmic rules to obtain analytic coupling expressions within the proposed Fractional Analytic Perturbation Theory from the standard QCD power-series expansion are supplied ready for phenomenological applications and numerical comparisons are given for illustration.

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arXiv2005

Analyticity properties of three-point functions in QCD beyond leading order

The removal of unphysical singularities in the perturbatively calculable part of the pion form factor--a classic example of a three-point function in QCD--is discussed. Different ``analytization'' procedures in the sense of Shirkov and Solovtsov re examined in comparison with standard QCD perturbation theory. We show that demanding the analyticity of the partonic amplitude as a \emph{whole}, as proposed before by Karanikas and Stefanis, one can make infrared finite not only the strong running coupling and its powers, but also cure potentially large logarithms (that first appear at next-to-leading order) containing the factorization scale and modifying the discontinuity across the cut along the negative real axis. The scheme used here generalizes the Analytic Perturbation Theory of Shirkov and Solovtsov to non-integer powers of the strong coupling and diminishes the dependence of QCD hadronic quantities on all perturbative scheme and scale-setting parameters, including the factorization scale.

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arXiv2004

Pion distribution amplitude -- from theory to data

We describe the present status of the pion distribution amplitude as originated from two sources: (i) a nonperturbative approach, based on QCD sum rules with nonlocal condensates, and (ii) a NLO QCD analysis of the CLEO data on F^{γγ^*π}(Q^2), supplemented by the E791 data on diffractive dijet production, and the JLab F(pi) data on the pion electromagnetic form factor.

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arXiv2004

Deep inside the pion. Reconciling QCD theory with data

Recent developments in the QCD description of the pion structure are reviewed. The CLEO pion-photon transition data analysis favors a distribution amplitude for the pion that is double-humped but endpoint-suppressed. After a short outline of the derivation of this amplitude from QCD sum rules with nonlocal condensates, we present the fully fledged analysis of the CLEO data prefaced by predictions for the $F^{γρπ}$ form factor and commenting on the inherent theoretical uncertainties due to higher twists and NNLO perturbative corrections. We supplement our discussion by considering within QCD factorization theory, the electromagnetic pion form factor at NLO accuracy on one hand, and diffractive di-jets production on the other, comparing our predictions with the respective experimental data from JLab and the Fermilab E791 collaboration. In all cases, the agreement is impressive.

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arXiv2004

Pion structure: from nonlocal condensates to NLO analytic perturbation theory

A pion distribution amplitude, derived from nonlocal QCD sum rules, has been employed to calculate $F_{γ^*γ\toπ}(Q^2)$ using light-cone sum rules, and $F_π(Q^2)$ 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.

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arXiv2004

Pion form factor in QCD: From nonlocal condensates to NLO analytic perturbation theory

We present an investigation of the pion's electromagnetic form factor F_π(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 1σlevel with the CLEO data on the $πγ$ transition--and (ii) analytic perturbation theory at the level of parton amplitudes for hadronic reactions. The computation of F_π(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 α_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.

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arXiv2004

QCD-based pion distribution amplitudes confronting experimental data

We use QCD sum rules with nonlocal condensates to re-calculate more accurately the moments and their confidence intervals of the twist-2 pion distribution amplitude including radiative corrections. We are thus able to construct an admissible set of pion distribution amplitudes which define a reliability region in the $a_{2}$, $a_{4}$ plane of the Gegenbauer polynomial expansion coefficients. We emphasize that models like that of Chernyak and Zhitnitsky, as well as the asymptotic solution, are excluded from this set. We show that the determined $a_{2}$, $a_{4}$ region strongly overlaps with that extracted from the CLEO data by Schmedding and Yakovlev and that this region is also not far from the results of the first direct measurement of the pion valence quark momentum distribution by the Fermilab E791 collaboration. Comparisons with recent lattice calculations and instanton-based models are briefly discussed.

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arXiv2003

Unbiased analysis of CLEO data at NLO and pion distribution amplitude

We discuss different QCD approaches to calculate the form factor F^{γ^*γπ}(Q^2) of the γ^*γ\toπ^{0} transition giving preference to the light-cone QCD sum rules (LCSR) approach as being the most adequate. In this context we revise the previous analysis of the CLEO experimental data on F^{γ^*γπ}(Q^{2}) by Schmedding and Yakovlev. Special attention is paid to the sensitivity of the results to the (strong radiative) α_s-corrections and to the value of the twist-four coupling δ^2. We present a full analysis of the CLEO data at the NLO level of LCSRs, focusing particular attention to the extraction of the relevant parameters to determine the pion distribution amplitude, i.e., the Gegenbauer coefficients a_2 and a_4. Our analysis confirms our previous results and also the main findings of Schmedding and Yakovlev: both the asymptotic, as well as the Chernyak--Zhitnitsky pion distribution amplitudes are completely excluded by the CLEO data. A novelty of our approach is to use the CLEO data as a means of determining the value of the QCD vacuum non-locality parameter λ^2_q = <\bar{q}D^2q>/<\bar{q}q> =0.4 GeV^2, which specifies the average virtuality of the vacuum quarks.

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arXiv2002

Lattice measurements of nonlocal quark condensates, vacuum correlation length, and pion distribution amplitude in QCD

Recent data of lattice measurements of the gauge-invariant nonlocal scalar quark condensates are analyzed to extract the short--distance correlation length, 1/λ_q, and to construct an admissible Ansatz for the condensate behaviour in a coordinate space. The correlation length values for both the quenched and full-QCD cases appear in a good agreement with the well-known QCD SR estimates of the mixed quark-gluon condensate, 2 λ_q^2 = <\bar{q}(igσ^{μν}G_{μν})q>/<\bar{q}q> = 0.8 - 1.1 GeV^2. We test two different Ansatzes for a nonlocal quark condensate and trace their influence on the twist-2 pion distribution amplitude by means of QCD SRs. The main features of the pion distribution amplitude are confirmed by the CLEO experimental results.

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arXiv2001

On a QCD-based pion distribution amplitude vs. recent experimental data

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.

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arXiv2001

New shapes of light-cone distributions of the transversely polarized ρ-mesons

We re-analyze the leading twist light-cone distributions for transversely polarized ρ-, ρ'- and b_1-mesons in the framework of QCD sum rules with nonlocal condensates. Using different kinds of sum rules to obtain reliable predictions, we estimate the 2-, 4-, 6- and 8-th moments for transversely polarized ρ- and ρ'-meson distributions and re-estimate tensor couplings f^T_{ρ,ρ',b_1}. We stress that the results of standard sum rules also support our estimation of the second moment of the transversely polarized ρ-meson distribution. New models for light-cone distributions of these mesons are constructed. Phenomenological consequences from these distributions are briefly discussed. Our results are compared with those found by Ball and Braun (1996), and the latter is shown to be incomplete.

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arXiv2000

New shapes of the rho-meson light-cone distribution amplitudes: how can they influence the B --> rho e nu decay form factors

We present new models of the rho-meson leading-twist light-cone distribution amplitudes based on the QCD sum rule approach with nonlocal condensates. Their shapes differ noticeably from that known in the literature. The phenomenological consequences for physically important process B --> rho e nu are discussed in the framework of the light-cone sum rules. The results are compared with those found recently by P.Ball and V.M.Braun (1997).

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arXiv2000

Form Factors and QCD in Spacelike and Timelike Region

We analyze the basic hard exclusive processes: πγ*γ- transition, pion and nucleon electromagnetic form factors, and discuss the analytic continuation of QCD formulas from the spacelike q^2<0 to the timelike region q^2 >0 of the relevant momentum transfers. We describe the construction of the timelike version of the coupling constant α_s. We show that due to the analytic continuation of the collinear logarithms each eigenfunction of the evolution equation acqiures a phase factor and investigate the resulting interference effects which are shown to be very small. We found no sources for the K-factor-type enhancements in the perturbative QCD contribution to the hadronic form factors. To study the soft part of the pion electromagnetic form factor, we use a QCD sum rule inspired model and show that there are non-canceling Sudakov double logarithms which result in a K-factor-type enhancement in the timelike region.

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arXiv1999

QCD vacuum tensor susceptibility and properties of transversely polarized mesons

We re-estimate the tensor susceptibility of QCD vacuum, $χ$, and to this end, we re-estimate the leptonic decay constants for transversely polarized $ρ$- ,~$ρ'$- and b_1-mesons. The origin of the susceptibility is analyzed using duality between $ρ$- and b_1- channels in a 2-point correlator of tensor currents. We confirm the results in Nucl.Phys. B283(1987)706 for the 2-point correlator of tensor currents and disagree with Phys.Lett. B395(1997)307 on both OPE expansion and the value of QCD vacuum tensor susceptibility. Using our value for the latter we determine new estimations of nucleon tensor charges related to the first moment of the transverse structure function h_1 of a nucleon.

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arXiv1998

The $ρ$-meson and related meson wave functions in QCD sum rules with nonlocal condensates

We apply the nonlocal condensate formalism to construct generalized sum rules (including $O(\as)$-radiative corrections) for $π$-, $ρ$- and $ρ'$-meson wave functions of twist 2. Besides, we predict the lepton decay constant $f_{ρ'}$ and estimate the mass of $ρ'$-meson. For all these mesons we obtain the first 10 moments of longitudinal wave functions, suggest the models for them and discuss their properties. We consider the peculiarities of the QCD sum rules with nonlocal condensates for transverse $ρ$- and $b_1$-meson wave functions. These results are compared with those found by Ball and Braun and by Chernyak and Zhitnitsky.

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arXiv1997

QCD Sum Rules For Pion Wave Function Revisited

We analyze new QCD sum rules for the pion wave function $ϕ_π(x)$, obtained recently by A.V. Radyushkin in the framework of the non-local vacuum condensates method for non-diagonal correlators, and suggest a new approach for extracting wave functions of the $π$-meson and of its first resonances. As a result we obtain approximately the same form of the pion wave function by using two different methods and for two different ansatzes of non-local quark condensates. We predict the mass of the $π'$-resonance and obtain the form of its wave function. The first method uses integrated (in a sense) properties of ansatzes and may be considered as an alternative to traditional borel SR.

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arXiv1997

Integral Transform Technique for Meson Wave Functions

In a recent paper [1] we have proposed a new approach for extracting the wave function of the $π$-meson $φ_π(x)$ and the masses and wave functions of its first resonances from the new QCD sum rules for non-diagonal correlators obtained in [2]. Here, we test our approach using an exactly solvable toy model as an illustrating example. We demonstrate the validity of the method and suggest a pure algebraic procedure for extracting the masses and wave functions relating to the case under investigation. We also explore the stability of the procedure under perturbations of the theoretical part of the sum rule. In application to the pion case, this results not only in the mass and wave function of the first resonance ($π'$), but also in the estimation of $π''$-mass.

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