1,714 research outputs found
Next-to-Maximal Helicity Violating Amplitudes in Gauge Theory
Using the novel diagrammatic rules recently proposed by Cachazo, Svrcek, and
Witten, I give a compact, manifestly Lorentz-invariant form for tree-level
gauge-theory amplitudes with three opposite helicities.Comment: 12 pages, 1 figur
How to Integrate Divergent Integrals: a Pure Numerical Approach to Complex Loop Calculations
Loop calculations involve the evaluation of divergent integrals.
Usually [1] one computes them in a number of dimensions different than four
where the integral is convergent and then one performs the analytical
continuation and considers the Laurent expansion in powers of epsilon =n-4. In
this paper we discuss a method to extract directly all coefficients of this
expansion by means of concrete and well defined integrals in a five dimensional
space. We by-pass the formal and symbolic procedure of analytic continuation;
instead we can numerically compute the integrals to extract directly both the
coefficient of the pole 1/epsilon and the finite part.Comment: 13 pages, 1 Postscript figur
Loops in Twistor Space
We elucidate the one-loop twistor-space structure corresponding to
momentum-space MHV diagrams. We also discuss the infrared divergences, and
argue that only a limited set of MHV diagrams contain them. We show how to
introduce a twistor-space regulator corresponding to dimensional regularization
for the infrared-divergent diagrams. We also evaluate explicitly the
`holomorphic anomaly' pointed out by Cachazo, Svrcek, and Witten, and use the
result to define modified differential operators which can be used to probe the
twistor-space structure of one-loop amplitudes.Comment: 21 pages, TeX. v3. missing citations added. v4. subtlety with the i
\epsilon prescription clarifie
A technique for loop calculations in non-Abelian gauge theories - with application to five gluon amplitude
A powerful tool for calculations in non-Abelian gauge theories is obtained by
combining the background field gauge, the helicity basis and the color
decomposition methods. It has reproduced the one-loop calculation of the
five-gluon amplitudes in QCD, is applicable to electroweak processes and
extendable to two-loop calculations.Comment: Latex 22 pages, 3 figure
On the Coupling of Gravitons to Matter
Using relationships between open and closed strings, we present a
construction of tree-level scattering amplitudes for gravitons minimally
coupled to matter in terms of gauge theory partial amplitudes. In particular,
we present examples of amplitudes with gravitons coupled to vectors or to a
single fermion pair. We also present two examples with massive graviton
exchange, as would arise in the presence of large compact dimensions. The gauge
charges are represented by flavors of dynamical scalars or fermions. This also
leads to an unconventional decomposition of color and kinematics in gauge
theories.Comment: RevTex, 4 page
Dual conformal constraints and infrared equations from global residue theorems in N=4 SYM theory
Infrared equations and dual conformal constraints arise as consistency
conditions on loop amplitudes in N=4 super Yang-Mills theory. These conditions
are linear relations between leading singularities, which can be computed in
the Grassmannian formulation of N=4 super Yang-Mills theory proposed recently.
Examples for infrared equations have been shown to be implied by global residue
theorems in the Grassmannian picture. Both dual conformal constraints and
infrared equations are mapped explicitly to global residue theorems for
one-loop next-to-maximally-helicity-violating amplitudes. In addition, the
identity relating the BCFW and its parity-conjugated form of tree-level
amplitudes, is shown to emerge from a particular combination of global residue
theorems.Comment: 21 page
One-Loop NMHV Amplitudes involving Gluinos and Scalars in N=4 Gauge Theory
We use Supersymmetric Ward Identities and quadruple cuts to generate n-pt
NMHV amplitudes involving gluinos and adjoint scalars from purely gluonic
amplitudes. We present a set of factors that can be used to generate one-loop
NMHV amplitudes involving gluinos or adjoint scalars in N=4 Super Yang-Mills
from the corresponding purely gluonic amplitude.Comment: 16 pages, JHEP versio
All Non-Maximally-Helicity-Violating One-Loop Seven-Gluon Amplitudes in N=4 Super-Yang-Mills Theory
We compute the non-MHV one-loop seven-gluon amplitudes in N=4
super-Yang-Mills theory, which contain three negative-helicity gluons and four
positive-helicity gluons. There are four independent color-ordered amplitudes,
(- - - + + + +), (- - + - + + +), (- - + + -+ +) and (- + - + - + +). The MHV
amplitudes containing two negative-helicity and five positive-helicity gluons
were computed previously, so all independent one-loop seven-gluon helicity
amplitudes are now known for this theory. We present partial information about
an infinite sequence of next-to-MHV one-loop helicity amplitudes, with three
negative-helicity and n-3 positive-helicity gluons, and the color ordering (- -
- + + ... + +); we give a new coefficient of one class of integral functions
entering this amplitude. We discuss the twistor-space properties of the
box-integral-function coefficients in the amplitudes, which are quite simple
and suggestive.Comment: 54 pages, v3 minor correction
Recursive Calculation of One-Loop QCD Integral Coefficients
We present a new procedure using on-shell recursion to determine coefficients
of integral functions appearing in one-loop scattering amplitudes of gauge
theories, including QCD. With this procedure, coefficients of integrals,
including bubbles and triangles, can be determined without resorting to
integration. We give criteria for avoiding spurious singularities and boundary
terms that would invalidate the recursion. As an example where the criteria are
satisfied, we obtain all cut-constructible contributions to the one-loop
n-gluon scattering amplitude, A_n^{oneloop}(...--+++...), with split-helicity
from an N=1 chiral multiplet and from a complex scalar. Using the
supersymmetric decomposition, these are ingredients in the construction of QCD
amplitudes with the same helicities. This method requires prior knowledge of
amplitudes with sufficiently large numbers of legs as input. In many cases,
these are already known in compact forms from the unitarity method.Comment: 36 pages; v2 clarification added and typos fixed, v3 typos fixe
Inherited Twistor-Space Structure of Gravity Loop Amplitudes
At tree-level, gravity amplitudes are obtainable directly from gauge theory
amplitudes via the Kawai, Lewellen and Tye closed-open string relations. We
explain how the unitarity method allows us to use these relations to obtain
coefficients of box integrals appearing in one-loop N=8 supergravity amplitudes
from the recent computation of the coefficients for N=4 super-Yang-Mills
non-maximally-helicity-violating amplitudes. We argue from factorisation that
these box coefficients determine the one-loop N=8 supergravity amplitudes,
although this remains to be proven. We also show that twistor-space properties
of the N=8 supergravity amplitudes are inherited from the corresponding
properties of N=4 super-Yang-Mills theory. We give a number of examples
illustrating these ideas.Comment: 32 pages, minor typos correcte
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