905 research outputs found
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 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 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 . A
power-like evolution of the spin-singlet heavy quark operators is obtained to
the same accuracy. In particular, 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
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