arXiv subjects

William J. Torres Bobadilla

Publications and source records attributed to William J. Torres Bobadilla.

44 records · Page 3Linked to original sources

arXiv2018

Interplay of colour kinematics duality and analytic calculation of multi-loop scattering amplitudes: one and two loops

In this talk, we review recent developments towards the calculation of multi-loop scattering amplitudes. In particular, we discuss how the colour-kinematics duality can provide new integral relations at one-loop level via the Loop-Tree duality formalism. On the other hand, in order to compute scattering amplitudes at one- and two-loop level, numerically and analytically, we describe the preliminary automation of the adaptive integrand decomposition algorithm. We show preliminary results on the analytic reduction of the $μe$-elastic scattering at one- and two-loop level.

hep-ph↗

arXiv2017

From Jacobi off-shell currents to integral relations

In this paper, we study off-shell currents built from the Jacobi identity of the kinematic numerators of $gg\to X$ with $X=ss,q\bar{q},gg$. We find that these currents can be schematically written in terms of three-point interaction Feynman rules. This representation allows for a straightforward understanding of the Colour-Kinematics duality as well as for the construction of the building blocks for the generation of higher-multiplicity tree-level and multi-loop numerators. We also provide one-loop integral relations through the Loop-Tree duality formalism with potential applications and advantages for the computation of relevant physical processes at the Large Hadron Collider. We illustrate these integral relations with the explicit examples of QCD one-loop numerators of $gg\to ss$.

hep-ph↗

arXiv2016

Adaptive Integrand Decomposition

We present a simplified variant of the integrand reduction algorithm for multiloop scattering amplitudes in $d = 4 - 2ε$ dimensions, which exploits the decomposition of the integration momenta in parallel and orthogonal subspaces, $d=d_\parallel+d_\perp$, where $d_\parallel$ is the dimension of the space spanned by the legs of the diagrams. We discuss the advantages of a lighter polynomial division algorithm and how the orthogonality relations for Gegenbauer polynomilas can be suitably used for carrying out the integration of the irreducible monomials, which eliminates spurious integrals. Applications to one- and two-loop integrals, for arbitrary kinematics, are discussed.

hep-ph↗

arXiv2016

BCJ Identities and $d$-Dimensional Generalized Unitarity

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 BCJ identities between d-dimensional tree-levels. We provide explicit examples for multi-gluon scattering amplitudes at one-loop.

hep-ph↗

arXiv2016

Generalised unitarity for dimensionally regulated amplitudes within FDF

We review the Four-Dimensional-Formulation variant of the Four-Dimensional-Helicity scheme, by showing two applications of this regularisation scheme. The first one is the computation of one-loop helicity amplitudes, for which we present preliminary results for the analytic expressions of the one-loop Higgs plus five- gluon amplitudes. In the second part, we study the Colour-Kinematics duality for off-shell diagrams in gauge theories coupled to matter, showing in a diagrammatic way that the Jacobi relations for the kinematic numerators of off-shell diagrams, built with Feynman rules in axial gauge, reduce to definite set of violating terms due to the contributions of sub-graphs only.

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arXiv2015

Off-shell Currents and Color-Kinematics Duality

We elaborate on the color-kinematics duality for off-shell diagrams in gauge theories coupled to matter, by investigating the scattering process $gg\to ss, q\bar q, gg$, 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 $gg\to q\bar{q}g$.

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arXiv2014

On the Subleading-Soft Behaviour of QCD Amplitudes

We elaborate on the radiative behaviour of tree-level scattering amplitudes in the soft regime. We show that the sub-leading soft term in single-gluon emission of quark-gluon amplitudes in QCD is controlled by differential operators, whose universal form can be derived from both on-shell recursion relation and gauge invariance, as it was shown to hold for graviton- and gluon-scattering.

hep-th↗

arXiv2014

On the Four-Dimensional Formulation of Dimensionally Regulated Amplitudes

We propose a pure four-dimensional formulation (FDF) of the d-dimensional regularization of one-loop scattering amplitudes. In our formulation particles propagating inside the loop are represented by massive internal states regulating the divergences. The latter obey Feynman rules containing multiplicative selection rules which automatically account for the effects of the extra-dimensional regulating terms of the amplitude. The equivalence between the FDF and the Four Dimensional Helicity scheme is discussed. We present explicit representations of the polarization and helicity states of the four-dimensional particles propagating in the loop. They allow for a complete, four-dimensional, unitarity-based construction of d-dimensional amplitudes. Generalized unitarity within the FDF does not require any higher-dimensional extension of the Clifford and the spinor algebra. Finally we show how the FDF allows for the recursive construction of $d$-dimensional one-loop integrands, generalizing the four-dimensional open-loop approach.

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