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Scattering amplitudes in the Regge limit and the soft anomalous dimension through four loops

Using rapidity evolution equations we study two-to-two gauge-theory scattering amplitudes in the Regge limit. We carry out explicit computations at next-to-next-to-leading logarithmic accuracy through four loops and present new results for both infrared-singular and finite contributions to the ampli...

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Autores principales: Falcioni, Giulio, Gardi, Einan, Maher, Niamh, Milloy, Calum, Vernazza, Leonardo
Lenguaje:eng
Publicado: 2021
Materias:
Acceso en línea:https://dx.doi.org/10.1007/JHEP03(2022)053
http://cds.cern.ch/record/2791306
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author Falcioni, Giulio
Gardi, Einan
Maher, Niamh
Milloy, Calum
Vernazza, Leonardo
author_facet Falcioni, Giulio
Gardi, Einan
Maher, Niamh
Milloy, Calum
Vernazza, Leonardo
author_sort Falcioni, Giulio
collection CERN
description Using rapidity evolution equations we study two-to-two gauge-theory scattering amplitudes in the Regge limit. We carry out explicit computations at next-to-next-to-leading logarithmic accuracy through four loops and present new results for both infrared-singular and finite contributions to the amplitude. New techniques are devised in order to derive the colour structure stemming from three-Reggeon exchange diagrams in terms of commutators of channel operators, obtaining results that are valid for any gauge group, and apply to scattered particles in any colour representation. We also elucidate the separation between contributions to the Regge cut and Regge pole in the real part of the amplitude to all loop orders. We show that planar contributions due to multiple-Reggeon exchange diagrams can be factorised as a Regge pole along with the single-Reggeon exchange, and when this is done, the singular part of the gluon Regge trajectory is directly determined by the cusp anomalous dimension. We explicitly compute the Regge cut component of the amplitude through four loops and show that it is non-planar. From a different perspective, the new results provide important information on soft singularities in general kinematics beyond the planar limit: by comparing the computed corrections to the general form of the four-loop soft anomalous dimension we derive powerful constraints on its kinematic dependence, opening the way for a bootstrap-based determination.
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institution Organización Europea para la Investigación Nuclear
language eng
publishDate 2021
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spelling cern-27913062023-10-04T06:04:36Zdoi:10.1007/JHEP03(2022)053http://cds.cern.ch/record/2791306engFalcioni, GiulioGardi, EinanMaher, NiamhMilloy, CalumVernazza, LeonardoScattering amplitudes in the Regge limit and the soft anomalous dimension through four loopshep-thParticle Physics - Theoryhep-phParticle Physics - PhenomenologyUsing rapidity evolution equations we study two-to-two gauge-theory scattering amplitudes in the Regge limit. We carry out explicit computations at next-to-next-to-leading logarithmic accuracy through four loops and present new results for both infrared-singular and finite contributions to the amplitude. New techniques are devised in order to derive the colour structure stemming from three-Reggeon exchange diagrams in terms of commutators of channel operators, obtaining results that are valid for any gauge group, and apply to scattered particles in any colour representation. We also elucidate the separation between contributions to the Regge cut and Regge pole in the real part of the amplitude to all loop orders. We show that planar contributions due to multiple-Reggeon exchange diagrams can be factorised as a Regge pole along with the single-Reggeon exchange, and when this is done, the singular part of the gluon Regge trajectory is directly determined by the cusp anomalous dimension. We explicitly compute the Regge cut component of the amplitude through four loops and show that it is non-planar. From a different perspective, the new results provide important information on soft singularities in general kinematics beyond the planar limit: by comparing the computed corrections to the general form of the four-loop soft anomalous dimension we derive powerful constraints on its kinematic dependence, opening the way for a bootstrap-based determination.Using rapidity evolution equations we study two-to-two gauge-theory scattering amplitudes in the Regge limit. We carry out explicit computations at next-to-next-to-leading logarithmic accuracy through four loops and present new results for both infrared-singular and finite contributions to the amplitude. New techniques are devised in order to derive the colour structure stemming from three-Reggeon exchange diagrams in terms of commutators of channel operators, obtaining results that are valid for any gauge group, and apply to scattered particles in any colour representation. We also elucidate the separation between contributions to the Regge cut and Regge pole in the real part of the amplitude to all loop orders. We show that planar contributions due to multiple-Reggeon exchange diagrams can be factorised as a Regge pole along with the single-Reggeon exchange, and when this is done, the singular part of the gluon Regge trajectory is directly determined by the cusp anomalous dimension. We explicitly compute the Regge cut component of the amplitude through four loops and show that it is non-planar. From a different perspective, the new results provide important information on soft singularities in general kinematics beyond the planar limit: by comparing the computed corrections to the general form of the four-loop soft anomalous dimension we derive powerful constraints on its kinematic dependence, opening the way for a bootstrap-based determination.arXiv:2111.10664CERN-TH-2021-200oai:cds.cern.ch:27913062021-11-20
spellingShingle hep-th
Particle Physics - Theory
hep-ph
Particle Physics - Phenomenology
Falcioni, Giulio
Gardi, Einan
Maher, Niamh
Milloy, Calum
Vernazza, Leonardo
Scattering amplitudes in the Regge limit and the soft anomalous dimension through four loops
title Scattering amplitudes in the Regge limit and the soft anomalous dimension through four loops
title_full Scattering amplitudes in the Regge limit and the soft anomalous dimension through four loops
title_fullStr Scattering amplitudes in the Regge limit and the soft anomalous dimension through four loops
title_full_unstemmed Scattering amplitudes in the Regge limit and the soft anomalous dimension through four loops
title_short Scattering amplitudes in the Regge limit and the soft anomalous dimension through four loops
title_sort scattering amplitudes in the regge limit and the soft anomalous dimension through four loops
topic hep-th
Particle Physics - Theory
hep-ph
Particle Physics - Phenomenology
url https://dx.doi.org/10.1007/JHEP03(2022)053
http://cds.cern.ch/record/2791306
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AT maherniamh scatteringamplitudesinthereggelimitandthesoftanomalousdimensionthroughfourloops
AT milloycalum scatteringamplitudesinthereggelimitandthesoftanomalousdimensionthroughfourloops
AT vernazzaleonardo scatteringamplitudesinthereggelimitandthesoftanomalousdimensionthroughfourloops