Fixing the conformal window in QCD

A physical characterization of Landau singularities is emphasized, which should trace the lower boundary N_f^* of the conformal window in QCD and supersymmetric QCD. A natural way to disentangle ``perturbative'' from ``non-perturbative'' contributions to amplitudes below N_f^* is suggested. Assuming an infrared fixed point persists in the perturbative part of the QCD coupling even below N_f^* leads to the condition \gamma(N_f^*)=1, where \gamma is the critical exponent. Using the Banks-Zaks expansion, one gets 4<N_f^*<6. This result is incompatible with the existence of an analogue of Seiberg duality in QCD. The presence of a negative ultraviolet fixed point is required both in QCD and in supersymmetric QCD to preserve causality within the conformal window. Evidence for the existence of such a fixed point in QCD is provided.Comment: 10 pages, 1 figure, extended version of a talk given at the QCDNET2000 meeting, Paris, September 11-14 2000; main new material added is evidence for negative ultraviolet fixed point in QC

Nonperturbative Contributions in an Analytic Running Coupling of QCD

In the framework of analytic approach to QCD the nonperturbative contributions in running coupling of strong interaction up to 4-loop order are obtained in an explicit form. For all $Q>\Lambda$ they are shown to be represented in the form of an expansion in inverse powers of Euclidean momentum squared. The expansion coefficients are calculated for different numbers of active quark flavors $n_f$ and for different number of loops taken into account. On basis of the stated expansion the effective method for precise calculation of the analytic running coupling can be developed.Comment: 9 pages, LaTeX, 1 table, 1 eps figur

Infrared renormalons and analyticity structure in pQCD

Relation between the infrared renormalons, the Borel resummation prescriptions, and the analyticity structure of Green functions in perturbative QCD (pQCD) is investigated. A specific recently suggested Borel resummation prescription resulted in the Principal Value and an additional power-suppressed correction that is consistent with the Operator Product Expansion. Arguments requiring the finiteness of the result for any power coefficient of the leading infrared renormalon, and the consistency in the case of the absence of that renormalon, require that this prescription be modified. The apparently most natural modification leads to the result represented by the Principal Value. The analytic structure of the amplitude in the complex coupling plane, obtained in this way, is consistent with that obtained in the literature by other methods.Comment: 6 pages, revtex4, 1 eps-figure; improved version - the paragraph containing Eqs.(18) and (19) is new, as well as the next paragraph; the Title modified; some references added; version to appear in Phys. Rev.

Analytic Approach to Perturbative QCD

The two-loop invariant (running) coupling of QCD is written in terms of the Lambert W function. The analyticity structure of the coupling in the complex Q^2-plane is established. The corresponding analytic coupling is reconstructed via a dispersion relation. We also consider some other approximations to the QCD beta-function, when the corresponding couplings are solved in terms of the Lambert function. The Landau gauge gluon propagator has been considered in the renormalization group invariant analytic approach (IAA). It is shown that there is a nonperturbative ambiguity in determination of the anomalous dimension function of the gluon field. Several analytic solutions for the propagator at the one-loop order are constructed. Properties of the obtained analytical solutions are discussed.Comment: Latex-file, 19 pages, 2 tables, 51 references, to be published in Int. J. Mod. Phys.

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 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.Comment: 30 pages, 14 eps-figures; v3: parameters of the analytic QCD models M1 and M2 were refined, the numerical results modified accordingly, new paragraph at the end of Sec.II and at the end of Sec.III, discussion of Figs.4 extended, references added; version to appear in PR

Seismicity induced during the development of the Rittershoffen geothermal field, France

The development of the Rittershoffen deep geothermal field (Alsace, Upper Rhine Graben) between 2012 and 2014 induced unfelt seismicity with a local magnitude of less than 1.6. This seismicity occurred during two types of operations: (1) mud losses in the Muschelkalk formation during the drilling of both wells of the doublet and (2) thermal and hydraulic stimulations of the GRT-1 well. Seismicity was also observed 4 days after the main hydraulic stimulation, although no specific operation was performed. During chemical stimulation, however, no induced seismicity was detected. In the context of all field development operations and their injection parameters (flow rates, overpressures, volumes), we detail the occurrence or lack of seismicity, its magnitude distribution and its spatial distribution. The observations suggest the presence of the rock stress memory effect (Kaiser effect) of the geothermal reservoir as well as uncritically stressed zones connected to the GRT-1 well and/or rock cohesion. A reduction of the seismic rate concurrent with an increase of injectivity was noticed as well as the reactivation of a couple of faults, including the Rittershoffen fault, which was targeted by the wells. These results are derived from the homogeneous and consistent catalogue of more than 1300 local earthquakes that is provided. This reference catalogue is based on a standard detection method, whose output was manually verified and improved. The given absolute locations have been computed in a calibrated, geologically realistic 3D velocity model. Our work builds on previous analyses addressing the seismicity induced by the GRT-1 hydraulic stimulation and places the results into a historical context, thus considering the full dynamics of the observed phenomena. This paper also complements existing descriptions of the hydrothermal characteristics of the deep reservoir by providing insights separate from the wells

QED Renormalization Given in A Mass-Dependent Subtraction and The Renormalization Group Approach

The QED renormalization is restudied by using a mass-dependent subtraction which is performed at a time-like renormalization point. The subtraction exactly respects necessary physical and mathematical requirements such as the gauge symmetry, the Lorentz- invariance and the mathematical convergence. Therefore, the renormalized results derived in the subtraction scheme are faithful and have no ambiguity. Especially, it is proved that the solution of the renormalization group equation satisfied by a renormalized wave function, propagator or vertex can be fixed by applying the renormalization boundary condition and, thus, an exact S-matrix element can be expressed in the form as written in the tree diagram approximation provided that the coupling constant and the fermion mass are replaced by their effective ones. In the one-loop approximation, the effective coupling constant and the effective fermion mass obtained by solving their renormalization group equations are given in rigorous and explicit expressions which are suitable in the whole range of distance and exhibit physically reasonable asymptotic behaviors.Comment: 29 pages, 4 figure

Non-Abelian Dipole Radiation and the Heavy Quark Expansion

Dipole radiation in QCD is derived to the second order in $\alpha_s$. A power-like evolution of the spin-singlet heavy quark operators is obtained to the same accuracy. In particular, ${\cal O}(\alpha_s^2)$ relation between a short-distance low-scale running heavy quark mass and the \barMS mass is given. We discuss the properties of the effective QCD coupling \aw(E) which governs the dipole radiation. This coupling is advantageous for heavy quark physics.Comment: 12 pages, Late

Perturbative QCD relations inspired by hypothetical tau leptons

We review our recent works on tests of perturbative QCD, inspired by the relation between the hadronic decay of the tau lepton and the e+ e- annihilation into hadrons. First, we present a set of commensurate scale relations that probe the self-consistency of leading-twist QCD predictions for any observable which defines an effective charge. These tests are independent of the renormalization scheme and scale, and are applicable over wide data ranges. As an example we apply this approach to R_{e+ e-}. Second, using a differential form of these conmensurate scale relations, we present a method to measure the QCD Gell-Mann--Low Psi function.Comment: To appear in the proceedings of the QCD 99 Euroconference, 7-13th July 1999 Montpellier, France 4 pages, uses espcrc2.sty (included