Search results for "Dual representation"

showing 3 items of 3 documents

Causal representation of multi-loop Feynman integrands within the loop-tree duality

2021

The numerical evaluation of multi-loop scattering amplitudes in the Feynman representation usually requires to deal with both physical (causal) and unphysical (non-causal) singularities. The loop-tree duality (LTD) offers a powerful framework to easily characterise and distinguish these two types of singularities, and then simplify analytically the underling expressions. In this paper, we work explicitly on the dual representation of multi-loop Feynman integrals generated from three parent topologies, which we refer to as Maximal, Next-to-Maximal and Next-to-Next-to-Maximal loop topologies. In particular, we aim at expressing these dual contributions, independently of the number of loops an…

High Energy Physics - TheoryPhysicsNuclear and High Energy PhysicsParticle physics010308 nuclear & particles physicsDuality (mathematics)PropagatorDual representation01 natural sciencesAlgebraHigh Energy Physics - Phenomenologysymbols.namesakeIntegerSimple (abstract algebra)Perturbative QCD0103 physical sciencessymbolslcsh:QC770-798Feynman diagramlcsh:Nuclear and particle physics. Atomic energy. RadioactivityGravitational singularityScattering Amplitudes010306 general physicsRepresentation (mathematics)Duality in Gauge Field TheoriesJournal of High Energy Physics
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On the singular behaviour of scattering amplitudes in quantum field theory

2014

We analyse the singular behaviour of one-loop integrals and scattering amplitudes in the framework of the loop--tree duality approach. We show that there is a partial cancellation of singularities at the loop integrand level among the different components of the corresponding dual representation that can be interpreted in terms of causality. The remaining threshold and infrared singularities are restricted to a finite region of the loop momentum space, which is of the size of the external momenta and can be mapped to the phase-space of real corrections to cancel the soft and collinear divergences.

PhysicsNuclear and High Energy PhysicsParticle physicsFOS: Physical sciencesDuality (optimization)FísicaPosition and momentum spaceDual representationScattering amplitudeCausality (physics)Loop (topology)High Energy Physics - PhenomenologyHigh Energy Physics - Phenomenology (hep-ph)Gravitational singularityQuantum field theoryMathematical physics
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The loop-tree duality at work

2014

We review the recent developments of the loop-tree duality method, focussing our discussion on analysing the singular behaviour of the loop integrand of the dual representation of one-loop integrals and scattering amplitudes. We show that within the loop-tree duality method there is a partial cancellation of singularities at the integrand level among the different components of the corresponding dual representation. The remaining threshold and infrared singularities are restricted to a finite region of the loop momentum space, which is of the size of the external momenta and can be mapped to the phase-space of real corrections to cancel the soft and collinear divergences.

PhysicsWork (thermodynamics)010308 nuclear & particles physicsFOS: Physical sciencesDuality (optimization)Position and momentum spaceDual representation01 natural sciencesScattering amplitudeLoop (topology)High Energy Physics - PhenomenologyTree (descriptive set theory)High Energy Physics - Phenomenology (hep-ph)0103 physical sciencesGravitational singularity010303 astronomy & astrophysicsMathematical physicsProceedings of Loops and Legs in Quantum Field Theory — PoS(LL2014)
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