Dmitry V. Shirkov

Bjorken sum rule and perturbative QCD frontier on the move

The reasonableness of the use of perturbative QCD notions in the region close to the scale of hadronization, i.e., below 1GeV is under study. First, the interplay between higher orders of pQCD expansion and higher-twist contributions in the analysis of recent Jefferson Lab (JLab) data on the generalized Bjorken sum rule function Γ1p-n(Q2) at 0.1

Four-loop QCD analysis of the Bjorken sum rule

Abstract We study the polarized Bjorken sum rule (BSR) at low momentum transfers in the range 0.22 Q 1.73 GeV with the four-loop N3LO expression for the coefficient function C Bj ( α s ) in the framework of the common QCD perturbation theory (PT) and the singularity-free analytic perturbation theory (APT). The analysis of the PT series for C Bj ( α s ) gives a hint to its asymptotic nature manifesting itself in the region Q 1 GeV . It relates to the observation that the accuracy of both the three- and four-loop PT predictions happens to be at the same 10% level. On the other hand, the usage of the two-loop APT allows one to describe the precise low energy JLab data down to Q ∼ 300 MeV and gives a possibility for reliable extraction of the higher twist (HT) corrections. At the same time, above Q ∼ 700 MeV the APT two-loop order with HT is equivalent to the four-loop PT with HT compatible to zero and is adequate to current accuracy of the data.

Nucleon spin structure and perturbative QCD frontier on the move

We discuss the interplay between higher orders of the perturbative QCD expansion and higher-twist contributions in the analysis of recent Jefferson Lab data on the lowest moments of spin-dependent proton and neutron structure functions Γ1p,n(Q2) and Bjorken sum rule function Γ1p-n(Q2) at 0.05

LARGE REGULAR QCD COUPLING AT LOW ENERGY

The issue is the expediency of the QCD notions use in the low energy region down to the confinement scale, and, in particular, the efficacy of the QCD invariant coupling \bar{\alpha}_s(Q^2) with a minimal analytic modification in this domain. To this goal, we overview a quite recent progress in application of the ghost-free Analytic Perturbative Theory approach (with no adjustable parameters) for QCD in the region below 1 GeV. Among them the Bethe--Salpeter analysis of the meson spectra and spin-dependent (polarization) Bjorken sum rule. The impression is that there is a chance for the theoretically consistent and numerically correlated description of hadronic events from Z_0 till a few hundred MeV scale by combination of analytic pQCD and some explicit non-perturbative contribution in the spirit of duality. This is an invitation to the practitioner community for a more courageous use of ghost-free QCD coupling models for data analysis in the low energy region.

Analytic Perturbation Theory Model for QCD and Upsilon Decay

An elegant and more precise (Denominator) formula for the 3-loop perturbative QCD coupling is discussed. It improves the common expression (e.g., canonized by PDG) in few GeV region. On its base, we propose simple analytic Model for ghost-free QCD running couplings and their effective powers within the Analytic Perturbation Theory, in both the space-like (Euclidean) and time-like (Minkowskian) regions, very accurate in the range above 1 GeV. Effectiveness of the new Model is illustrated by the example of ϒ ( 1 S ) decay where the standard analysis gives α s ( M ϒ ) = 0.170 ± 0.004 value that is inconsistent with the bulk of data for α s . Instead, we obtain α s M o d ( M ϒ ) = 0.185 ± 0.005 that corresponds to α s M o d ( M Z ) = 0.120 ± 0.002 that is close to the world average.

A Few Lessons from pQCD Analysis at Low Energies

Motivated by the recent 4-loop analysis of the JLab data on Bjorken Sum Rule, where the pQCD series seems to blow up at

ANATOLY VASILIEVICH EFREMOV – KNOWN AND UNKNOWN

|Q|\lesssim 1.5\,\GeV, \alpha_s \gtrsim 0.33\,,

60 YEARS OF BROKEN SYMMETRIES IN QUANTUM PHYSICS: FROM THE BOGOLIUBOV THEORY OF SUPERFLUIDITY TO THE STANDARD MODEL

we overview the general origin of the divergency of common perturbation expansion over powers of a small coupling parameter in QFT and consider in detail the {\it blowing-up phenomenon} and accuracy of finite sums for simple alternating and non-alternating examples of divergent series.

Nonpower expansions for QCD observables at low energies

Short illustrated description of the Professor A.V. Efremov story in life and science on the occasion of his 75th birthday.

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

A retrospective historical overview of the phenomenon of spontaneous symmetry breaking (SSB) in quantum theory, the issue that has been implemented in particle physics in the form of the Higgs mechanism. The main items are: – The Bogoliubovs microscopical theory of superfluidity (1946); – The BCS-Bogoliubov theory of superconductivity (1957); – Superconductivity as a superfluidity of Cooper pairs (Bogoliubov - 1958); – Transfer of the SSB into the QFT models (early 60s); – The Higgs model triumph in the electro-weak theory (early 80s). The role of the Higgs mechanism and its status in the current Standard Model is also touched upon. Note from Publisher: This article contains the abstract only.