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$_{1/2}$, 2d$_{3/2}$ and 2d$_{5/2}$ states in $^{208}$Pb, at an incident laboratory kinetic energy of 202 MeV, and for coincident coplanar scattering angles ($28.0^{\circ}$, $-54.6^{\circ}$), 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 1/Nf1/N_{f}

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, $N_{f}$. 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 $\zeta$-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($N$) QCD is shown to occur for $N=3,6$ 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 $n\to\infty$ behaviour of the portion of perturbative coefficients proportional to $N_f^{n-r} N^r$, for SU(N) QCD with $N_f$ 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 208Pb(p⃗,2p)207Tℓ^{208}Pb(\vec{p},2p) ^{207}T\ell 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$_{1/2}$, 2d$_{3/2}$ and 2d$_{5/2}$ states in $^{208}$Pb, at an incident laboratory kinetic energy of 202 MeV, and for coincident coplanar scattering angles ($28.0^{\circ}$, $-54.6^{\circ}$) - 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 $\sigma$-, $\rho$- and $\omega$-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