230 research outputs found
Infrared freezing of Euclidean QCD observables
We consider the leading one-chain term in a skeleton expansion for QCD observables and show that for energies Q2>Lambda2, where Q2=Lambda2 is the Landau pole of the coupling, the skeleton expansion result is equivalent to the standard Borel integral representation, with ambiguities related to infrared (IR) renormalons. For Q2<Lambda2 the skeleton expansion result is equivalent to a previously proposed modified Borel representation where the ambiguities are connected with ultraviolet (UV) renormalons. We investigate the Q2-dependence of the perturbative corrections to the Adler-D function, the GLS sum rule and the polarized and unpolarized Bjorken sum rules. In all these cases the one-chain result changes sign in the vicinity of Q2=Lambda2, and then exhibits freezing behavior, vanishing at Q2=0. Finiteness at Q2=Lambda2 implies specific relations between the residues of IR and UV renormalon singularities in the Borel plane. These relations, only one of which has previously been noted (though it remained unexplained), are shown to follow from the continuity of the characteristic function in the skeleton expansion. By considering the compensation of nonperturbative and perturbative ambiguities we are led to a result for the Q2-dependence of these observables at all Q2, in which there is a single undetermined nonperturbative parameter, and which involves the skeleton expansion characteristic function. The observables freeze to zero in the infrared. We briefly consider the freezing behavior of the Minkowskian Re+e- ratio
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
Relativistic predictions of spin observables for exclusive proton knockout reactions
Within the framework of the relativistic distorted wave impulse approximation
(DWIA), we investigate the sensitivity of complete sets of polarization
transfer observables for exclusive proton knockout from the 3s,
2d and 2d states in Pb, at an incident laboratory
kinetic energy of 202 MeV, and for coincident coplanar scattering angles
(, ), to different distorting optical potentials,
finite-range (FR) versus zero-range (ZR) approximations to the DWIA, as well as
medium-modified meson-nucleon coupling constants and meson masses. Results are
also compared to the nonrelativistic DWIA predictions based on the
Schr\"{o}dinger equation.Comment: Submitted for publication to Physicical Review C, 23 pages, 7 figure
Direct extraction of QCD LambdaMSbar from moments of structure functions in neutrino-nucleon scattering, using the CORGI approach
We use recently calculated next-to-next-to-leading (NNLO) anomalous dimension
coefficients for the n=1,3,5,...,13 moments of the xF3 structure function in
nuN scattering, together with the corresponding three-loop Wilson coefficients,
to obtain improved QCD predictions for the moments. The Complete
Renormalization Group Improvement (CORGI) approach is used, in which all
dependence on renormalization or factorization scales is avoided by a complete
resummation of ultraviolet logarithms. The Bernstein Polynomial method is used
to compare these QCD predictions to the xF3 data of the CCFR collaboration.
Direct fits for LambdaMSbar(5), with Nf=5 effective quark flavours, over the
range 20<Q^2<125.9 GeV^2 were performed. We obtain LambdaMSbar(5)=202+54/-45
MeV, corresponding to the three-loop running coupling
alphas(MZ)=0.1174+0.0043-0.0043. Including target mass corrections as well we
obtain LambdaMSbar(5)=228+35/-36 MeV, corresponding to
alphas(MZ)=0.1196+0.0027-0.0031.Comment: 1 figure, 16 pages, corrected values of alphas(MZ
Renormalon Singularities of the QCD Vacuum Polarization Function to Leading Order in
We explicitly determine the residues and orders of all the ultra-violet (UV)
and infra-red (IR) renormalon poles in the Borel plane for the QCD vacuum
polarization function (Adler D-function), to leading order in an expansion in
the number of quark flavours, . The singularity structure is precisely
as anticipated on general grounds. In particular, the leading IR renormalon is
absent, in agreement with operator product expansion ideas. There is a curious
and unexplained symmetry between the third and higher UV and IR renormalon
residues. We are able to sum up separately UV and IR contributions to obtain
closed form results involving -functions. We argue that the leading UV
renormalon should have a more complicated structure than conventionally
assumed. The disappearance of IR renormalons in flavour-saturated SU() QCD
is shown to occur for or 9.Comment: 22 pages of LaTeX, revisions to this paper are mainly typographica
Large-order Behaviour of the QCD Adler D-function in Planar Approximation
We consider the structure of the leading ultra-violet (UV) renormalon
singularity associated with the QCD vacuum polarization Adler D-function, in
the approximation that only planar Feynman diagrams are retained. This ``planar
approximation'' results in some simplifications, in particular three of the
four potential contributions from four-fermion operators are shown to be
absent. We are able to obtain a fully normalized result for the leading
behaviour of the portion of perturbative coefficients proportional
to , for SU(N) QCD with quark flavours.Comment: 10 pages, uses LaTe
Direct Extraction of QCD Lambda MS-bar from e+e- Jet Observables
We directly fit the QCD dimensional transmutation parameter, Lambda MS-bar,
to experimental data on e+e- jet observables, making use of next-to-leading
order (NLO) perturbative calculations. In this procedure there is no need to
mention, let alone to arbitrarily vary, the unphysical renormalisation scale
mu, and one avoids the spurious and meaningless ``theoretical error''
associated with standard alpha_s determinations. PETRA, SLD, and LEP data are
considered in the analysis. An attempt is made to estimate the importance of
uncalculated next-NLO and higher order perturbative corrections, and power
corrections, by studying the scatter in the values of Lambda MS-bar obtained
for different observables.Comment: 46 pages, 22 figure
Relativistic predictions of exclusive analyzing powers at an incident energy of 202 MeV
Within the framework of the relativistic distorted wave impulse approximation
(DWIA), we investigate the sensitivity of the analyzing power - for exclusive
proton knockout from the 3s, 2d and 2d states in
Pb, at an incident laboratory kinetic energy of 202 MeV, and for
coincident coplanar scattering angles (, ) - to
different distorting optical potentials, finite-range (FR) versus zero-range
(ZR) approximations to the DWIA, as well as medium-modified coupling constants
and meson masses. Results are also compared to the nonrelativistic DWIA
predictions based on the Schr\"{o}dinger equation. Whereas the nonrelativistic
model fails severely, both ZR and FR relativistic DWIA models provide an
excellent description of the data. For the FR predictions, it is necessary to
invoke a 20% reduction of sigma-nucleon and omega-nucleon coupling constants as
well as for -, - and -meson masses, by the nuclear
medium. On the other hand, the ZR predictions suggest that the strong
interaction in the nuclear medium is adequately represented by the free
nucleon-nucleon interaction associated with the impulse approximation. We also
demonstrate that, although the analyzing power is relatively insensitive to the
use different relativistic global optical potential parameter sets, the
prominent oscillatory behavior of this observable is largely attributed to
distortion of the scattering wave functions relative to their plane wave
values.Comment: 16 pages, 3 figures, submitted to Phys. Rev.
Renormalon-inspired resummations for vector and scalar correlators- estimating the uncertainty in {alpha}_{s}({m}_{\tau}^{2}) and and {\alpha}({M}_{Z}^{2})
We perform an all-orders resummation of the QCD Adler D-function for the
vector correlator, in which the portion of perturbative coefficients involving
the leading power of b, the first beta-function coefficient, is resummed. To
avoid a renormalization scale dependence when we match the resummation to the
exactly known NLO and NNLO results, we employ the Complete Renormalization
Group Improvement (CORGI) approach. These fixed-order and resummed CORGI
results are analytically continued by numerically performing a contour integral
to obtain corresponding fixed and all-orders ``contour-improved'' results for
the e+e- R-ratio ands its tau decay analogue R_{\tau}. The difference between
these fixed-order and all-order results is used to estimate the uncertainty in
the extraction of {alpha}_{s}({M}_{Z}^{2}} from R_{\tau} measurements, and that
in the QED coupling {\alpha}({M}_{Z}^{2}) due to hadronic corrections related
to R. Analogous resummations for the scalar correlator are performed, and used
to assess the uncertainty in the Higgs decay width to a heavy quark pair. We
point out that CORGI fixed-order contour-improved results for R and the Higgs
decay width, can be given explicitly in terms of the Lambert-W function and
hypergeometric functions, avoiding the need for numerical integration.Comment: 33 pages, 8 figure
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