Generalised Unitarity for Dimensionally Regulated Amplitudes

Bobadilla, William J. Torres; Fazio, A. R.; Mastrolia, Pierpaolo; Mirabella, Edoardo

doi:10.1016/j.nuclphysbps.2015.10.095

Cited by 9 publications

(10 citation statements)

References 42 publications

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“…At one-loop, fdf has been successfully applied to compute the scattering amplitudes for multi-gluon scattering gg → n gluons with n = 2, 3, 4, and for gg → H + n gluons with n = 2, 3 [39,40]. The use of dimensionally regularized tree-amplitudes within fdf has been employed to study the colour-kinematics duality [41] for one-loop dimensionally regularized amplitudes [42].…”

Section: Established Properties and Future Developments Of Fdfmentioning

confidence: 99%

To $${d}$$ d , or not to $${d}$$ d : recent developments and comparisons of regularization schemes

et al. 2017

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Section: Established Properties and Future Developments Of Fdfmentioning

confidence: 99%

To $${d}$$ d , or not to $${d}$$ d : recent developments and comparisons of regularization schemes

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“…Within FDF, the additional degrees of freedom which naturally enters when the space-time dimensions are continued beyond four, such as spinors and polarizations, admit a purely fourdimensional representation. FDF has been successfully applied to reproduce one-loop corrections to gg → gg, qq → gg, gg → Hg (in the heavy top limit), as well as gg → gggg [59]. Accordingly, the states propagating around the loop are described as four dimensional massive particles.…”

Section: Color-kinematics Duality In D-dimensionsmentioning

confidence: 99%

Off-shell currents and color–kinematics duality

et al. 2016

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We elaborate on the color-kinematics duality for off-shell diagrams in gauge theories coupled to matter, by investigating the scattering process gg → ss, qq, gg, and show that the Jacobi relations for the kinematic numerators of off-shell diagrams, built with Feynman rules in axial gauge, reduce to a color-kinematics violating term due to the contributions of sub-graphs only. Such anomaly vanishes when the four particles connected by the Jacobi relation are on their mass shell with vanishing squared momenta, being either external or cut particles, where the validity of the color-kinematics duality is recovered. We discuss the role of the off-shell decomposition in the direct construction of higher-multiplicity numerators satisfying color-kinematics identity in four as well as in d dimensions, for the latter employing the Four Dimensional Formalism variant of the Four Dimensional Helicity scheme. We provide explicit examples for the QCD process gg → qqg.

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“…FDF is a dimensional regularization scheme, first introduced in [8], which allows a purely four-dimensional representation of the additional degrees of freedom associated to the analytic continuation of the space-time dimension. FDF has been recently applied to the computation of one-loop QCD corrections in [39,40], where the processes gg → gg, qq → gg, gg → Hg, gg → Hgg (in the heavy top limit) and gg → ggg(g) were studied. In this formulation, virtual states are associated to massive four-dimensional particles, whose mass acts as regulating parameter.…”

Section: Color-kinematics Duality In D Dimensionsmentioning

confidence: 99%

BCJ identities and d-dimensional generalized unitarity

Primo

Bobadilla

2016

J. High Energ. Phys.

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We present a set of relations between one-loop integral coefficients for dimensionally regulated QCD amplitudes. Within dimensional regularization, the combined use of color-kinematics duality and integrand reduction yields the existence of relations between the integrand residues of partial amplitudes with different orderings of the external particles. These relations can be established for the cut-constructible contributions as well for the ones responsible for rational terms. Starting from the general parametrization of one-loop residues and applying Laurent expansion in order to extract the coefficients of the amplitude decomposition in terms of master integrals, we show that the full set of relations can be obtained by considering the BCJ identities between d-dimensional tree-level amplitudes. We provide explicit examples for multi-gluon scattering amplitudes at one loop.

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Generalised Unitarity for Dimensionally Regulated Amplitudes

Cited by 9 publications

References 42 publications

To $${d}$$ d , or not to $${d}$$ d : recent developments and comparisons of regularization schemes

To $${d}$$ d , or not to $${d}$$ d : recent developments and comparisons of regularization schemes

Off-shell currents and color–kinematics duality

BCJ identities and d-dimensional generalized unitarity

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