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Alexander P. Bakulev

Publications and source records attributed to Alexander P. Bakulev.

At least 19 recordsLinked to original sources
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↗
arXiv2012

FAPT: a Mathematica package for calculations in QCD Fractional Analytic Perturbation Theory

We provide here all the procedures in \texttt{Mathematica} which are needed for the computation of the analytic images of the strong coupling constant powers in Minkowski (${\bar{\mathfrak A}_ν(s;n_f)}$ and ${\mathfrak A_ν^\text{glob}(s)}$) and Euclidean (${\bar{\mathcal A}_ν(Q^2;n_f)}$ and ${\mathcal A_ν^\text{glob}(Q^2)}$) domains at arbitrary energy scales (${s}$ and ${Q^2}$, correspondingly) for both schemes --- with fixed number of active flavours ${n_f=3, 4, 5, 6}$ and the global one with taking into account all heavy-quark thresholds. These singularity-free couplings are inevitable elements of Analytic Perturbation Theory (APT) in QCD and its generalization --- Fractional APT, needed to apply the APT imperative for renormalization-group improved hadronic observables.

hep-ph↗
arXiv2011

Resummation Approach in QCD Analytic Perturbation Theory

We discuss the resummation approach in QCD Analytic Perturbation Theory (APT). We start with a simple example of asymptotic power series for a zero-dimensional analog of the scalar $g\,ϕ^4$ model. Then we give a short historic preamble of APT and show that renormgroup improvement of the QCD perturbation theory dictates to use the Fractional APT (FAPT). After that we discuss the (F)APT resummation of nonpower series and provide the one-, two-, and three-loop resummation recipes. We show the results of applications of these recipes to the estimation of the Adler function $D(Q^2)$ in the $N_f=4$ region of $Q^2$ and of the Higgs-boson-decay width $Γ_{H\to b\bar{b}}(m_H^2)$ for $M_H=100-180$ GeV$^2$.

hep-ph↗
arXiv2011

Inevitability and Importance of Non-Perturbative Elements in Quantum Field Theory

The subject of the first section-lecture is concerned with the strength and the weakness of the perturbation theory (PT) approach, that is expansion in powers of a small parameter $α$, in Quantum Theory. We start with outlining a general troublesome feature of the main quantum theory instrument, the perturbation expansion method. The striking issue is that perturbation series in powers of $α\ll 1$ is not a convergent series. The formal reason is an essential singularity of quantum amplitude (matrix element) $C(α)$ at the origin $α=0$. In many physically important cases one needs some alternative means of theoretical analysis. In particular, this refers to perturbative QCD (pQCD) in the low-energy domain. In the second section-lecture, we discuss the approach of Analytic Perturbation Theory (APT). We start with a short historic preamble and then discuss how combining the Dispersion Relation with the Renormalization Group (RG) techniques yields the APT with \myMath{\displaystyle e^{-1/α}} nonanalyticity. Next we consider the results of APT applications to low-energy QCD processes and show that in this approach the fourth-loop contributions, which appear to be on the asymptotic border in the pQCD approach, are of the order of a few per mil. Then we note that using the RG in QCD dictates the need to use the Fractional APT (FAPT) and describe its basic ingredients. As an example of the FAPT application in QCD we consider the pion form factor $F_π(Q^2)$ calculation. At the end, we discuss the resummation of nonpower series in {(F)APT} with application to the estimation of the Higgs-boson-decay width $Γ_{H\to\bar{b}b}(m_H^2)$.

hep-ph↗
arXiv2010

Global Fractional Analytic Perturbation Theory in QCD with Selected Applications

We give the generalization of Fractional Analytic Perturbation Theory (FAPT) for QCD observables, recently developed both for the Euclidean and Minkowski regions of squared momentum transfer q^2, which takes into account heavy-quark thresholds. The original analytic approach to QCD, initiated by Jones, Solovtsov and Shirkov, is shortly summarized. We also shortly consider the basic aspects of FAPT and then concentrate on the accounting for the heavy-quark thresholds problem and the construction of global version of FAPT. We discuss what one should use as an analytic coupling in the timelike region q^2=s>0 for the e^{+}e^{-}-annihilation and the pion form factor, and consider applications to phenomenologically relevant processes (the factorizable part of the pion form factor and the Higgs boson decay into a b\bar{b} pair), as well as to the summation of perturbative series.

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arXiv2010

Pion Form Factor in QCD: How to Calculate?

We discuss the pion form factor calculation in QCD.We shortly consider the main points of the nonlocal condensate QCD sum rule approach and show its results for the pion form factor, $F_π(Q^2)$. These results are compared with predictions of the perturbative and lattice QCD. Then we consider the Local Duality (LD) approach for the pion FF in QCD and show that for $Q^2\gtrsim 2$ GeV$^2$ the main parameter of the approach, namely, $s_0^{\text{LD}}(Q^2)$ should grow with $Q^2$ rather than be a constant.

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arXiv2010

Two-loop Resummation in Fractional Analytic Perturbation Theory

This talk describes the resummation approach in (Fractional) Analytic Perturbation Theory (FAPT) in QCD. First, we make a short historical review of the (F)APT approach and then shortly describe the global scheme of FAPT which allows one to take into account heavy-quark thresholds. After that we show how it is possible to resum a non-power series in (F)APT both in the one- and two-loop approximations. As an application we suggest our analysis of the Higgs boson decay ${H^0\to b\bar{b}}$, important for the LHC program, and of the vector-current Adler function.

hep-ph↗
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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arXiv2009

Pion Form Factor in QCD Sum Rules with Nonlocal Condensates and in the Local-Duality Approach

We discuss the QCD sum-rule approach for the spacelike electromagnetic pion form factor in the $O(α_s)$ approximation. We show that the nonlocality of the condensates is a key point to include nonperturbative contributions to the pion form factor. We compare our results with the Local-Duality predictions and show that the continuum threshold $s_0(Q^2)$ parameter is highly underestimated in the Local-Duality approach at $Q^2\gtrsim 2$ GeV$^2$. Using our fit for this parameter, $s_0^\text{LD}(Q^2)$, and applying the fractional analytic perturbation theory, we estimate with an accuracy of the order of 1% the $O(α_s^2)$ contribution to the pion's form factor.

hep-ph↗
arXiv2009

Resummation in Fractional APT: How many loops do we need to take into account?

We give a short introduction to the Analytic Perturbation Theory (APT) and its generalization to Fractional powers -- FAPT. We describe how to treat heavy-quark thresholds in FAPT and then show how to resum perturbative series in both the one-loop APT and FAPT. As an application we consider FAPT description of the Higgs boson decay $H^0\to b\bar{b}$.

hep-ph↗
arXiv2009

Resummation in QCD Fractional Analytic Perturbation Theory

We describe the generalization of Analytic Perturbation Theory (APT) for QCD observables, initiated by Radyushkin, Krasnikov, Pivovarov, Shirkov and Solovtsov, to fractional powers of coupling -- Fractional APT (FAPT). The basic aspects of FAPT is shortly summarized. We describe how to treat heavy-quark thresholds in FAPT and then show how to resum perturbative series in both the one-loop APT and FAPT. As an application we consider FAPT description of the Higgs boson decay $H^0\to b\bar{b}$. The main conclusion is: To achieve an accuracy of the order of 1% it is enough to take into account up to the third correction.

hep-ph↗
arXiv2008

Resummation approach in Fractional APT: How many loops do we need to calculate?

We give a short introduction to the Analytic Perturbation Theory (APT) in QCD, discuss its problems and how they can be resolved in Fractional APT (FAPT), and give a brief report about taking into account heavy-quark thresholds in FAPT. Then we describe the resummation approach in the one-loop APT and FAPT, which produces finite answers in both Euclidean and Minkowski regions, provided the generating function P(t) of perturbative coefficients d_n is known. We consider its applications in estimations of the width of Higgs boson decay H^0\to b\bar{b} and of the Adler function D(Q^2) and the ratio R(s) in the N_f=4 region. In order to provide numerical answers we suggest very simple factorially growing models for perturbative coefficients d_n. We see that for the case of Higgs boson decay an accuracy of the order of 1% is reached at N^3LO approximation, when term d_3{\mathcal A}_3 is taken into account. In the case of Adler function D(Q^2) we have an accuracy of the order of 0.1% already at N^2LO (i. e., with taking into account d_2{\mathcal A}_2 term). The main conclusion is: In order to achieve an accuracy of the order of 1%, we do not need to calculate more than four loops and d_4 coefficients are needed only to estimate corresponding generating functions P(t).

hep-ph↗
arXiv2008

Thresholds in FAPT: Euclid vs Minkowski

We give a short introduction to the Analytic Perturbation Theory (APT) in QCD, describe its problems and suggest as a tool for their resolution the Fractional APT (FAPT). We also describe shortly how to treat heavy-quark thresholds in FAPT. As an applications of this technique we discuss (i) the pion form factor calculation in the Euclidean FAPT and (ii) the Higgs boson decay $H^0\to b\bar{b}$ in Minkowskian FAPT. We conclude with comparison of both approaches, Euclidean and Minkowskian FAPT.

hep-ph↗
arXiv2006

QCD Sum Rules: From quantum-mechanical oscillator to pion structure in QCD

We illustrate the general scheme of the Sum Rule (SR) method using 2D Quantum Harmonic Oscillator (2DQHO) as a toy model. We introduce correlator, related to Green function of 2DQHO, and describe the property of Asymptotic Freedom for 2DQHO. We explain how the duality conception allows one to describe excited states. Finally we present numerical results and extract some lessons to learn from our exposition. Then we switch to the QCD and show that QCD SRs supply us the method to study hadrons in non-perturbative QCD. Here the main emphasis is put on the pion and its distribution amplitude and form factors.

hep-ph↗
arXiv2005

Renormalization-group improved evolution of the meson distribution amplitude at the two-loop level

We discuss the two-loop evolution of the flavor-nonsinglet meson distribution amplitude in perturbative QCD. After reviewing previous two-loop computations, we outline the incompatibility of these solutions with the group property of the renormalization-group transformations. To cure this deficiency, we compute a correction factor for the non-diagonal part of the meson evolution equation and prove that with this modification the two-loop solution conforms with the group properties of the renormalization-group transformations. The special case of a fixed strong coupling (no Q^2 dependence) is also discussed and comparison is given to previously obtained results.

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