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43
Recursion relations for gauge theory amplitudes with massive particles
"... Preprint typeset in JHEP style PAPER VERSION hepth/0507161 ..."
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Cited by 51 (7 self)
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Preprint typeset in JHEP style PAPER VERSION hepth/0507161
From Trees to Loops and Back
, 2008
"... We argue that generic oneloop scattering amplitudes in supersymmetric YangMills theories can be computed equivalently with MHV diagrams or with Feynman diagrams. We first present a general proof of the covariance of oneloop nonMHV amplitudes obtained from MHV diagrams. This proof relies only on ..."
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Cited by 27 (8 self)
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We argue that generic oneloop scattering amplitudes in supersymmetric YangMills theories can be computed equivalently with MHV diagrams or with Feynman diagrams. We first present a general proof of the covariance of oneloop nonMHV amplitudes obtained from MHV diagrams. This proof relies only on the local character in Minkowski space of MHV vertices and on an application of the Feynman Tree Theorem. We then show that the discontinuities of oneloop scattering amplitudes computed with MHV diagrams are precisely the same as those computed with standard methods. Furthermore, we analyse collinear limits and soft limits of generic nonMHV amplitudes in supersymmetric YangMills theories with oneloop MHV diagrams. In particular, we find a simple explicit derivation of the universal oneloop splitting functions in supersymmetric YangMills theories to all orders in the dimensional regularisation parameter, which is in complete agreement with known results. Finally, we present concrete and illustrative applications of Feynman’s Tree Theorem to oneloop MHV diagrams as well as to oneloop Feynman diagrams.
Loop Amplitudes in Pure YangMills From Generalised Unitarity
, 2005
"... We show how generalised unitarity cuts in D = 4 − 2ǫ dimensions can be used to calculate efficiently complete oneloop scattering amplitudes in nonsupersymmetric YangMills theory. This approach naturally generates the rational terms in the amplitudes, as well as the cutconstructible parts. We tes ..."
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Cited by 26 (5 self)
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We show how generalised unitarity cuts in D = 4 − 2ǫ dimensions can be used to calculate efficiently complete oneloop scattering amplitudes in nonsupersymmetric YangMills theory. This approach naturally generates the rational terms in the amplitudes, as well as the cutconstructible parts. We test the validity of our method by rederiving the oneloop ++++, −+++, −−++, −+−+ and +++++ gluon scattering amplitudes using generalised quadruple cuts and triple cuts in D dimensions.
All split helicity treelevel gluon amplitudes
, 2006
"... Recently a new recursion relation for treelevel gluon amplitudes in gauge theory has been discovered. We solve this recursion to obtain explicit formulas for the closed set of amplitudes with arbitrarily many positive and negative helicity gluons in a split helicity configuration. The solution admi ..."
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Cited by 20 (1 self)
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Recently a new recursion relation for treelevel gluon amplitudes in gauge theory has been discovered. We solve this recursion to obtain explicit formulas for the closed set of amplitudes with arbitrarily many positive and negative helicity gluons in a split helicity configuration. The solution admits a simple diagrammatic expansion in terms of âzigzagâ diagrams. We comment on generalizations of this result.
Taming tree amplitudes in general relativity
 JHEP
"... Abstract: We give a proof of BCFW recursion relations for all treelevel amplitudes of gravitons in General Relativity. The proof follows the same basic steps as in the BCFW construction and it is an extension of the one given for nexttoMHV amplitudes by one of the authors and P. Svrček in hepth/ ..."
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Cited by 15 (3 self)
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Abstract: We give a proof of BCFW recursion relations for all treelevel amplitudes of gravitons in General Relativity. The proof follows the same basic steps as in the BCFW construction and it is an extension of the one given for nexttoMHV amplitudes by one of the authors and P. Svrček in hepth/0502160. The main obstacle to overcome is to prove that deformed graviton amplitudes vanish as the complex variable parameterizing the deformation is taken to infinity. This step is done by first proving an auxiliary recursion relation where the vanishing at infinity follows directly from a Feynman diagram analysis. The auxiliary recursion relation gives rise to a representation of gravity amplitudes where the vanishing under the BCFW deformation can be directly proven. Since all our steps are based only on Feynman diagrams, our proof completely establishes the validity of BCFW recursion relations. This means that results in the literature that were derived assuming
Multi gluon collinear limits from mhv amplitudes
"... Abstract: We consider the multicollinear limit of multigluon QCD amplitudes at tree level. We use the MHV rules for constructing colour ordered tree amplitudes and the general collinear factorization formula to derive timelike splitting functions that are valid for specific numbers of negative hel ..."
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Cited by 14 (2 self)
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Abstract: We consider the multicollinear limit of multigluon QCD amplitudes at tree level. We use the MHV rules for constructing colour ordered tree amplitudes and the general collinear factorization formula to derive timelike splitting functions that are valid for specific numbers of negative helicity gluons and an arbitrary number of positive helicity gluons (or vice versa). As an example we present new results describing the collinear limits of up to six gluons.
A duality for the S matrix
, 2010
"... We propose a dual formulation for the S Matrix of N = 4 SYM. The dual provides a basis for the “leading singularities ” of scattering amplitudes to all orders in perturbation theory, which are sharply defined, IR safe data that uniquely determine the full amplitudes at tree level and 1loop, and ar ..."
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Cited by 10 (1 self)
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We propose a dual formulation for the S Matrix of N = 4 SYM. The dual provides a basis for the “leading singularities ” of scattering amplitudes to all orders in perturbation theory, which are sharply defined, IR safe data that uniquely determine the full amplitudes at tree level and 1loop, and are conjectured to do so at all loop orders. The scattering amplitude for n particles in the sector with k negative helicity gluons is associated with a simple integral over the space of k planes in n dimensions, with the action of parity and cyclic symmetries manifest. The residues of the integrand compute a basis for the leading singularities. A given leading singularity is associated with a particular choice of integration contour, which we explicitly identify at tree level and 1loop for all NMHV amplitudes as well as the 8 particle N2MHV amplitude. We also identify a number of 2loop leading singularities for up to 8 particles. There are a large number of relations among residues which follow from the multivariable generalization of Cauchy’s theorem known as the “global residue theorem”. These relations imply highly nontrivial identities guaranteeing the equivalence of many different representations of the same amplitude. They also enforce the cancellation of nonlocal poles as well as consistent infrared structure at
Recursion relations, Helicity Amplitudes and Dimensional Regularization
, 2006
"... Using the method of onshell recursion relations we compute tree level amplitudes including Ddimensional scalars and fermions. These tree level amplitudes are needed for calculations of oneloop amplitudes in QCD involving external quarks and gluons. ..."
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Cited by 9 (0 self)
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Using the method of onshell recursion relations we compute tree level amplitudes including Ddimensional scalars and fermions. These tree level amplitudes are needed for calculations of oneloop amplitudes in QCD involving external quarks and gluons.