0000000000319819

AUTHOR

Isabella Bierenbaum

showing 4 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
researchProduct

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)
researchProduct

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
researchProduct

The next-to-ladder approximation for linear Dyson–Schwinger equations

2007

We solve the linear Dyson Schwinger equation for a massless vertex in Yukawa theory, iterating the first two primitive graphs.

Massless particleVertex (graph theory)PhysicsGeneral Relativity and Quantum CosmologyHigh Energy Physics::TheoryNuclear and High Energy PhysicsHigh Energy Physics::LatticeHigh Energy Physics::PhenomenologyYukawa potentialLinear approximationMathematical physicsDyson seriesPhysics Letters B
researchProduct