48 research outputs found
The One-loop QCD Corrections for
We calculate the one-loop QCD corrections for the decay of an off-shell
vector boson with vector couplings into two pairs of quarks of equal or unequal
flavours keeping all orders in the number of colours. These matrix elements are
relevant for the calculation of the next-to-leading order corrections to four jet production in electron-positron
annihilation, the production of a gauge boson accompanied by two jets in
hadron-hadron collisions and three jet production in deep inelastic scattering.
We use standard techniques for computing the interference of one-loop and tree
level Feynman diagrams, but organise the results in terms of combinations of
scalar loop integrals that are finite in the limit of vanishing Gram
determinants and are therefore numerically stable.Comment: 8 pages, 1 Postscript figure, LaTeX,sign changed in eq 5 and
Supersymmetric Regularization, Two-Loop QCD Amplitudes and Coupling Shifts
We present a definition of the four-dimensional helicity (FDH) regularization
scheme valid for two or more loops. This scheme was previously defined and
utilized at one loop. It amounts to a variation on the standard 't
Hooft-Veltman scheme and is designed to be compatible with the use of helicity
states for "observed" particles. It is similar to dimensional reduction in that
it maintains an equal number of bosonic and fermionic states, as required for
preserving supersymmetry. Supersymmetry Ward identities relate different
helicity amplitudes in supersymmetric theories. As a check that the FDH scheme
preserves supersymmetry, at least through two loops, we explicitly verify a
number of these identities for gluon-gluon scattering (gg to gg) in
supersymmetric QCD. These results also cross-check recent non-trivial two-loop
calculations in ordinary QCD. Finally, we compute the two-loop shift between
the FDH coupling and the standard MS-bar coupling, alpha_s. The FDH shift is
identical to the one for dimensional reduction. The two-loop coupling shifts
are then used to obtain the three-loop QCD beta function in the FDH and
dimensional reduction schemes.Comment: 44 pages, minor corrections and clarifications include
Two-Loop Diagrammatics in a Self-Dual Background
Diagrammatic rules are developed for simplifying two-loop QED diagrams with
propagators in a constant self-dual background field. This diagrammatic
analysis, using dimensional regularization, is used to explain how the fully
renormalized two-loop Euler-Heisenberg effective Lagrangian for QED in a
self-dual background field is naturally expressed in terms of one-loop
diagrams. The connection between the two-loop and one-loop vacuum diagrams in a
background field parallels a corresponding connection for free vacuum diagrams,
without a background field, which can be derived by simple algebraic
manipulations. It also mirrors similar behavior recently found for two-loop
amplitudes in N=4 SUSY Yang-Mills theory.Comment: 16 pp, Latex, Axodra
The Intermediate Coupling Regime in the AdS/CFT Correspondence
The correspondence between the 't Hooft limit of N=4 super Yang-Mills theory
and tree-level IIB superstring theory on AdS(5)xS(5) in a Ramond-Ramond
background at values of lambda=g^2 N ranging from infinity to zero is examined
in the context of unitarity. A squaring relation for the imaginary part of the
holographic scattering of identical string fields in the two-particle channels
is found, and a mismatch between weak and strong 't Hooft coupling is pointed
out within the correspondence. Several interpretations and implications are
proposed.Comment: 10 pages, LaTeX, reference adde
Zero modes, beta functions and IR/UV interplay in higher-loop QED
We analyze the relation between the short-distance behavior of quantum field
theory and the strong-field limit of the background field formalism, for QED
effective Lagrangians in self-dual backgrounds, at both one and two loop. The
self-duality of the background leads to zero modes in the case of spinor QED,
and these zero modes must be taken into account before comparing the
perturbative beta function coefficients and the coefficients of the
strong-field limit of the effective Lagrangian. At one-loop this is familiar
from instanton physics, but we find that at two-loop the role of the zero
modes, and the interplay between IR and UV effects in the renormalization, is
quite different. Our analysis is motivated in part by the remarkable simplicity
of the two-loop QED effective Lagrangians for a self-dual constant background,
and we also present here a new independent derivation of these two-loop
results.Comment: 15 pages, revtex
Review of AdS/CFT Integrability, Chapter V.2: Dual Superconformal Symmetry
Scattering amplitudes in planar N=4 super Yang-Mills theory reveal a
remarkable symmetry structure. In addition to the superconformal symmetry of
the Lagrangian of the theory, the planar amplitudes exhibit a dual
superconformal symmetry. The presence of this additional symmetry imposes
strong restrictions on the amplitudes and is connected to a duality relating
scattering amplitudes to Wilson loops defined on polygonal light-like contours.
The combination of the superconformal and dual superconformal symmetries gives
rise to a Yangian, an algebraic structure which is known to be related to the
appearance of integrability in other regimes of the theory. We discuss two dual
formulations of the symmetry and address the classification of its invariants.Comment: 22 pages, see also overview article arXiv:1012.3982, v2: references
to other chapters updated, v3 added references, typos fixe
Global conformal anomaly in N=2 string
We show the existence of a global anomaly in the one-loop graphs of N=2
string theory, defined by sewing tree amplitudes, unless spacetime
supersymmetry is imposed. The anomaly is responsible for the non-vanishing
maximally helicity violating amplitudes. The supersymmetric completion of the
N=2 string spectrum is formulated by extending the previous cohomological
analysis with an external spin factor; the target space-time spin-statistics of
these individual fields in a selfdual background are compatible with previous
cohomological analysis as fields of arbitrary spin may be bosonized into one
another. We further analyze duality relations between the open and closed
string amplitudes and demonstrate this in the supersymmetric extension of the
target space-time theory through the insertion of zero-momentum operators.Comment: 29 pages, LaTeX, one figur
Analytic Methods in Nonperturbative QCD
Recently developed analytic methods in the framework of the Field Correlator
Method are reviewed in this series of four lectures and results of calculations
are compared to lattice data and experiment. Recent lattice data demonstrating
the Casimir scaling of static quark interaction strongly support the FCM and
leave very little space for all other theoretical models, e.g. instanton
gas/liquid model. Results of calculations for mesons, baryons, quark-gluon
plasma and phase transition temperature demonstrate that new analytic methods
are a powerful tool of nonperturbative QCD along with lattice simulations.Comment: LaTeX, 34 pages; Lectures given at the 13th Indian-Summer School
"Understanding the Structure of Hadrons", August 28 - September 1, 2000,
Prague, Czech Republi
A magic connection between massive and massless diagrams
A useful connection between two-loop massive vacuum integrals and one-loop
off-shell triangle diagrams with massless internal particles is established for
arbitrary values of the space-time dimension n.Comment: 11 pages, plain latex, 1 figure (in latex); ps file available by
anonymous ftp at ftp://vsfys1.fi.uib.no/anonymous/pub/bergen95-07.p