The conventional series in powers of the coupling in perturbative QCD have zero radius of convergence and fail to reproduce the singularity of the QCD correlators like the Adler function at αs = 0. Using the technique of conformal mapping of the Borel plane, combined with the "softening" of the leading singularities, we define a set of new expansion functions that resemble the expanded correlator and share the same singularity at zero coupling. Several different conformal mappings and different ways of implementing the known nature of the first branch-points of the Adler function in the Borel plane are investigated, in both the contour-improved (CI) and fixed-order (FO) versions of renormalization-group resummation. We prove the remarkable convergence properties of a set of new CI expansions and use them for a determination of the strong coupling from the hadronic τ decay width. By taking the average upon this set, with a conservative treatment of the errors, we obtain αs(M 2 τ ) = 0.3195 +0.0189 −0.0138 . PACS numbers: 12.38.Bx, 12.38.Cy 1 In the so-called "order-dependent" conformal mappings, which were defined also in the coupling plane [12,13], the singularity is shifted away from the origin by a certain amount at each finiteorder, and tends to the origin only when an infinite number of terms are considered.

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The technique of conformal mapping is applied to enlarge the convergence domain of the Borel series and to accelerate the convergence of Borel-summed Green functions in perturbative QCD. We use the optimal mapping, which takes into account the location of all the singularities of the Borel transform as well as the present knowledge about its behavior near the first branch points. The determination of ␣ s (m 2 ) from the hadronic decay rate of the lepton is discussed as an illustration of the method.

We consider the determination of αs from τ hadronic decays, by investigating the contourimproved (CI) and the fixed-order (FO) renormalization group summations in the frame of a new perturbation expansion of QCD, which incorporates in a systematic way the available information about the divergent character of the series. The new expansion functions, which replace the powers of the coupling, are defined by the analytic continuation in the Borel complex plane, achieved through an optimal conformal mapping. Using a physical model recently discussed by Beneke and Jamin, we show that the new CIPT approaches the true results with great precision when the perturbative order is increased, while the new FOPT gives a less accurate description in the regions where the imaginary logarithms present in the expansion of the running coupling are large. With the new expansions, the discrepancy of 0.024 in αs(m 2 τ ) between the standard CI and FO summations is reduced to only 0.009. From the new CIPT we predict αs(m 2 τ ) = 0.320 +0.011 −0.009 , which practically coincides with the result of the standard FOPT, but has a more solid theoretical basis.

Starting from the divergence pattern of perturbative quantum chromodynamics, we propose a novel, non-power series replacing the standard expansion in powers of the renormalized coupling constant $a$. The coefficients of the new expansion are calculable at each finite order from the Feynman diagrams, while the expansion functions, denoted as $W_n(a)$, are defined by analytic continuation in the Borel complex plane. The infrared ambiguity of perturbation theory is manifest in the prescription dependence of the $W_n(a)$. We prove that the functions $W_n(a)$ have branch point and essential singularities at the origin $a=0$ of the complex $a$-plane and their perturbative expansions in powers of $a$ are divergent, while the expansion of the correlators in terms of the $W_n(a)$ set is convergent under quite loose conditionsComment: 18 pages, latex, 5 figures in EPS forma

The post-translational modification poly(ADP-ribosyl)ation (PARylation) plays key roles in genome maintenance and transcription. Both non-covalent poly(ADP-ribose) binding and covalent PARylation control protein functions, however, it is unknown how the two modes of modification crosstalk mechanistically. Employing the tumor suppressor p53 as a model substrate, this study provides detailed insights into the interplay between non-covalent and covalent PARylation and unravels its functional significance in the regulation of p53. We reveal that the multifunctional C-terminal domain (CTD) of p53 acts as the central hub in the PARylation-dependent regulation of p53. Specifically, p53 bound to auto-PARylated PARP1 via highly specific non–covalent PAR-CTD interaction, which conveyed target specificity for its covalent PARylation by PARP1. Strikingly, fusing the p53-CTD to a protein that is normally not PARylated, renders this a target for covalent PARylation as well. Functional studies revealed that the p53–PAR interaction had substantial implications on molecular and cellular levels. Thus, PAR significantly influenced the complex p53–DNA binding properties and controlled p53 functions, with major implications on the p53-dependent interactome, transcription, and replication-associated recombination. Remarkably, this mechanism potentially also applies to other PARylation targets, since a bioinformatics analysis revealed that CTD-like regions are highly enriched in the PARylated proteome.

We examine the large-order behaviour of a recently proposed renormalization-group-improved expansion of the Adler function in perturbative QCD, which sums in an analytically closed form the leading logarithms accessible from renormalization-group invariance. The expansion is first written as an effective series in powers of the one-loop coupling, and its leading singularities in the Borel plane are shown to be identical to those of the standard "contour-improved" expansion. Applying the technique of conformal mappings for the analytic continuation in the Borel plane, we define a class of improved expansions, which implement both the renormalization-group invariance and the knowledge about the large-order behaviour of the series. Detailed numerical studies of specific models for the Adler function indicate that the new expansions have remarkable convergence properties up to high orders. Using these expansions for the determination of the strong coupling from the the hadronic width of the τ lepton we obtain, with a conservative estimate of the uncertainty due to the nonperturbative corrections, αs(M

The optimal conformal mapping of the Borel plane was recently used to accelerate the convergence of the perturbation expansions in QCD. In this work we discuss the relevance of the method for the calculation of the Laplace-Borel integral expressing formally the QCD Green functions. We define an optimal expansion of the Laplace-Borel integral in the principal value prescription and establish conditions under which the expansion is convergent.PACS number͑s͒: 13.35.Dx, 12.38.Bx, 12.38.Cy 1 The conformal mapping that maps the whole holomorphy domain of the expanded function onto the unit disk will be called optimal. In this case, the singularities are mapped onto the boundary circle, and the requirement of holomorphy implies convergence of the power series at every point of the disk, which is the map of the holomorphy domain.