arXiv subjects

S. V. Mikhailov

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

At least 37 records · Page 2Linked to original sources

arXiv2016

Systematic estimation of theoretical uncertainties in the calculation of the pion-photon transition form factor using light-cone sum rules

We consider the calculation of the pion-photon transition form factor $F^{γ^*γπ^0}(Q^2)$ within light-cone sum rules focusing attention to the low-mid region of momenta. The central aim is to estimate the theoretical uncertainties which originate from a wide variety of sources related to (i) the relevance of next-to-next-to-leading order radiative corrections (ii) the influence of the twist-four and the twist-six term (iii) the sensitivity of the results on auxiliary parameters, like the Borel scale $M^2$, (iv) the role of the phenomenological description of resonances, and (v) the significance of a small but finite virtuality of the quasireal photon. Predictions for $F^{γ^*γπ^0}(Q^2)$ are presented which include all these uncertainties and found to comply within the margin of experimental error with the existing data in the $Q^2$ range between 1 and 5 GeV$^2$, thus justifying the reliability of the applied calculational scheme. This provides a solid basis for confronting theoretical predictions with forthcoming data bearing small statistical errors.

hep-ph↗

arXiv2015

Generalized DGLAP evolution

We present progress in development of the truncated Mellin moments approach (TMMA). We show our recent results on the generalization of DGLAP evolution equations and discuss some their applications in spin physics.

hep-ph↗

arXiv2015

How to perform QCD analysis of DIS in Analytic Perturbation Theory

We apply (Fractional) Analytic Perturbation Theory (FAPT) to the QCD analysis of the nonsinglet nucleon structure function $F_2(x,Q^2)$ in deep inelastic scattering up to the next leading order and compare the results with ones obtained within the standard perturbation QCD. Based on a popular parameterization of the corresponding parton distribution we perform the analysis within the Jacobi Polynomial formalism and under the control of the numerical inverse Mellin transform. To reveal the main features of the FAPT two-loop approach, we consider a wide range of momentum transfer from high $Q^2\sim 100 {\rm GeV}^2$ to low $Q^2\sim 0.3 {\rm GeV}^2$ where the approach still works.

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arXiv2015

$\{β\}$-expansion in QCD, its conformal symmetry limit: theory + applications

The basis of the $\{β\}$-expansion for the perturbative series evaluated in the $\overline{MS}$ scheme for the renormalization group invariant quantities is summarized.Comparison with a similar representation,used within the BLM-motivated Principle of Maximal Conformality,is discussed.We stress that the original $\{β\}$-expansion contains a completed list of terms rather than its PMC analog. The arguments in favour of the complete $\{β\}$-expansion are presented. They are based on the relations which follow from the power $β$-function generalization of the Crewther relation for the nonsinglet $\overline{MS}$ contributions to the Adler $D^{NS}$-functionand to the Bjorken sum rule $C^{Bjp}_{NS}$ of the polarized lepton-nucleon scattering. The terms of the complete $\{β\}$-expansionat the $O(α_s^3)$ level for $D^{NS}$ and $C^{Bjp}_{NS}$ are presented. These perturbative results are expressed in the PMC-type form. The problem of applications of these expressions for phenomenological applications is summarized.

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arXiv2015

Generalization of the Brodsky-Lepage-Mackenzie optimization within the $\{β\}$-expansion and the Principle of Maximal Conformality

We discuss generalizations of the BLM optimization procedure for renormalization group invariant quantities. In this respect, we discuss in detail the features and construction of the $\{β\}$--expansion representation instead of the standard perturbative series with regards to the Adler $D$-function and Bjorken polarized sum rules obtained in order of ${\cal O}(α_s^4)$. Based on the $\{β\}$--expansion we analyse different schemes of optimization, including the corrected Principle of Maximal Conformality, numerically illustrating their results. We suggest our scheme for the series optimization and apply it to both the above quantities.

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arXiv2014

On the pion distribution amplitude. Derivation, properties, predictions

We provide an in-depth analysis of the $π$ distribution amplitude in terms of two different Gegenbauer representations. Detailed predictions for the $π-γ$ transition form factor are presented, obtained with light-cone sum rules. Various $π$ distribution amplitudes are tested and the crucial role of their endpoint behavior in the form-factor analysis is discussed. Comparison with the data is given.

hep-ph↗

arXiv2014

Cut moments and a generalization of DGLAP equations

We elaborate a cut (truncated) Mellin moments (CMM) approach that is constructed to study deep inelastic scattering in lepton-hadron collisions at the natural kinematic constraints. We show that generalized CMM obtained by multiple integrations of the original parton distribution $f(x,μ^2)$ as well as ones obtained by multiple differentiations of this $f(x,μ^2)$ also satisfy the DGLAP equations with the correspondingly transformed evolution kernel $P(z)$. Appropriate classes of CMM for the available experimental kinematic range are suggested and analyzed. Similar relations can be obtained for the structure functions $F(x)$, being the Mellin convolution $F= C \ast f$, where $C$ is the coefficient function of the process.

hep-th↗

arXiv2014

Theoretical description and measurement of the pion-photon transition form factor

Detailed predictions for the scaled pion-photon transition form factor are given, derived with the method of light-cone sum rules and using pion distribution amplitudes with two and three Gegenbauer coefficients obtained from QCD sum rules with nonlocal condensates. These predictions agree well with all experimental data that are compatible with QCD scaling (and collinear factorization), but disagree with the high-$Q^2$ data of the BaBar Collaboration that grow with the momentum. A good agreement of our predictions with results obtained from AdS/QCD models and Dyson-Schwinger computations is found.

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arXiv2014

Rho meson distribution amplitudes from QCD sum rules with nonlocal condensates

The leading-twist distribution amplitude for the longitudinal rho-meson was studied using QCD Sum Rules with nonlocal condensates and a spectral density which includes next-to-leading order radiative corrections. The obtained profile is compared with results from standard QCD sum rules, lattice QCD, holographic QCD, a light-front quark model, and the instanton liquid model. Preliminary estimates for the first two moments of the transverse $ρ$-meson distribute amplitude are also given.

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arXiv2013

Can we understand an auxetic pion-photon transition form factor within QCD? BaBar faces Belle

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 $γ^*γ\toπ^0$ 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 $γ^*γ\toη/η'$ 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.

hep-ph↗

arXiv2013

Pion-Photon Transition Form Factor and Pion Distribution Amplitude in QCD: Facing the Enigmatic Behavior of the BaBar Data

We present an extended analysis of the data for the pion-photon transition form factor from different experiments, CELLO, CLEO, and BaBar, and discuss various theoretical approaches which try to reason from them. We focus on the divergent behavior of the BaBar data for the pion and those for the $η(η')$ pseudoscalar mesons and comment on recently proposed explanations for this discrepancy. We argue that it is not possible at present to accommodate these data within the standard QCD framework self-consistently.

hep-ph↗

arXiv2013

Pion-photon transition form factor in light-cone sum rules

We extract constraints on the pion distribution amplitude from available data on the pion-photon transition form factor in the framework of light-cone sum rules. A pronounced discrepancy $(2.7-3)σ$ between the Gegenbauer expansion coefficients extracted from the CELLO, CLEO, and Belle experimental data relative to those from BaBar is found. Predictions for the pion-photon transition form factor are presented by employing a pion distribution amplitude obtained long ago from QCD sum rules with nonlocal condensates. These predictions comply with the Belle data but disagree with those of BaBar beyond 9 GeV$^2$.

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arXiv2012

Emphasizing the different trends of the existing data for the $γ^*γ\to π^0$ transition form factor

The new data on the $γ^*γ\to π^0$ 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 $1σ$ level. While the Belle data agree with our predictions, the Babar data are in conflict with them.

hep-ph↗

arXiv2012

Comparing antithetic trends of data for the pion-photon transition form factor

We perform a comparative theoretical study of the data at spacelike momentum transfer for the $γ^*γ\toπ^0$ transition form factor, just reported by the Belle Collaboration, vs. those published before by BaBar, also including the older CLEO and CELLO data. Various implications for the structure of the $π^0$ distribution amplitude vis-à-vis those data are discussed and the existing theoretical predictions are classified into three distinct categories. We argue that the actual bifurcation of the data with antithetic trends is artificial and reason that the Belle data are the better option.

hep-ph↗

arXiv2012

New perturbation theory representation of the conformal symmetry breaking effects in gauge quantum field theory models

We propose a hypothesis on the detailed structure for the representation of the conformal symmetry breaking term in the basic Crewther relation generalized in the perturbation theory framework in QCD renormalized in the ${\rm \bar{MS}}$ scheme. We establish the validity of this representation in the $O(α_s^4)$ approximation. Using the variant of the generalized Crewther relation formulated here allows finding relations between specific contributions to the QCD perturbation series coefficients for the flavor nonsinglet part of the Adler function $D^{ns}_A$ for the electron-positron annihilation in hadrons and to the perturbation series coefficients for the Bjorken sum rule $S_\text{Bjp}$ for the polarized deep-inelastic lepton-nucleon scattering. We find new relations between the $α_s^4$ coefficients of $D^{ns}_A$ and $S_\text{Bjp}$. Satisfaction of one of them serves as an additional theoretical verification of the recent computer analytic calculations of the terms of order $α_s^4$ in the expressions for these two quantities.

hep-ph↗

arXiv2011

Pion-photon transition form factor using light-cone sum rules: theoretical results, expectations, and a global-data fit

A global fit to the data from different collaborations (CELLO, CLEO, BaBar) on the pion-photon transition form factor is carried out using light-cone sum rules. The analysis includes the next-to-leading QCD radiative corrections and the twist-four contributions, while the main next-to-next-to-leading term and the twist-six contribution are taken into account in the form of theoretical uncertainties. We use the information extracted from the data to investigate the pivotal characteristics of the pion distribution amplitude. This is done by dividing the data into two sets: one containing all data up to 9 GeV$^2$, whereas the other incorporates also the high-$Q^2$ tail of the BaBar data. We find that it is not possible to accommodate into the fit these BaBar data points with the same accuracy and conclude that it is difficult to explain these data in the standard scheme of OCD.

hep-ph↗

arXiv2011

Pion-photon transition---the new QCD frontier

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 NLO QCD radiative corrections and the twist-four contributions. The NNLO 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 $1σ$ 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 $1σ$ error ellipsoid on the $(a_2,a_4)$ 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.

hep-ph↗

arXiv2011

Transition form factors of the pion in light-cone QCD sum rules with next-to-next-to-leading order contributions

The transition pion-photon form factor is studied within the framework of Light-Cone QCD Sum Rules. The spectral density for the next-to-leading order corrections is calculated for any Gegenbauer harmonic. At the level of the next-to-next-to-leading (NNLO) radiative corrections, only that part of the hard-scattering amplitude is included that is proportional to the $β$-function, taking into account the leading zeroth-order harmonic. The relative size of the NNLO contribution in the prediction for the form factor $F^{γ^{*}γπ}(Q^2)$ has been analyzed, making use of the BLM scale-setting procedure. In addition, predictions for the form factor $F^{γ^{*}ρπ}$ are obtained that turn out to be sensitive to the endpoint behavior of the pion distribution amplitude, thus providing in connection with experimental data an additional adjudicator for the pion distribution amplitude. In a note added, we comment on the preliminary high-$Q^2$ BaBar data on $F^{γ^{*}γπ}$ arguing that the significant growth of the form factor between 10 and 40 GeV$^2$ cannot be explained in terms of higher-order perturbative corrections at the NNLO.

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