Versions Of QCD Research Articles

AnQCD: A Mathematica package for calculations in general analytic QCD models (new version announcement)

A previously submitted Mathematica package (Ayala and Cvetič, 2015), which evaluates the QCD couplings in several analytic (holomorphic) versions of QCD, has been adjusted (anQCDv2.m) so that it now works in the newest version of Mathematica (version 11) as well. New version program summaryProgram Title: anQCDv2.m; and the supplementary packages s0r.m and Li__nu.mProgram Files doi:http://dx.doi.org/10.17632/vsnjr4bhr9.1Licensing provisions: GPLv3Programming language: Mathematica, versions 9, 10 and 11Supplementary material: file READMEanQCDv2Journal reference of previous version: Comput. Phys. Commun. 190 (2015) 182–199Does the new version supersede the previous version? For the use with Mathematica 11, yes.Reasons for the new version: The previous version (anQCD.m) does not work in Mathematica version 11.Summary of revisions: When calling the previous version (anQCD.m) with Mathematica 11, the message SystemException[“MemoryAllocationFailure”] appears, because version 11 of Mathematica apparently cannot deal efficiently with numerical dispersion integrals where the integration is over semiinfinite interval and is slowly converging. Therefore, in the new version, in the integrals J0[Nf] for the Two-delta analytic QCD model the upper integration bound is changed from ‘Infinity’ to $wmaxJ=108.5. This modification does not change the precision of evaluations in any significant manner.Nature of problem: Evaluation of spacelike physical QCD quantities D(Q2) (Q2≡−q2 nonnegative) in terms of a truncated perturbation series of the perturbative QCD coupling a(Q2)≡αs(Q2)∕π gives us a quantity which has singularities at low positive Q2, because a(Q2) has such singularities. This is incompatible with the holomorphic (analytic) properties of D(Q2) as required by the general principles of Quantum Field Theories. Further, for low |Q2| such evaluations give very unreliable results dominated by the vicinity of the mentioned (unphysical) singularities. However, if using instead a coupling A(Q2) which respects the mentioned analyticity properties in the complex Q2-plane, then such problems do not appear.Solution method: anQCDv2.m package evaluates the coupling A(Q2) and the analogs Aν(Q2) of the powers a(Q2)ν, for three versions of QCD with couplings with aforementioned analytic properties: Analytic Perturbation Theory (APT); Two-delta analytic QCD (2δanQCD); and Massive Perturbation Theory (MPT). The couplings are evaluated by numerical evaluation of the corresponding dispersion integrals.Reference:C. Ayala and G. Cvetič, anQCD: a Mathematica package for calculations in general analytic QCD models, Comput. Phys. Commun. 190 (2015) 182–199 [arXiv:1408.6868 [hep-ph]].

Erratum: Various versions of analytic QCD and skeleton-motivated evaluation of observables [Phys. Rev. D74, 114030 (2006)

We present skeleton-motivated evaluation of QCD observables. The approach can be applied in analytic versions of QCD in certain classes of renormalization schemes. We present two versions of analytic QCD which can be regarded as low-energy modifications of the ``minimal'' analytic QCD and which reproduce the measured value of the semihadronic tau decay ratio r{tau}. Further, we describe an approach of calculating the higher order analytic couplings Ak (k=2,3,...) on the basis of logarithmic derivatives of the analytic coupling A1(Q^2). This approach can be easily applied in any version of analytic QCD. We adjust the free parameters of the afore-mentioned two analytic models in such a way that the skeleton-motivated evaluation reproduces the correct known values of r{tau} and of the Bjorken polarized sum rule (BjPSR) db(Q^2) at a given point (e.g., at Q^2=2 GeV^2). We then evaluate the low-energy behavior of the Adler function dv(Q^2) and the BjPSR db(Q^2) in the afore-mentioned evaluation approach, in the three analytic versions of QCD. We compare with the results obtained in the ``minimal'' analytic QCD and with the evaluation approach of Milton et al. and Shirkov.

Reconciling the analytic QCD with the ITEP operator product expansion philosophy

Analytic QCD models are those versions of QCD in which the running coupling parameter a(Q^2) has the same analytic properties as the spacelike physical quantities, i.e., no singularities in the complex Q^2 plane except on the timelike semiaxis. In such models, a(Q^2) usually differs from its perturbative analog by power terms ~(Lambda^2/Q^2)^k for large momenta, introducing thus nonperturbative terms in spacelike physical quantities whose origin is the UV regime. Consequently, it contradicts the ITEP-OPE philosophy which states that such terms can come only from the IR regimes. We investigate whether it is possible to construct analytic QCD models which respect the ITEP-OPE philosophy and, at the same time, reproduce not just the high-energy QCD observables, but also the low-energy ones, among them the well-measured semihadronic tau decay ratio.

Analytic QCD - a Short Review

Analytic versions of QCD are those whose coupling αs(Q2) does not have the unphysical Landau singularities on the space-like axis (-q2= Q2 > 0). The coupling is analytic in the entire complex plane except the time-like axis (Q2 < 0). Such couplings are thus suitable for application of perturbative methods down to energies of order GeV. We present a short review of the activity in the area which started with a seminal paper of Shirkov and Solovtsov ten years ago. Several models for analytic QCD coupling are presented. Strengths and weaknesses of some of these models are pointed out. Further, for such analytic couplings, constructions of the corresponding higher order analytic couplings (the analogs of the higher powers of the perturbative coupling) are outlined, and an approach based on the renormalization group considerations is singled out. Methods of evaluation of the leading-twist part of space-like observables in such analytic frameworks are described. Such methods are applicable also to the inclusive time-like observables. Two analytic models are outlined which respect the ITEP Operator Product Expansion philosophy, and thus allow for an evaluation of higher-twist contributions to observables.

’t Hooft vertices, partial quenching, and rooted staggered QCD

We discuss the properties of 't Hooft vertices in partially quenched and rooted versions of QCD in the continuum. These theories have a physical subspace, equivalent to ordinary QCD, that is contained within a larger space that includes many unphysical correlation functions. We find that the 't Hooft vertices in the physical subspace have the expected form, despite the presence of unphysical 't Hooft vertices appearing in correlation functions that have an excess of valence quarks (or ghost quarks). We also show that, due to the singular behavior of unphysical correlation functions as the massless limit is approached, order parameters for nonanomalous symmetries can be nonvanishing in finite volume if these symmetries act outside of the physical subspace. Using these results, we demonstrate that arguments recently given by Creutz---claiming to disprove the validity of rooted staggered QCD---are incorrect. In particular, the unphysical 't Hooft vertices do not present an obstacle to the recovery of taste symmetry in the continuum limit.

Various versions of analytic QCD and skeleton-motivated evaluation of observables

We present skeleton-motivated evaluation of QCD observables. The approach can be applied in analytic versions of QCD in certain classes of renormalization schemes. We present two versions of analytic QCD which can be regarded as low-energy modifications of the ``minimal'' analytic QCD and which reproduce the measured value of the semihadronic $\ensuremath{\tau}$ decay ratio ${r}_{\ensuremath{\tau}}$. Further, we describe an approach of calculating the higher-order analytic couplings ${\mathcal{A}}_{k}$ $(k=2,3,\dots{})$ on the basis of logarithmic derivatives of the analytic coupling ${\mathcal{A}}_{1}({Q}^{2})$. This approach can be applied in any version of analytic QCD. We adjust the free parameters of the aforementioned two analytic models in such a way that the skeleton-motivated evaluation reproduces the correct known values of ${r}_{\ensuremath{\tau}}$ and of the Bjorken polarized sum rule (BjPSR) ${d}_{b}({Q}^{2})$ at a given point (e.g., at ${Q}^{2}=2\text{ }\text{ }{\mathrm{GeV}}^{2}$). We then evaluate the low-energy behavior of the Adler function ${d}_{v}({Q}^{2})$ and the BjPSR ${d}_{b}({Q}^{2})$ in the aforementioned evaluation approach, in the three analytic versions of QCD. We compare with the results obtained in the minimal analytic QCD and with the evaluation approach of Milton et al. and Shirkov.

AdS/CFT correspondence and QCD with quarks in fundamental representations

The most straightforward use of AdS/CFT correspondence gives versions of QCD where quarks are in adjoint representations. Using an asymmetric orbifold approach we obtain nonsupersymmetric QCD with four quark flavors in fundamental representations of color.

Regge trajectories in QCD: can they keep on rising?

Perturbative asymptotics for Regge trajectories at large negative t seem to leed to a contradiction with their proposed string-like behaviour at large positive t, and, more generally, to confined versions of QCD.