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Warren B. Perkins

Publications and source records attributed to Warren B. Perkins.

At least 19 recordsLinked to original sources
arXiv2024

The Seven-Point Two-Loop Full-Color All-Plus Helicity Yang-Mills Amplitude

The seven-gluon two-loop full-color Yang-Mills amplitude is presented in a compact analytic form where we use the methods of four-dimensional unitarity cuts to obtain the polylogarithmic pieces and augmented recursion to obtain the rational pieces. Furthermore, an $n$-point form for the full-color polylogarithmic piece is presented. We use these results to probe for potential relations amongst the two-loop partial amplitudes.

hep-ph↗
arXiv2020

An $n$-point QCD two-loop amplitude

We present an explicit expression for a particular $n$-gluon two loop scattering partial amplitude. Specifically we present an analytic form for the single trace $N_c$ independent colour partial amplitude for the case where all external gluons have positive helicity.

hep-ph↗
arXiv2019

Color Dressed Unitarity and Recursion for Yang-Mills Two-Loop All-Plus Amplitudes

We present a direct computation of the full color two-loop five-point all-plus Yang-Mills amplitude using four dimensional unitarity and recursion. We present the $SU(N_c)$ amplitudes in compact analytic forms. Our results match the explicit expressions previously computed but do not require full two-loop integral methods.

hep-ph↗
arXiv2018

Loop Amplitudes in an Extended Gravity Theory

We extend the $S$-matrix of gravity by the addition of the minimal three-point amplitude or equivalently adding $R^3$ terms to the Lagrangian. We demonstrate how Unitarity can be used to simply examine the renormalisability of this theory and determine the $R^4$ counter-terms that arise at one-loop. We find that the combination of $R^4$ terms that arise in the extended theory is complementary to the $R^4$ counter-term associated with supersymmetric Lagrangians.

hep-th↗
arXiv2017

Analytic results for two-loop Yang-Mills

Recent Developments in computing very specific helicity amplitudes in two loop QCD are presented. The techniques focus upon the singular structure of the amplitude rather than on a diagramatic and integration approach

hep-ph↗
arXiv2017

Analytic all-plus-helicity gluon amplitudes in QCD

We detail the calculation of two-loop all-plus helicity amplitudes for pure Yang-Mills theory. The four dimensional unitarity methods and augmented recursion techniques we have developed, together with a knowledge of the singular structure of the amplitudes allow us to compute these in compact analytic forms. Specifically we present the computation and analytic results for the six- and seven-gluon leading colour two-loop amplitudes these being the first QCD two-loop amplitudes beyond five-points.

hep-th↗
arXiv2017

Diagrammar in an Extended Theory of Gravity

We show how the $S$-matrix of an extended theory of gravity defined by its three-point amplitudes can be constructed by demanding factorisation. The resultant $S$-matrix has tree amplitudes obeying the same soft singularity theorems as Einstein gravity including the sub-sub-leading terms.

hep-th↗
arXiv2017

Two-Loop Gravity amplitudes from four dimensional Unitarity

We compute the polylogarithmic parts of the two-loop four and five-graviton amplitudes where the external helicities are positive and express these in a simple compact analytic form. We use these to extract the $\ln(μ^2)$ terms from both the four and five-point amplitudes and show that these match the same $R^3$ counterterm.

hep-th↗
arXiv2016

The ${\cal N}=4$ Supergravity NMHV six-point one-loop amplitude

We construct the six-point NMHV one-loop amplitude in ${\cal N}=4$ supergravity using unitarity and recursion. The use of recursion requires the introduction of rational descendants of the cut-constructible pieces of the amplitude and the computation of the non-standard factorisation terms arising from the loop integrals.

hep-th↗
arXiv2016

Two-loop six gluon all plus helicity amplitude

We present an analytic expression for the six-point all-plus helicity amplitude in QCD at two-loops. We compute the rational terms in a compact analytic form organised by their singularity structure.

hep-th↗
arXiv2016

Two-loop five-point all plus helicity Yang-Mills amplitude

We re-compute the recently derived two-loop five-point all plus Yang-Mills amplitude using Unitarity and Recursion. Recursion requires augmented recursion to determine the sub-leading pole. Using these methods the simplicity of this amplitude is understood.

hep-th↗
arXiv2015

$n$-point amplitudes with a single negative-helicity graviton

We construct an expression for the n-point one-loop graviton scattering amplitude with a single negative helicity external leg using an augmented recursion technique. We analyse the soft-limits of these amplitudes and demonstrate that they have soft behaviour beyond the conjectured universal behaviour.

hep-th↗
arXiv2012

Complex Factorisation and Recursion for One-Loop Amplitudes

We consider the factorisation of one-loop amplitudes at complex kinematic points. By determining the terms that are absent for real kinematics, we can construct a recursive ansatz for the purely rational pieces of one-loop amplitudes in massless theories. We illustrate this method by verifying the Bern et.al. n-point ansatze for the single-minus one-loop amplitudes in Yang-Mills theory and by constructing the scalar contribution to the one-loop five graviton MHV scattering amplitude.

hep-th↗
arXiv2012

Constructing Gravity Amplitudes from Real Soft and Collinear Factorisation

Soft and collinear factorisations can be used to construct expressions for amplitudes in theories of gravity. We generalise the "half-soft" functions used previously to "soft-lifting" functions and use these to generate tree and one-loop amplitudes. In particular we construct expressions for MHV tree amplitudes and the rational terms in one-loop amplitudes in the specific context of N=4 supergravity. To completely determine the rational terms collinear factorisation must also be used. The rational terms for N=4 have a remarkable diagrammatic interpretation as arising from algebraic link diagrams.

hep-th↗
arXiv2011

Obtaining One-loop Gravity Amplitudes Using Spurious Singularities

The decomposition of a one-loop scattering amplitude into elementary functions with rational coefficients introduces spurious singularities which afflict individual coefficients but cancel in the complete amplitude. These cancellations create a web of interactions between the various terms. We explore the extent to which entire one-loop amplitudes can be determined from these relationships starting with a relatively small input of initial information, typically the coefficients of the scalar integral functions as these are readily determined. In the context of one-loop gravity amplitudes, of which relatively little is known, we find that some amplitudes with a small number of legs can be completely determined from their box coefficients. For increasing numbers of legs, ambiguities appear which can be determined from the physical singularity structure of the amplitude. We illustrate this with the four-point and N=1,4 five-point (super)gravity one-loop amplitudes.

hep-th↗