Correlator of heavy-quark currents at small q^2 in the large-beta_0 limit

The correlator of vector heavy-quark currents at small q^2 is considered in the large-beta_0 limit. The leading IR renormalon ambiguity of the sum of the perturbative series is canceled by the UV renormalon ambiguity of the gluon condensate. Asymptotic behaviour of the perturbative series is obtained in a model-independent way, up to a single unknown normalization factor. Gluon-virtuality distribution functions for the perturbative correction are calculated.Comment: 8 pages, 3 figure

Quantum Electrodynamics at Extremely Small Distances

The asymptotics of the Gell-Mann - Low function in QED can be determined exactly, \beta(g)= g at g\to\infty, where g=e^2 is the running fine structure constant. It solves the problem of pure QED at small distances L and gives the behavior g\sim L^{-2}.Comment: Latex, 6 pages, 1 figure include

O(1/N_f) Corrections to the Thirring Model in 2<d<4

The Thirring model, that is, a relativistic field theory of fermions with a contact interaction between vector currents, is studied for dimensionalities 2<d<4 using the 1/N_f expansion, where N_f is the number of fermion species. The model is found to have no ultraviolet divergences at leading order provided a regularization respecting current conservation is used. Explicit O(1/N_f) corrections are computed, and the model shown to be renormalizable at this order in the massless limit; renormalizability appears to hold to all orders due to a special case of Weinberg's theorem. This implies there is a universal amplitude for four particle scattering in the asymptotic regime. Comparisons are made with both the Gross-Neveu model and QED.Comment: 22 pages in plain TeX, with 7 figs included using psfig.tex (Minor conceptual changes - algebra unaffected

A multiloop improvement of non-singlet QCD evolution equations

An approach is elaborated for calculation of "all loop" contributions to the non-singlet evolution kernels from the diagrams with renormalon chain insertions. Closed expressions are obtained for sums of contributions to kernels $P(z)$ for the DGLAP equation and $V(x,y)$ for the "nonforward" ER-BL equation from these diagrams that dominate for a large value of $b_0$, the first $\beta$-function coefficient. Calculations are performed in the covariant $\xi$-gauge in a MS-like scheme. It is established that a special choice of the gauge parameter $\xi=-3$ generalizes the standard "naive nonabelianization" approximation. The solutions are obtained to the ER-BL evolution equation (taken at the "all loop" improved kernel), which are in form similar to one-loop solutions. A consequence for QCD descriptions of hard processes and the benefits and incompleteness of the approach are briefly discussed.Comment: 13 pages, revtex, 2 figures are enclosed as eps-file, the text style and figures are corrected following version, accepted for publication to Phys. Rev.

The Cross Section of e^+ e^- Annihilation into Hadrons of Order alpha_s^4 n_f^2 in Perturbative QCD

We present the first genuine QCD five-loop calculation of the vacuum polarization functions: analytical terms of order alpha_s^4 n_f^2 to the absorptive parts of vector and scalar correlators. These corrections form an important gauge-invariant subset of the full O(alpha_s^4) correction to $e^+ e^- annihilation into hadrons and the Higgs decay rate into hadrons respectively. They discriminate between different widely used estimates of the full result.Comment: 4 pages, revtex4 styl

Non-Equilibrium Quantum Fields in the Large N Expansion

An effective action technique for the time evolution of a closed system consisting of one or more mean fields interacting with their quantum fluctuations is presented. By marrying large $N$ expansion methods to the Schwinger-Keldysh closed time path (CTP) formulation of the quantum effective action, causality of the resulting equations of motion is ensured and a systematic, energy conserving and gauge invariant expansion about the quasi-classical mean field(s) in powers of $1/N$ developed. The general method is exposed in two specific examples, $O(N)$ symmetric scalar \l\F^4 theory and Quantum Electrodynamics (QED) with $N$ fermion fields. The \l\F^4 case is well suited to the numerical study of the real time dynamics of phase transitions characterized by a scalar order parameter. In QED the technique may be used to study the quantum non-equilibrium effects of pair creation in strong electric fields and the scattering and transport processes in a relativistic $e^+e^-$ plasma. A simple renormalization scheme that makes practical the numerical solution of the equations of motion of these and other field theories is described.Comment: 43 pages, LA-UR-94-783 (PRD, in press), uuencoded PostScrip

Resummation of Running Coupling Effects in Semileptonic B Meson Decays and Extraction of ∣Vcb∣|V_{cb}|

We present a determination of $|V_{cb}|$ from semileptonic B decays that includes resummation of supposedly large perturbative corrections, originating from the running of the strong coupling. We argue that the low value of the BLM scale found previously for inclusive decays is a manifestation of the renormalon divergence of the perturbative series starting already in third order. A reliable determination of $|V_{cb}|$ from inclusive decays is possible if one either uses a short-distance b quark mass or eliminates all unphysical mass parameters in terms of measured observables, such that all infra-red contributions of order $1/m_b$ cancel explicitly. We find that using the $\overline{\rm MS}$ running mass significantly reduces the perturbative coefficients already in low orders. For a semileptonic branching ratio of $10.9\%$ we obtain $|V_{cb}|(\tau_B/1.50\,{\rm ps})^{1/2}= 0.041\pm 0.002$ from inclusive decays, in good agreement with the value extracted from exclusive decays.Comment: 37 pages + 4 figures, final version accepted for publication in Phys. Rev.

Asymptotic Pade Approximant Predictions: up to Five Loops in QCD and SQCD

We use Asymptotic Pade Approximants (APAP's) to predict the four- and five-loop \beta-functions in QCD and N=1 supersymmetric QCD (SQCD), as well as the quark mass anomalous dimensions in Abelian and non-Abelian gauge theories. We show how the accuracy of our previous \beta-function predictions at the four-loop level may be further improved by using estimators weighted over negative numbers of flavours (WAPAP's). The accuracy of the improved four-loop results encourages confidence in the new five-loop \beta-function predictions that we present. However, the WAPAP approach does not provide improved results for the anomalous mass dimension, or for Abelian theories.Comment: Title page revised with deep regret following the untimely death of our friend and collaborator Mark Samuel; 25 pages, harvmac (b), including 3 figures; requires epsf.tex and tables.te

Looking through the QCD conformal window with perturbation theory

We study the conformal window of QCD using perturbation theory, starting from the perturbative upper edge and going down as much as we can towards the strongly coupled regime. We do so by exploiting the available five-loop computation of the $overline{{m MS}}$ $eta$-function and employing Borel resummation techniques both for the ordinary perturbative series and for the Banks-Zaks conformal expansion. Large-$n_f$ results are also used. We argue that the perturbative series for the $overline{{m MS}}$ $eta$-function is most likely asymptotic and non-Borel resummable, yet Borel resummation techniques allow to improve on ordinary perturbation theory. We find substantial evidence that QCD with $n_f=12$ flavours flows in the IR to a conformal field theory. Though the evidence is weaker, we find indications that also $n_f=11$ might sit within the conformal window. We also compute the value of the mass anomalous dimension $gamma$ at the fixed point and compare it with the available lattice results. The conformal window might extend for lower values of $n_f$, but our methods break down for n_f<11, where we expect that non-perturbative effects become important. A similar analysis is performed in the Veneziano limit

Matching QCD and HQET heavy--light currents at two loops and beyond

Heavy--light QCD currents are matched with HQET currents at two loops and leading order in $1/m$. A single formula applies to all current matchings. As a by--product, a master formula for the two--loop anomalous dimension of the QCD current $\bar{q}\gamma^{[\mu_1}\ldots\gamma^{\mu_n]}q$ is obtained, yielding a new result for the tensor current. The dependence of matching coefficients on $\gamma_5$ prescriptions is elucidated. Ratios of QCD matrix elements are obtained, independently of the three--loop anomalous dimension of HQET currents. The two--loop coefficient in $f_{{\rm B}^*}/f_{\rm B} =1-2\alpha_{\rm s}(m_b)/3\pi-K_b\alpha_{\rm s}^2/\pi^2 +{\rm O}(\alpha_{\rm s}^3,1/m_b)$ is $$K_b=\frac{83}{12}+\frac{4}{81}\pi^2+\frac{2}{27}\pi^2\log2-\frac19\zeta(3) -\frac{19}{54}N_l+\Delta_c=6.37+\Delta_c$$ with $N_l=4$ light flavours, and a correction, $\Delta_c=0.18\pm0.01$, that takes account of the non--zero ratio $m_c/m_b=0.28\pm0.03$. Fastest apparent convergence would entail $\alpha_{\rm s}(\mu)$ at $\mu=370$~MeV. ``Naive non--abelianization'' of large--$N_l$ results, via $N_l\to N_l-\frac{33}{2}$, gives reasonable approximations to exact two--loop results. All--order results for anomalous dimensions and matching coefficients are obtained at large $\beta_0=11-\frac23N_l$. Consistent cancellation between infrared-- and ultraviolet--renormalon ambiguities is demonstrated.Comment: 26 pages, preprint OUT-4102-52, LaTeX with epsf style option, uuencoded PostScript figure (compressed by gzip) appended at the en