On the singular behaviour of scattering amplitudes in quantum field theory

Buchta, Sebastian; Chachamis, Grigorios; Draggiotis, Petros; Malamos, Ioannis; Rodrigo, Germán

doi:10.1007/jhep11(2014)014

Cited by 74 publications

(87 citation statements)

References 59 publications

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“…The integrand of the dual representation of one-loop integrals or scattering amplitudes feature certain types of singularities leading to ultraviolet (UV), infrared (IR) or threshold singularities. This singular behaviour has already been thoroughly discussed in [29,33]. We briefly recapitulate here the main points that are relevant in the present context.…”

Section: Loop-tree Duality At One Loopmentioning

confidence: 57%

“…As was demonstrated in [29], the integrand singularities appearing from the intersection of forward with forward onshell hyperboloids cancel among dual contributions. One needs to keep in mind that propagators are positive inside the on-shell hyperboloids and negative outside.…”

Section: Loop-tree Duality At One Loopmentioning

confidence: 68%

“…This duality relation is realized by a modification of the customary +i0 prescription of the Feynman propagators and encodes the causal structure of the scattering amplitudes in the expected way. The analysis of the singular behaviour of one-loop integrals and scattering amplitudes in this framework at the integrand level in the loop-momentum space shows that there is a partial cancellation of singularities among different dual contributions such that physical infrared and threshold singularities remain restricted to a compact region of the loop three-momentum [28][29][30]. This feature opens up the possibility that virtual and real radiative corrections can be brought together under a common integral and be treated simultaneously with Monte Carlo techniques though a convenient mapping of the momenta entering the virtual and real scattering amplitudes [33][34][35][36].…”

Section: Introductionmentioning

confidence: 98%

“…The loop-tree duality (LTD) method [24][25][26][27][28][29][30][31][32][33][34][35][36][37] establishes that generic loop quantities (loop integrals and scattering amplitudes) in any relativistic, local and unitary field theory can be written as a sum of tree-level-like objects obtained after making all possible cuts to the internal lines of the corresponding Feynman diagrams, with one single cut per loop and integrated over a measure that closely resembles the phase space of the corresponding real corrections [24,25]. This duality relation is realized by a modification of the customary +i0 prescription of the Feynman propagators and encodes the causal structure of the scattering amplitudes in the expected way.…”

Section: Introductionmentioning

confidence: 99%

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Numerical implementation of the loop–tree duality method

et al. 2017

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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 threemomentum space to carry out the numerical integration. Then we apply the LTD method to the computation of ultraviolet and infrared finite integrals, and we present explicit results for scalar and tensor integrals with up to eight external legs (octagons). The LTD method features an excellent performance independently of the number of external legs.

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Section: Loop-tree Duality At One Loopmentioning

confidence: 57%

Section: Loop-tree Duality At One Loopmentioning

confidence: 68%

Section: Introductionmentioning

confidence: 98%

Section: Introductionmentioning

confidence: 99%

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Numerical implementation of the loop–tree duality method

et al. 2017

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“…Multiple unresolved limits at zero and one loop order were understood already some time ago [18][19][20]. Two-loop corrections to simple soft and simple collinear limits were derived only to finite order in the regulator [21,22] by taking the appropriate limits of the two-loop three-parton decay matrix elements [23,24].…”

Section: Jhep02(2015)077mentioning

confidence: 99%

Two-loop splitting amplitudes and the single-real contribution to inclusive Higgs production at N3LO

Duhr

Gehrmann

Jaquier

2015

J. High Energ. Phys.

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The factorisation of QCD matrix elements in the limit of two external partons becoming collinear is described by process-independent splitting amplitudes, which can be expanded systematically in perturbation theory. Working in conventional dimensional regularisation, we compute the two-loop splitting amplitudes for all simple collinear splitting processes, including subleading terms in the regularisation parameter. Our results are then applied to derive an analytical expression for the two-loop single-real contribution to inclusive Higgs boson production in gluon fusion to fourth order (N 3 LO) in perturbative QCD.

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

Aguilera-Verdugo

Hernández-Pinto

Rodrigo

et al. 2021

J. High Energ. Phys.

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145

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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 and internal configurations, in terms of causal propagators only. Thus, providing very compact and causal integrand representations to all orders. In order to do so, we reconstruct their analytic expressions from numerical evaluation over finite fields. This procedure implicitly cancels out all unphysical singularities. We also interpret the result in terms of entangled causal thresholds. In view of the simple structure of the dual expressions, we integrate them numerically up to four loops in integer space-time dimensions, taking advantage of their smooth behaviour at integrand level.

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On the singular behaviour of scattering amplitudes in quantum field theory

Cited by 74 publications

References 59 publications

Numerical implementation of the loop–tree duality method

Numerical implementation of the loop–tree duality method

Two-loop splitting amplitudes and the single-real contribution to inclusive Higgs production at N3LO

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

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