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We discuss different QCD approaches to calculate the form factor F γ * γπ (Q 2 ) of the γ * γ → π 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 , 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 = qD 2 q / qq = 0.4 GeV 2 , which specifies the average virtuality of the vacuum quarks.Recently, the CLEO collaboration [1] has measured the γ * γ → π 0 form factor F γ * γπ (Q 2 ) with high precision. This data has been processed by Schmedding and Yakovlev (SY) [2] using light-cone QCD sum rules (LCSR), taking also into account the perturbative QCD contributions in the next-to-leading order (NLO) approximation. In this way SY obtained useful constraints on the shape of the pion distribution amplitude (DA) in terms of confidence regions for the Gegenbauer coefficients a 2 and a 4 , the latter being the projection coefficients of the pion DA on the corresponding eigenfunctions. Note that SY have extended to the NLO the LCSR approach suggested before by Khodjamirian [3] for the leading order (LO) light-cone sum rule method.The present analysis gives further support to the claim, expressed by the above mentioned authors, that LCSRs provide the most appropriate basis in describing the form factor of the γ * γ → π 0 transition. This is intimately connected with peculiarities of real-photon processes in QCD [3,4]. But the method of the CLEO data processing, adopted in [2], seems to be not quite complete from our point of view. We think that an optimal analysis should take into account the correct ERBL evolution of the pion DA to the scale Q 2 exp of the process (the latter not to be fixed at some average point, µ SY = 2.4 GeV, as done in [2]) and to re-estimate the contribution δ 2 from the next twist term. The influence of both these effects appears to be important and it is examined here in detail. Furthermore, we are not satisfied with the error estimation performed in the SY analysis, for reasons to be explained later, and prefer therefore to use a more traditional treatment to determine the sensitivity to the input parameter δ 2 and the construction of the 1-σ and 2-σ error contours.Our main goal in the present work will be to obtain new constraints on the ...

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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.

We work out and discuss the Minkowski version of Fractional Analytic Perturbation Theory (MFAPT) for QCD observables, recently developed and presented by us for the Euclidean region. The original analytic approach to QCD, initiated by Shirkov and Solovtsov, is summarized and relations to other proposals to achieve an analytic strong coupling are pointed out. The developed framework is applied to the Higgs boson decay into a bb pair, using recent results for the massless correlator of two quark scalar currents in the MS scheme. We present calculations for the decay width within MFAPT including those non-power-series contributions that correspond to the O α 3 sterms, taking also into account evolution effects of the running coupling and the b-quark-mass renormalization. Comparisons with previous results within standard QCD perturbation theory are performed and the differences are pointed out. The interplay between effects originating from the analyticity requirement and the analytic continuation from the spacelike to the timelike region and those due to the evolution of the heavy-quark mass is addressed, highlighting the differences from the conventional QCD perturbation theory.

The Brodsky-Lepage-Mackenzie procedure is sequentially and unambiguously extended to any fixed order of perturbative QCD beyond the so called "large-β 0 approximation". As a result of this procedure, the obtained perturbation series looks like a continued-fraction representation. A subsequent generalization of this procedure is developed, in order to optimize the convergence of the final series, along the lines of the Fastest Convergence Prescription. This generalized BLM procedure is applied to the Adler D function and also to R e + e − in QCD at N 3 LO. A further extension of the sequential BLM is presented which makes use of additional parameters to optimize the convergence of the power-series at any fixed order of expansion.

We perform a detailed analysis of all existing data (CELLO, CLEO, BABAR) on the pion-photon transition form factor by means of light-cone sum rules in which we include the next-to-leading order QCD radiative corrections and the twist-four contributions. The next-to-next-to-leading order radiative correction together with the twist-six contribution are also taken into account in terms of theoretical uncertainties. Keeping only the first two Gegenbauer coefficients a 2 and a 4 , we show that the 1 error ellipse of all data up to 9 GeV 2 greatly overlaps with the set of pion distribution amplitudes obtained from nonlocal QCD sum rules-within the range of uncertainties due to twist-four. This remains valid also for the projection of the 1 error ellipsoid on the ða 2 ; a 4 Þ plane when including a 6 . We argue that it is not possible to accommodate the high-Q 2 tail of the BABAR data with the same accuracy, despite opposite claims by other authors, and conclude that the BABAR data still pose a challenge to QCD.