17 research outputs found
Complete Renormalization Group Improvement-Avoiding Factorization and Renormalization Scale Dependence in QCD Predictions
For moments of leptoproduction structure functions we show that all
dependence on the renormalization and factorization scales disappears, provided
that all the ultraviolet logarithms involving the physical energy scale Q are
completely resummed. The approach is closely related to Grunberg's method of
Effective Charges. A direct and simple method for extracting the universal
dimensional transmutation parameter of QCD from experimental data is advocated.Comment: 16 pages, no figure
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 ( and ) and Euclidean (
and ) domains at arbitrary energy scales
( and , correspondingly) for both schemes --- with fixed number of
active flavours 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.Comment: 23 pages, 6 figures. Citations added. Now it matches version approved
for publication in Comp. Phys. Commu
Analogs of noninteger powers in general analytic QCD
In contrast to the coupling parameter in the usual perturbative QCD (pQCD),
the coupling parameter in the analytic QCD models has cuts only on the negative
semiaxis of the Q^2-plane (where q^2 = -Q^2 is the momentum squared), thus
reflecting correctly the analytic structure of the spacelike observables. The
Minimal Analytic model (MA, named also APT) of Shirkov and Solovtsov removes
the nonphysical cut (at positive Q^2) of the usual pQCD coupling and keeps the
pQCD cut discontinuity of the coupling at negative Q^2 unchanged. In order to
evaluate in MA the physical QCD quantities whose perturbation expansion
involves noninteger powers of the pQCD coupling, a specific method of
construction of MA analogs of noninteger pQCD powers was developed by Bakulev,
Mikhailov and Stefanis (BMS). We present a construction, applicable now in any
analytic QCD model, of analytic analogs of noninteger pQCD powers; this method
generalizes the BMS approach obtained in the framework of MA. We need to know
only the discontinuity function of the analytic coupling (the analog of the
pQCD coupling) along its cut in order to obtain the analytic analogs of the
noninteger powers of the pQCD coupling, as well as their timelike (Minkowskian)
counterparts. As an illustration, we apply the method to the evaluation of the
width for the Higgs decay into b+(bar b) pair.Comment: 29 pages, 5 figures; sections II and III extended, appendix B is ne
A novel series solution to the renormalization group equation in QCD
Recently, the QCD renormalization group (RG) equation at higher orders in
MS-like renormalization schemes has been solved for the running coupling as a
series expansion in powers of the exact 2-loop order coupling. In this work, we
prove that the power series converges to all orders in perturbation theory.
Solving the RG equation at higher orders, we determine the running coupling as
an implicit function of the 2-loop order running coupling. Then we analyze the
singularity structure of the higher order coupling in the complex 2-loop
coupling plane. This enables us to calculate the radii of convergence of the
series solutions at the 3- and 4-loop orders as a function of the number of
quark flavours . In parallel, we discuss in some detail the
singularity structure of the coupling at the 3- and 4-loops in
the complex momentum squared plane for . The
correspondence between the singularity structure of the running coupling in the
complex momentum squared plane and the convergence radius of the series
solution is established. For sufficiently large values, we find
that the series converges for all values of the momentum squared variable
. For lower values of , in the scheme,
we determine the minimal value of the momentum squared above
which the series converges. We study properties of the non-power series
corresponding to the presented power series solution in the QCD Analytic
Perturbation Theory approach of Shirkov and Solovtsov. The Euclidean and
Minkowskian versions of the non-power series are found to be uniformly
convergent over whole ranges of the corresponding momentum squared variables.Comment: 29 pages,LateX file, uses IOP LateX class file, 2 figures, 13 Tables.
Formulas (4)-(7) and Table 1 were relegated to Appendix 1, some notations
changed, 2 footnotes added. Clarifying discussion added at the end of Sect.
3, more references and acknowledgments added. Accepted for publication in
Few-Body System
On the running coupling constant in QCD
We try to review the main current ideas and points of view on the running
coupling constant in QCD. We begin by recalling briefly the classic analysis
based on the Renormalization Group with some emphasis on the exact solutions of
the RG equation for a given number of loops, in comparison with the usual
approximate expressions. We give particular attention to the problem of
eliminating the unphysical Landau singularities, and of defining a coupling
that remains significant at the infrared scales. We consider various proposals
of couplings directly related to the quark-antiquark potential or to other
physical quantities (effective charges) and discuss optimization in the choice
of the scale parameter and of the RS. Our main focus is, however, on dispersive
methods, their application, their relation with non-perturbative effects. We
try also to summarize the main results obtained by Lattice simulations in
various MOM schemes. We conclude briefly recalling the traditional comparison
with the experimental data.Comment: 75 pages, 8 figures. Corrected typos, added references, replaced 1
figure. Accepted for publication in Progress in Particle and Nuclear Physic
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.Comment: 63 pages, 15 figures, in russian (first part of Doktor-Nauk thesis),
published in Physics of Particles and Nuclei, typos corrected (English
version avalable on request); corrected formulas (3.14b)-(3.14c) and (B9b