0000000000319817

AUTHOR

Petros Draggiotis

showing 5 related works from this author

Tree-Loop Duality Relation beyond simple poles

2013

We develop the Tree-Loop Duality Relation for two- and three-loop integrals with multiple identical propagators (multiple poles). This is the extension of the Duality Relation for single poles and multi-loop integrals derived in previous publications. We prove a generalization of the formula for single poles to multiple poles and we develop a strategy for dealing with higher-order pole integrals by reducing them to single pole integrals using Integration By Parts.

PhysicsHigh Energy Physics - TheoryNuclear and High Energy PhysicsPure mathematics010308 nuclear & particles physicsGeneralizationPropagatorDuality (optimization)FísicaFOS: Physical sciencesExtension (predicate logic)QCD Phenomenology01 natural sciencesDuality relationLoop (topology)Theoretical physicsHigh Energy Physics - PhenomenologyHigh Energy Physics - Phenomenology (hep-ph)High Energy Physics - Theory (hep-th)NLO Computations0103 physical sciencesIntegration by partsddc:530Tree (set theory)010306 general 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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A tree-loop duality relation at two loops and beyond

2010

The duality relation between one-loop integrals and phase-space integrals, developed in a previous work, is extended to higher-order loops. The duality relation is realized by a modification of the customary +i0 prescription of the Feynman propagators, which compensates for the absence of the multiple-cut contributions that appear in the Feynman tree theorem. We rederive the duality theorem at one-loop order in a form that is more suitable for its iterative extension to higher-loop orders. We explicitly show its application to two-and three-loop scalar master integrals, and we discuss the structure of the occurring cuts and the ensuing results in detail.

High Energy Physics - TheoryQuantum chromodynamicsPhysicsNuclear and High Energy PhysicsScalar (mathematics)Duality (mathematics)FOS: Physical sciencesPropagatorFísicaLoop integralDuality relationHigh Energy Physics - Phenomenologysymbols.namesakeHigh Energy Physics - Phenomenology (hep-ph)High Energy Physics - Theory (hep-th)Phase spacesymbolsFeynman diagramMathematical 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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Numerical implementation of the Loop-Tree Duality method

2015

We present a first numerical implementation of the Loop-Tree Duality (LTD) method for the direct numerical computation of multi-leg one-loop Feynman integrals. We discuss in detail the singular structure of the dual integrands and define a suitable contour deformation in the loop three-momentum space to carry out the numerical integration. Then, we apply the LTD method to the computation of ultraviolet and infrared finite integrals, and present explicit results for scalar integrals with up to five external legs (pentagons) and tensor integrals with up to six legs (hexagons). The LTD method features an excellent performance independently of the number of external legs.

High Energy Physics - PhenomenologyHigh Energy Physics - Phenomenology (hep-ph)FOS: Physical sciences
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