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S. D. Badger

Publications and source records attributed to S. D. Badger.

9 recordsLinked to original sources
arXiv2009

Direct Extraction Of One Loop Rational Terms

We present a method for the direct extraction of rational contributions to one-loop scattering amplitudes, missed by standard four-dimensional unitarity techniques. We use generalised unitarity in $D=4-2\e$ dimensions to write the loop amplitudes in terms of products of massive tree amplitudes. We find that the rational terms in $4-2\e$ dimensions can be determined from quadruple, triple and double cuts without the need for independent pentagon contributions using a massive integral basis. The additional mass-dependent integral coefficients may then be extracted from the large mass limit which can be performed analytically or numerically. We check the method by computing the rational parts of all gluon helicity amplitudes with up to six external legs. We also present a simple application to amplitudes with external massless fermions.

hep-ph↗
arXiv2008

Generalised Unitarity At One-Loop With Massive Fermions

We describe an application of generalised unitarity to the computation of one-loop amplitudes with massive external fermions. We present analytic results for the cut-constructible parts of the leading colour contributions to the all-plus helicity configuration of the $t\bar{t}gg$ amplitude. Using a special choice for the helicity basis of the massive fermions we are able to obtain extremely compact analytic expressions. In particular we describe how one can fix the divergent contributions from tadpole and wave-function renormalisation using universal UV and IR behaviour.

hep-ph↗
arXiv2007

One-loop phi-MHV amplitudes using the unitarity bootstrap

We consider a Higgs boson coupled to gluons via the five-dimensional effective operator H Tr G_{munu}G^{munu} produced by considering the heavy top quark limit of the one-loop coupling of Higgs and gluons in the standard model. We treat H as the real part of a complex field phi that couples to the selfdual gluon field strengths and compute the one-loop corrections to amplitudes involving phi, two colour adjacent negative helicity gluons and an arbitrary number of positive helicity gluons - the so-called phi-MHV amplitudes. We use four-dimensional unitarity to construct the cut-containing contributions and the recently developed recursion relations to obtain the rational contribution for an arbitrary number of external gluons. We solve the recursion relations and give explicit results for up to four external gluons. These amplitudes are relevant for Higgs plus jet production via gluon fusion in the limit where the top quark mass is large compared to all other scales in the problem.

hep-ph↗
arXiv2007

Higgs Amplitudes From Twistor Inspired Methods

We illustrate the use of new on-shell methods, 4-dimensional unitarity cuts combined with on-shell recursions relations, by computing the A_4^{(1)}(phi,1^-,2^-,3^+,4^+) amplitude in the large top mass limit where the Higgs boson couples to gluons through an effective interaction.

hep-ph↗
arXiv2005

Recursion Relations for Gauge Theory Amplitudes with Massive Vector Bosons and Fermions

We apply the on-shell tree-level recursion relations of Britto, Cachazo, Feng and Witten to a variety of processes involving internal and external massive particles with spin. We show how to construct multi-vector boson currents where one or more off-shell vector bosons couples to a quark pair and number of gluons. We give compact results for single vector boson currents with up to six partons and double vector boson currents with up to four partons for all helicity combinations. We also provide expressions for single vector boson currents with a quark pair and an arbitrary number of gluons for some specific helicity configurations. Finally, we show how to generalise the recursion relations to handle massive particles with spin on internal lines using $gg \to t\bar t$ as an example.

hep-th↗
arXiv2005

Recursion Relations for Gauge Theory Amplitudes with Massive Particles

We derive general tree-level recursion relations for amplitudes which include massive propagating particles. As an illustration, we apply these recursion relations to scattering amplitudes of gluons coupled to massive scalars. We provide new results for all amplitudes with a pair of scalars and n < 5 gluons. These amplitudes can be used as building blocks in the computation of one-loop 6-gluon amplitudes using unitarity based methods.

hep-th↗
arXiv2004

MHV Rules for Higgs Plus Multi-Parton Amplitudes

We present MHV-rules for constructing perturbative amplitudes for a Higgs boson and an arbitrary number of partons. We give explicit expressions for amplitudes involving a Higgs and three negative helicity partons and any number of positive helicity partons - the NMHV amplitudes. We also present a recursive formulation of MHV rules that incorporates the Higgs, quarks and gluons. The recursion relations are valid for all non-MHV amplitudes. The general results agree numerically with all of the available Higgs + n-parton amplitudes and in some cases provide considerably shorter expressions.

hep-th↗
arXiv2004

Two-loop splitting functions in QCD

We present the universal two-loop splitting functions that describe the limits of two-loop $n$-point amplitudes of massless particles when two of the momenta are collinear. To derive the splitting amplitudes, we take the collinear limits of explicit two-loop four-point helicity amplitudes computed in the 't Hooft-Veltman scheme. The $g \to gg$ splitting amplitude has recently been computed using the unitarity sewing method and we find complete agreement with the results of Ref. \cite{Bern:2lsplit}. The two-loop $q \to qg$ and $g \to q\bar q$ splitting functions are new results. We also provide an expression for the two-loop soft splitting function.

hep-ph↗