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S. V. Mikhailov

Publications and source records attributed to S. V. Mikhailov.

At least 55 records · Page 3Linked to original sources
arXiv2011

New extended Crewther-type relation and the consequences of multiloop perturbative results

We discuss the current status of the investigations of the conformal symmetry breaking contributions to three forms for the QCD generalizations of the Crewther relation. The new third form of the extension of this relation is considered in more detail. Particular attention is paid to the discussions of the applications of the $β$-expansion formalism proposed previously by one of us (SVM). Several relations between 5-loop contributions to the Adler D-function $D^{NS}_{A}$ and to the polarized Bjorken sum rule $S_\text{Bjp}$ are presented. One of them gives the additional confirmation of the correctness of the advanced analytical computer calculations of order $α_s^4$ contributions to $D^{NS}_{A}$ and $S_\text{Bjp}$ in the general $SU(N_c)$ gauge group.

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arXiv2010

End-point behavior of the pion distribution amplitude

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.

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arXiv2010

Higher-order QCD perturbation theory in different schemes: From FOPT to CIPT to FAPT

Results on the resummation of non-power-series expansions of the Adler function of a scalar, $D_S$, and a vector, $D_V$, correlator are presented within fractional analytic perturbation theory (FAPT). The first observable can be used to determine the decay width $Γ_{H\to b\bar{b}}$ of a scalar Higgs boson to a bottom-antibottom pair, while the second one is relevant for the $e^+e^-$ annihilation cross section. The obtained estimates are compared with those from fixed-order (FOPT) and contour-improved perturbation theory (CIPT), working out the differences. We prove that although FAPT and CIPT are conceptually different, they yield identical results. The convergence properties of these expansions are discussed and predictions are extracted for the resummed series of $R_S$ and $D_V$ using one- and two-loop coupling running, and making use of appropriate generating functions for the coefficients of the perturbative series.

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arXiv2010

Endpoint behavior of the pion distribution amplitude in QCD sum rules with nonlocal condensates

Starting from the QCD sum rules with nonlocal condensates for the pion distribution amplitude, we derive another sum rule for its derivative and its "integral" derivatives---defined in this work. We use this new sum rule to analyze the fine details of the pion distribution amplitude in the endpoint region $x\sim 0$. The results for endpoint-suppressed and flat-top (or flat-like) pion distribution amplitudes are compared with those we obtained with differential sum rules by employing two different models for the distribution of vacuum-quark virtualities. We determine the range of values of the derivatives of the pion distribution amplitude and show that endpoint-suppressed distribution amplitudes lie within this range, while those with endpoint enhancement---flat-type or CZ-like---yield values outside this range.

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arXiv2010

Pion Distribution Amplitude and Photon-to-Pion Transition Form Factor in QCD

We discuss the status of the pion distribution amplitude (DA) in connection with QCD sum rules and experimental data on the $γ^*γ^\to π^0$ 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 $γ^*γ\toπ^{0}$ transition form factor; (c) Recent lattice QCD data for the pion DA; (d) BaBar data---a challenge for QCD?

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arXiv2010

New extended Crewther-type relation

We propose a conjecture about the detailed structure of the conformal symmetry breaking term in the generalized Crewther relation. We conclude that this conjecture leads to new relations between the QCD expansion coefficients of the Adler D-function and the polarized Bjorken sum rule B$_{jp}$

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arXiv2009

Two-loop contribution to the pion transition form factor vs. experimental data

We present predictions for the pion-photon transition form factor, derived with the help of light-cone sum rules and including the main part of the NNLO radiative corrections. We show that, when the Bakulev-Mikhailov-Stefanis (BMS) pion distribution amplitude is used, the obtained predictions agree well with the CELLO and the CLEO data. We found that no model distribution amplitude can reproduce the observed $Q^2$ growth of the new BaBar data, though the BMS model complies with several BaBar data points.

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arXiv2009

Pion transition form factor at the two-loop level vis-à-vis experimental data

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.

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arXiv2008

Resummation in (F)APT

We present new results on the summation of nonpower-series expansions in QCD Analytic Perturbation Theory (APT) in the one-loop approximation. We show how to generalize the approach suggested by one of us earlier to the cases of APT and Fractional APT (FAPT) with heavy-quark thresholds. Using this approach we analyze the Higgs boson decay $H^0\to\bar{b}b$. We produce estimations of the higher-order corrections importance in (F)APT and present a very transparent interpretation of the resummation results in terms of $Λ_\text{QCD}$ shifts.

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arXiv2008

Fractional Analytic Perturbation Theory in Minkowski space and application to Higgs boson decay into a b\bar{b} pair

We work out and discuss the Minkowski version of Fractional Analytic Perturbation Theory (FAPT) 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 b\bar{b} pair, using recent results for the massless correlator of two quark scalar currents in the \bar{MS} scheme. We present calculations for the decay width within MFAPT including those non-power-series contributions that correspond to the O(α_{s}^{3})-terms, 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 to the conventional QCD perturbation theory.

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arXiv2007

Pion structure in QCD: From theory to lattice to experimental data

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 $O(α_s)$ QCD analysis of the CLEO data on F^{γγ^*π}(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_π(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 γγ^*\toπtransition form factor. We include a brief analysis of meson-induced massive lepton (muon) Drell--Yan production for the process π^{-}N\toμ^{+}μ^{-}X, considering both an unpolarized nucleon target and longitudinally polarized protons.

hep-ph↗
arXiv2007

Generalization of the BLM procedure and its scales in any order of pQCD

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.

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arXiv2006

Tagging the pion quark structure in QCD

We combine the constraints on the pion quark structure available from perturbative QCD, nonperturbative QCD (nonlocal QCD sum rules and light cone sum rules) with the analysis of current data on F_{πγγ^*}(Q^2), including recent high-precision lattice calculations of the second moment of the pion's distribution amplitude. We supplement these constraints with those extracted from the renormalon approach by means of the twist-four contributions to the pion distribution amplitude in order to further increase stability with respect to related theoretical uncertainties. We show which regions in the space of the first two non-trivial Gegenbauer coefficients a_2 and a_4 of all these constraints overlap, tagging this way the pion structure to the highest degree possible at present.

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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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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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