pQCD running couplings finite and monotonic in the infrared: when do they reflect the holomorphic properties of spacelike observables?

Abstract

We investigate a large class of perturbative QCD (pQCD) renormalization schemes whose beta functions $\beta (a)$ are meromorphic functions of the running coupling and give finite positive value of the coupling $a(Q^2)$ in the infrared regime ("freezing"), $a(Q^2)\to a_0$ for $Q^2\to 0$. Such couplings automatically have no singularities on the positive axis of the squared momenta $Q^2$ ($\equiv -q^2$). Explicit integration of the renormalization group equation (RGE) leads to the implicit (inverted) solution for the coupling, of the form $\ln (Q^2/Q_{\mathrm{in}}^2)=\mathcal{H}(a)$. An analysis of this solution leads us to an algebraic algorithm for the search of the Landau singularities of $a(Q^2)$ on the first Riemann sheet of the complex $Q^2$-plane, i.e., poles and branching points (with cuts) outside the negative semiaxis. We present specific representative examples of the use of such algorithm, and compare the found Landau singularities with those seen after the 2-dimensional numerical integration of the RGE in the entire first Riemann sheet, where the latter approach is numerically demanding and may not always be precise. The specific examples suggest that the presented algebraic approach is useful to find out whether the running pQCD coupling has Landau singularities and, if yes, where precisely these singularities are.

22 pages, 9 figures; v4: minor changes in the text, extended Sec.III, slightly changed input parameter in Sec.IV, additional Fig.9; version published in J. Phys. Commun

References in corpus (37)

• A refinement of the Gribov-Zwanziger approach in the Landau gauge: infrared propagators in harmony with the lattice results
• Gluon and ghost propagators in the Landau gauge: Deriving lattice results from Schwinger-Dyson equations
• Lattice gluodynamics computation of Landau-gauge Green's functions in the deep infrared
• Constraints on the IR behavior of the gluon propagator in Yang-Mills theories
• Pinch Technique: Theory and Applications
• New features of the gluon and ghost propagator in the infrared region from the Gribov-Zwanziger approach
• Constraints on the IR behavior of the ghost propagator in Yang-Mills theories
• Non-perturbative comparison of QCD effective charges
• Chiral phase boundary of QCD at finite temperature
• On the running coupling constant in QCD
• Gluon mass generation in the PT-BFM scheme
• Uniqueness of infrared asymptotics in Landau gauge Yang-Mills theory II
• Uniqueness of infrared asymptotics in Landau gauge Yang-Mills theory
• Strong-Coupling Constant with Flavor Thresholds at Five Loops in the MS-bar Scheme
• On the zero crossing of the three-gluon vertex
• Ten years of the Analytic Perturbation Theory in QCD
• Analytic Invariant Charge in QCD
• The strong running coupling from the gauge sector of Domain Wall lattice QCD with physical quark masses
• Bound state approach to the QCD coupling at low energy scales
• Small-x behavior of the structure function F_2 and its slope partial ln(F_2)/partial ln(1/x) for "frozen" and analytic strong-coupling constants
• The massive analytic invariant charge in QCD
• Power-law running of the effective gluon mass
• Higher-order QCD perturbation theory in different schemes: From FOPT to CIPT to FAPT
• QCD coupling below 1 GeV from quarkonium spectrum
• Infrared enhanced analytic coupling and chiral symmetry breaking in QCD
• Extended analytic QCD model with perturbative QCD behavior at high momenta
• FAPT: a Mathematica package for calculations in QCD Fractional Analytic Perturbation Theory
• Reconciling the analytic QCD with the ITEP operator product expansion philosophy
• Nucleon spin structure at low momentum transfers
• anQCD: a Mathematica package for calculations in general analytic QCD models
• QCD effective charge and the structure function $F_2$ at small-$x$
• Hadronic vacuum polarization function within dispersive approach to QCD
• Calculation of binding energies and masses of quarkonia in analytic QCD models
• QCDMAPT_F: Fortran version of QCDMAPT package
• Perturbative QCD in acceptable schemes with holomorphic coupling
• Gauge-variant propagators and the running coupling from lattice QCD
• Elimination of the Landau pole in QCD with the spontaneously generated anomalous three-gluon interaction

Cited by in corpus (4)

• QCD Running Couplings and Effective Charges
• Determination of perturbative QCD coupling from ALEPH $\tau$ decay data using pinched Borel-Laplace and Finite Energy Sum Rules
• Borel-Laplace Sum Rules with $\tau$ decay data, using OPE with improved anomalous dimensions
• Nonperturbative gluon exchange in $pp$ elastic scattering at TeV energies