Random polarizations of the dipoles

Götz, Daniel; Schwan, Christopher; Weinzierl, Stefan

doi:10.1103/physrevd.85.116011

Cited by 11 publications

(23 citation statements)

References 74 publications

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“…The two contributions are individually divergent, only their sum is finite. In order to render the individual contributions finite, one either employs phase space slicing [13][14][15][16][17][18][19] or the subtraction method [20][21][22][23][24][25][26][27][28][29][30][31][32][33][34][35][36][37][38][39]. Within the subtraction method one subtracts and adds a suitable approximation term A(φ n+1 ) and rewrites eq.…”

Section: Next-to-leading Order Calculationsmentioning

confidence: 99%

Matrix element method at next-to-leading order for arbitrary jet algorithms

Baumeister

Weinzierl

2017

Phys. Rev. D

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The matrix element method usually employs leading-order matrix elements. We discuss the generalisation towards higher orders in perturbation theory and show how the matrix element method can be used at next-to-leading order for arbitrary infrared-safe jet algorithms. We discuss three variants at next-to-leading order. The first two variants work at the level of the jet momenta. The first variant adheres to strict fixed-order in perturbation theory. We present a method for the required integration over the radiation phase space. The second variant is inspired by the POWHEG method and works as the first variant at the level of the jet momenta. The third variant is a more exclusive POWHEG version. Here we resolve exactly one jet into two sub-jets. If the two sub-jets are resolved above a scale p min ⊥ , the likelihood is computed from the POWHEG-modified real emission part, otherwise it is given by the POWHEG-modified virtual part.

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Section: Next-to-leading Order Calculationsmentioning

confidence: 99%

Matrix element method at next-to-leading order for arbitrary jet algorithms

Baumeister

Weinzierl

2017

Phys. Rev. D

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“…If on the other hand we choose 1 and 2 ′ as representatives, we obtain the chain diagram shown on the right in fig. (2). Although there can be more than one chain diagram associated to a given Feynman graph, this non-uniqueness does not affect our algorithm.…”

Section: Notationmentioning

confidence: 99%

“…C (1) C (2) C (3) C (1) C (2) C (3) C (5) C (6) C (4) Figure 3: The generic chain diagrams at two-loop (left) and three-loop (right). The two-loop chain diagram consists of three chains, the three-loop chain diagram consists of six chains.…”

Section: Notationmentioning

confidence: 99%

Direct numerical integration for multi-loop integrals

Becker

Weinzierl

2013

Eur. Phys. J. C

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We present a method to construct a suitable contour deformation in loop momentum space for multi-loop integrals. This contour deformation can be used to perform the integration for multi-loop integrals numerically. The integration can be performed directly in loop momentum space without the introduction of Feynman or Schwinger parameters. The method can be applied to finite multi-loop integrals and to divergent multi-loop integrals with suitable subtraction terms. The algorithm extends techniques from the one-loop case to the multiloop case. Examples at two and three loops are discussed explicitly.

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“…Consequently higher order corrections for an observable cover kinematic regions not accessible to the Born results, leading to instabilities in the predictions. Finally, in contrast to Leading Order (LO), one cannot define a weight at higher orders to a single event [10][11][12][13]. At LO each V + 1 jet event has a probabilistic weight associated with it, allowing the events to be unweighted.…”

Section: Introductionmentioning

confidence: 99%

A forward branching phase space generator for hadron colliders

Figy

Giele

2018

J. High Energ. Phys.

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In this paper we develop a projective phase space generator appropriate for hadron collider geometry. The generator integrates over bremsstrahlung events which project back to a single, fixed Born event. The projection is dictated by the experimental jet algorithm allowing for the forward branching phase space generator to integrate out the jet masses and initial state radiation. When integrating over the virtual and bremsstrahlung amplitudes this results in a single K-factor, assigning an event probability to each Born event. This K-factor is calculable as a perturbative expansion in the strong coupling constant.One can build observables from the Born kinematics, giving identical results to traditional observables as long as the observable does not depend on the infrared sensitive jet mass or initial state radiation.where Q =Q, p ab =p ab − αp L 1 , p J =p J − p T 1 − (1 + α)p L 1 and α is given by the constraint that p 2 J =p 2 J .

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Random polarizations of the dipoles

Cited by 11 publications

References 74 publications

Matrix element method at next-to-leading order for arbitrary jet algorithms

Matrix element method at next-to-leading order for arbitrary jet algorithms

Direct numerical integration for multi-loop integrals

A forward branching phase space generator for hadron colliders

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