1,869 research outputs found
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 , in 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
, and achieve highly accelerated convergence of its expansions in powers of
or , for .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
-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 to evaluate to multiple zeta values. The
criterion depends only on the topology of , 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 roots of unity. Our
method fails for the five loop graphs with crossing number 2 obtained by
breaking open the bipartite graph 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
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