1,445 research outputs found
Unitarity Cuts with Massive Propagators and Algebraic Expressions for Coefficients
In the first part of this paper, we extend the d-dimensional unitarity cut
method of hep-ph/0609191 to cases with massive propagators. We present formulas
for integral reduction with which one can obtain coefficients of all pentagon,
box, triangle and massive bubble integrals. In the second part of this paper,
we present a detailed study of the phase space integration for unitarity cuts.
We carry out spinor integration in generality and give algebraic expressions
for coefficients, intended for automated evaluation.Comment: 33 pages. v2: notation modified. v3: typos fixe
On the Numerical Evaluation of One-Loop Amplitudes: the Gluonic Case
We develop an algorithm of polynomial complexity for evaluating one-loop
amplitudes with an arbitrary number of external particles. The algorithm is
implemented in the Rocket program. Starting from particle vertices given by
Feynman rules, tree amplitudes are constructed using recursive relations. The
tree amplitudes are then used to build one-loop amplitudes using an integer
dimension on-shell cut method. As a first application we considered only three
and four gluon vertices calculating the pure gluonic one-loop amplitudes for
arbitrary external helicity or polarization states. We compare our numerical
results to analytical results in the literature, analyze the time behavior of
the algorithm and the accuracy of the results, and give explicit results for
fixed phase space points for up to twenty external gluons.Comment: 22 pages, 9 figures; v2: references added, version accepted for
publicatio
Scalar diagrammatic rules for Born amplitudes in QCD
We show that all Born amplitudes in QCD can be calculated from scalar
propagators and a set of three- and four-valent vertices. In particular, our
approach includes amplitudes with any number of quark pairs. The quarks may be
massless or massive. The proof of the formalism is given entirely within
quantum field theory.Comment: 20 pages, references adde
On-Shell Recursion Relations for Generic Theories
We show that on-shell recursion relations hold for tree amplitudes in generic
two derivative theories of multiple particle species and diverse spins. For
example, in a gauge theory coupled to scalars and fermions, any amplitude with
at least one gluon obeys a recursion relation. In (super)gravity coupled to
scalars and fermions, the same holds for any amplitude with at least one
graviton. This result pertains to a broad class of theories, including QCD, N=4
SYM, and N=8 supergravity.Comment: 19 pages, 3 figure
Integrand reduction of one-loop scattering amplitudes through Laurent series expansion
We present a semi-analytic method for the integrand reduction of one-loop
amplitudes, based on the systematic application of the Laurent expansions to
the integrand-decomposition. In the asymptotic limit, the coefficients of the
master integrals are the solutions of a diagonal system of equations, properly
corrected by counterterms whose parametric form is konwn a priori. The Laurent
expansion of the integrand is implemented through polynomial division. The
extension of the integrand-reduction to the case of numerators with rank larger
than the number of propagators is discussed as well.Comment: v2: Published version: references and two appendices added. v3:
Eq.(6.11) corrected, Appendix B updated accordingl
Superconformal Quantum Mechanics of Small Black Holes
Recently, Gaiotto, Strominger and Yin have proposed a holographic dual
description for the near-horizon physics of certain N=2 black holes in terms of
the superconformal quantum mechanics on D0-branes in the attractor geometry. We
provide further evidence for their proposal by applying it to the case of
`small' black holes which have vanishing horizon area in the leading
supergravity approximation. We consider 2-charge black holes in type IIA on
, where can be either or , made up out of
D0-branes and D4-branes wrapping . We construct the corresponding
superconformal quantum mechanics and show that the asymptotic growth of chiral
primaries exactly matches with the known entropy of these black holes. The
state-counting problem reduces to counting lowest Landau levels on and
Dolbeault cohomology classes on .Comment: Latex, 16 pages; v2: minor corrections, references added, published
versio
Single Cut Integration
We present an analytic technique for evaluating single cuts for one-loop
integrands, where exactly one propagator is taken to be on shell. Our method
extends the double-cut integration formalism of one-loop amplitudes to the
single-cut case. We argue that single cuts give meaningful information about
amplitudes when taken at the integrand level. We discuss applications to the
computation of tadpole coefficients.Comment: v2: corrected typo in abstrac
The Cut-Constructible Part of QCD Amplitudes
Unitarity cuts are widely used in analytic computation of loop amplitudes in
gauge theories such as QCD. We expand upon the technique introduced in
hep-ph/0503132 to carry out any finite unitarity cut integral. This technique
naturally separates the contributions of bubble, triangle and box integrals in
one-loop amplitudes and is not constrained to any particular helicity
configurations. Loop momentum integration is reduced to a sequence of algebraic
operations. We discuss the extraction of the residues at higher-order poles.
Additionally, we offer concise algebraic formulas for expressing coefficients
of three-mass triangle integrals. As an application, we compute all remaining
coefficients of bubble and triangle integrals for nonsupersymmetric six-gluon
amplitudes.Comment: 78 pages, 3 fig
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