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

Using the Hopf Algebra Structure of QFT in Calculations

We employ the recently discovered Hopf algebra structure underlying perturbative Quantum Field Theory to derive iterated integral representations for Feynman diagrams. We give two applications: to massless Yukawa theory and quantum electrodynamics in four dimensions.Comment: 28 p, Revtex, epsf for figures, minor changes, to appear in Phys.Rev.

Two-loop two-point functions with masses: asymptotic expansions and Taylor series, in any dimension

In all mass cases needed for quark and gluon self-energies, the two-loop master diagram is expanded at large and small $q^2$, in $d$ dimensions, using identities derived from integration by parts. Expansions are given, in terms of hypergeometric series, for all gluon diagrams and for all but one of the quark diagrams; expansions of the latter are obtained from differential equations. Pad\'{e} approximants to truncations of the expansions are shown to be of great utility. As an application, we obtain the two-loop photon self-energy, for all $d$, and achieve highly accelerated convergence of its expansions in powers of $q^2/m^2$ or $m^2/q^2$, for $d=4$.Comment: 25 pages, OUT--4102--43, BI--TP/92--5

On Motives Associated to Graph Polynomials

The appearance of multiple zeta values in anomalous dimensions and $\beta$-functions of renormalizable quantum field theories has given evidence towards a motivic interpretation of these renormalization group functions. In this paper we start to hunt the motive, restricting our attention to a subclass of graphs in four dimensional scalar field theory which give scheme independent contributions to the above functions.Comment: 54

The massless higher-loop two-point function

We introduce a new method for computing massless Feynman integrals analytically in parametric form. An analysis of the method yields a criterion for a primitive Feynman graph $G$ to evaluate to multiple zeta values. The criterion depends only on the topology of $G$, and can be checked algorithmically. As a corollary, we reprove the result, due to Bierenbaum and Weinzierl, that the massless 2-loop 2-point function is expressible in terms of multiple zeta values, and generalize this to the 3, 4, and 5-loop cases. We find that the coefficients in the Taylor expansion of planar graphs in this range evaluate to multiple zeta values, but the non-planar graphs with crossing number 1 may evaluate to multiple sums with $6^\mathrm{th}$ roots of unity. Our method fails for the five loop graphs with crossing number 2 obtained by breaking open the bipartite graph $K_{3,4}$ at one edge

Dimensional renormalization: ladders to rainbows

Renormalization factors are most easily extracted by going to the massless limit of the quantum field theory and retaining only a single momentum scale. We derive factors and renormalized Green functions to all orders in perturbation theory for rainbow graphs and vertex (or scattering diagrams) at zero momentum transfer, in the context of dimensional renormalization, and we prove that the correct anomalous dimensions for those processes emerge in the limit D -> 4.Comment: RevTeX, no figure

Using Weak Lensing Dilution to Improve Measurements of the Luminous and Dark Matter in A1689

The E/SO sequence of a cluster defines a boundary redward of which a reliable weak lensing signal can be obtained from background galaxies, uncontaminated by cluster members. For bluer colors, both background and cluster members are present, reducing the distortion signal by the proportion of unlensed cluster members. In deep Subaru and HST/ACS images of A1689 the tangential distortion of galaxies with bluer colors falls rapidly toward the cluster center relative to the lensing signal of the red background. We use this dilution effect to derive the cluster light profile and luminosity function to large radius, with the advantage that no subtraction of far-field background counts is required. The light profile declines smoothly to the limit of the data, r<2Mpc/h, with a constant slope, dlog(L)/dlog(r)=-1.12+-0.06, unlike the lensing mass profile which steepens continuously with radius, so that M/L peaks at an intermediate radius, ~100kpc/h. A flatter behavior is found for the more physically meaningful ratio of dark-matter to stellar-matter, when accounting for the color-mass relation of cluster members. The cluster luminosity function has a flat slope, alpha=-1.05+-0.07, independent of radius and with no faint upturn to M_i'<-12. We establish that the very bluest objects are negligibly contaminated by the cluster V-i'<0.2, because their distortion profile rises towards the center following the red background, but offset higher by ~20%. This larger amplitude is consistent with the greater estimated depth of the faint blue galaxies, z~=2.0 compared to z~=0.85 for the red background, a purely geometric effect related to cosmological parameters. Finally, we improve upon our earlier mass profile by combining both the red and blue background populations, clearly excluding low concentration CDM profiles.Comment: 17 pages, 21 figures, revised version in response to referee comments,(added some discussion, references), conclusions unchanged. Accepted for publication in Ap

Hubble Frontier Field Free-Form Mass Mapping of the Massive Multiple-Merging Cluster MACSJ0717.5+3745

We examine the latest data on the cluster MACSJ0717.5+3745 from the Hubble Frontier Fields campaign. The critically lensed area is the largest known of any lens and very irregular making it a challenge for parametric modelling. Using our Free-Form method we obtain an accurate solution, identify here many new sets of multiple images, doubling the number of constraints and improving the reconstruction of the dark matter distribution. Our reconstructed mass map shows several distinct central substructures with shallow density profiles, clarifying earlier work and defining well the relation between the dark matter distribution and the luminous and X-ray peaks within the critically lensed region. Using our free-form method, we are able to meaningfully subtract the mass contribution from cluster members to the deflection field to trace the smoothly distributed cluster dark matter distribution. We find 4 distinct concentrations, 3 of which are coincident with the luminous matter. The fourth peak has a significant offset from both the closest luminous and X-ray peaks. These findings, together with dynamical data from the motions of galaxies and gas will be important for uncovering the potentially important implications of this extremely massive and intriguing system.Comment: 16 pages, 10 figures, 2 tables. Matches the verson submitted to mnras. New table (A2) included with additional system candidate