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Caola F, Chakraborty A, Gambuti G, von Manteuffel A, Tancredi L. Three-Loop Gluon Scattering in QCD and the Gluon Regge Trajectory. PHYSICAL REVIEW LETTERS 2022; 128:212001. [PMID: 35687450 DOI: 10.1103/physrevlett.128.212001] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/23/2022] [Accepted: 04/21/2022] [Indexed: 06/15/2023]
Abstract
We compute the three-loop helicity amplitudes for the scattering of four gluons in QCD. We employ projectors in the 't Hooft-Veltman scheme and construct the amplitudes from a minimal set of physical building blocks, which allows us to keep the computational complexity under control. We obtain relatively compact results that can be expressed in terms of harmonic polylogarithms. In addition, we consider the Regge limit of our amplitude and extract the gluon Regge trajectory in full three-loop QCD. This is the last missing ingredient required for studying single-Reggeon exchanges at next-to-next-to-leading logarithmic accuracy.
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Affiliation(s)
- Fabrizio Caola
- Rudolf Peierls Centre for Theoretical Physics, University of Oxford, Clarendon Laboratory, Parks Road, Oxford OX1 3PU, United Kingdom
- Wadham College, University of Oxford, Parks Road, Oxford OX1 3PN, United Kingdom
| | - Amlan Chakraborty
- Department of Physics and Astronomy, Michigan State University, East Lansing, Michigan 48824, USA
| | - Giulio Gambuti
- Rudolf Peierls Centre for Theoretical Physics, University of Oxford, Clarendon Laboratory, Parks Road, Oxford OX1 3PU, United Kingdom
- New College, University of Oxford, Holywell Street, Oxford OX1 3BN, United Kingdom
| | - Andreas von Manteuffel
- Department of Physics and Astronomy, Michigan State University, East Lansing, Michigan 48824, USA
| | - Lorenzo Tancredi
- Physik Department, James-Franck-Straße 1, Technische Universität München, D-85748 Garching, Germany
- Exzellenzcluster ORIGINS, Boltzmannstraße 2, D-85748 Garching, Germany
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2
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Falcioni G, Gardi E, Maher N, Milloy C, Vernazza L. Disentangling the Regge Cut and Regge Pole in Perturbative QCD. PHYSICAL REVIEW LETTERS 2022; 128:132001. [PMID: 35426721 DOI: 10.1103/physrevlett.128.132001] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/31/2021] [Accepted: 03/03/2022] [Indexed: 06/14/2023]
Abstract
The high-energy limit of gauge-theory amplitudes features both a Regge pole and Regge cuts. We show how to disentangle these, and hence how to determine the Regge trajectory beyond two loops. While the nonplanar part of multiple Reggeon t-channel exchange forms a Regge cut, the planar part contributes to the pole along with the single Reggeon. With this, we find that the infrared singularities of the trajectory are given by the cusp anomalous dimension. By matching to recent QCD results, we determine the quark and gluon impact factors to two loops and the Regge trajectory to three loops.
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Affiliation(s)
- Giulio Falcioni
- Higgs Centre for Theoretical Physics, School of Physics and Astronomy, The University of Edinburgh, Edinburgh EH9 3FD, Scotland, United Kingdom
| | - Einan Gardi
- Higgs Centre for Theoretical Physics, School of Physics and Astronomy, The University of Edinburgh, Edinburgh EH9 3FD, Scotland, United Kingdom
| | - Niamh Maher
- Higgs Centre for Theoretical Physics, School of Physics and Astronomy, The University of Edinburgh, Edinburgh EH9 3FD, Scotland, United Kingdom
| | - Calum Milloy
- Dipartimento di Fisica and Arnold-Regge Center, Università di Torino, and INFN, Sezione di Torino, Via P. Giuria 1, I-10125 Torino, Italy
| | - Leonardo Vernazza
- Dipartimento di Fisica and Arnold-Regge Center, Università di Torino, and INFN, Sezione di Torino, Via P. Giuria 1, I-10125 Torino, Italy
- Theoretical Physics Department, CERN, Geneva 1211, Switzerland
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3
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Agarwal B, Buccioni F, von Manteuffel A, Tancredi L. Two-Loop Helicity Amplitudes for Diphoton Plus Jet Production in Full Color. PHYSICAL REVIEW LETTERS 2021; 127:262001. [PMID: 35029492 DOI: 10.1103/physrevlett.127.262001] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/15/2021] [Revised: 09/27/2021] [Accepted: 11/30/2021] [Indexed: 06/14/2023]
Abstract
We present the two-loop QCD amplitudes for the production of two photons and a jet at hadron colliders with full-color dependence. This is the first time that radiative corrections for a five-particle scattering process have been computed beyond the leading-color approximation at this perturbative order in QCD. The results presented in this Letter will be crucial to guaranteeing reliable predictions with unprecedented precision for diphoton production at hadron colliders. The methodologies that we describe lead to a significant simplification of the calculation and their applicability extends to a wider range of five-point scattering processes.
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Affiliation(s)
- Bakul Agarwal
- Department of Physics and Astronomy, Michigan State University, East Lansing, Michigan 48824, USA
| | - Federico Buccioni
- Rudolf Peierls Centre for Theoretical Physics, University of Oxford, Clarendon Laboratory, Parks Road, Oxford OX1 3PU, United Kingdom
| | - Andreas von Manteuffel
- Department of Physics and Astronomy, Michigan State University, East Lansing, Michigan 48824, USA
| | - Lorenzo Tancredi
- Rudolf Peierls Centre for Theoretical Physics, University of Oxford, Clarendon Laboratory, Parks Road, Oxford OX1 3PU, United Kingdom
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Lin G, Yang G, Zhang S. Three-Loop Color-Kinematics Duality: A 24-Dimensional Solution Space Induced by New Generalized Gauge Transformations. PHYSICAL REVIEW LETTERS 2021; 127:171602. [PMID: 34739262 DOI: 10.1103/physrevlett.127.171602] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/26/2021] [Accepted: 09/30/2021] [Indexed: 06/13/2023]
Abstract
We obtain full-color three-loop, three-point form factors of the stress-tensor supermultiplet and also of a length-3 half-Bogomol'nyi-Prasad-Sommerfield operator in N=4 supersymmetric Yang-Mills (SYM) theory based on the color-kinematics duality and on-shell unitarity. The integrand results are verified by all planar and nonplanar unitarity cuts, and they satisfy the minimal power counting of loop momenta and diagrammatic symmetries. Interestingly, these three-loop solutions, while manifesting all dual Jacobi relations, contain a large number of free parameters; in particular, there are 24 free parameters for the form factor of the stress-tensor supermultiplet. Such degrees of freedom are due to a new type of generalized gauge transformation associated with the operator insertion for form factors. We also perform numerical integration and obtain consistent full-color infrared divergences and the known planar remainder. The form factors we obtain can be understood as the N=4 SYM counterparts of three-loop Higgs plus three-gluon amplitudes in QCD and are expected to provide the maximally transcendental parts of the latter.
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Affiliation(s)
- Guanda Lin
- School of Physics, Peking University, Beijing 100871, China
| | - Gang Yang
- CAS Key Laboratory of Theoretical Physics, Institute of Theoretical Physics, Chinese Academy of Sciences, Beijing, 100190, China
- School of Physical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China
- School of Fundamental Physics and Mathematical Sciences, Hangzhou Institute for Advanced Study, UCAS, Hangzhou 310024, China
- International Centre for Theoretical Physics Asia-Pacific (Beijing/Hangzhou), UCAS, Beijing 100190, China
| | - Siyuan Zhang
- CAS Key Laboratory of Theoretical Physics, Institute of Theoretical Physics, Chinese Academy of Sciences, Beijing, 100190, China
- School of Physical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China
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Caola F, von Manteuffel A, Tancredi L. Diphoton Amplitudes in Three-Loop Quantum Chromodynamics. PHYSICAL REVIEW LETTERS 2021; 126:112004. [PMID: 33798349 DOI: 10.1103/physrevlett.126.112004] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/09/2020] [Accepted: 02/09/2021] [Indexed: 06/12/2023]
Abstract
We consider the three-loop scattering amplitudes for the production of a pair of photons in quark-antiquark annihilation in QCD. We use suitably defined projectors to efficiently calculate all helicity amplitudes. We obtain relatively compact analytic results that we write in terms of harmonic polylogarithms or, alternatively, multiple polylogarithms of up to depth three. This is the first calculation of a three-loop four-point scattering amplitude in full QCD.
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Affiliation(s)
- Fabrizio Caola
- Rudolf Peierls Centre for Theoretical Physics, University of Oxford, Clarendon Laboratory, Parks Road, Oxford OX1 3PU, United Kingdom
- Wadham College, University of Oxford, Parks Road, Oxford OX1 3PN, United Kingdom
| | - Andreas von Manteuffel
- Department of Physics and Astronomy, Michigan State University, East Lansing, Michigan 48824, USA
| | - Lorenzo Tancredi
- Rudolf Peierls Centre for Theoretical Physics, University of Oxford, Clarendon Laboratory, Parks Road, Oxford OX1 3PU, United Kingdom
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von Manteuffel A, Panzer E, Schabinger RM. Cusp and Collinear Anomalous Dimensions in Four-Loop QCD from Form Factors. PHYSICAL REVIEW LETTERS 2020; 124:162001. [PMID: 32383907 DOI: 10.1103/physrevlett.124.162001] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/24/2020] [Accepted: 04/01/2020] [Indexed: 06/11/2023]
Abstract
We calculate the complete quark and gluon cusp anomalous dimensions in four-loop massless QCD analytically from first principles. In addition, we determine the complete matter dependence of the quark and gluon collinear anomalous dimensions. Our approach is to Laurent expand four-loop quark and gluon form factors in the parameter of dimensional regularization. We employ finite field and syzygy techniques to reduce the relevant Feynman integrals to a basis of finite integrals, and subsequently evaluate the basis integrals directly from their standard parametric representations.
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Affiliation(s)
- Andreas von Manteuffel
- Department of Physics and Astronomy, Michigan State University, East Lansing, Michigan 48824, USA
| | - Erik Panzer
- All Souls College, University of Oxford, OX1 4AL Oxford, United Kingdom
| | - Robert M Schabinger
- Department of Physics and Astronomy, Michigan State University, East Lansing, Michigan 48824, USA
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Bourjaily JL, Herrmann E, Langer C, McLeod AJ, Trnka J. All-Multiplicity Nonplanar Amplitude Integrands in Maximally Supersymmetric Yang-Mills Theory at Two Loops. PHYSICAL REVIEW LETTERS 2020; 124:111603. [PMID: 32242737 DOI: 10.1103/physrevlett.124.111603] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/23/2019] [Accepted: 02/28/2020] [Indexed: 06/11/2023]
Abstract
We give a prescriptive representation of all-multiplicity two-loop maximally-helicity-violating (MHV) amplitude integrands in fully-color-dressed (nonplanar) maximally supersymmetric Yang-Mills theory.
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Affiliation(s)
- Jacob L Bourjaily
- Niels Bohr International Academy and Discovery Center, Niels Bohr Institute, University of Copenhagen, Blegdamsvej 17, DK-2100 Copenhagen Ø, Denmark
- Center for the Fundamental Laws of Nature, Department of Physics, Jefferson Physical Laboratory, Harvard University, Cambridge, Massachusetts 02138, USA
- Institute for Gravitation and the Cosmos, Department of Physics, Pennsylvania State University, University Park, Pennsylvania 16892, USA
| | - Enrico Herrmann
- SLAC National Accelerator Laboratory, Stanford University, Stanford, California 94039, USA
| | - Cameron Langer
- Center for Quantum Mathematics and Physics (QMAP), Department of Physics, University of California, Davis, California 95616, USA
| | - Andrew J McLeod
- Niels Bohr International Academy and Discovery Center, Niels Bohr Institute, University of Copenhagen, Blegdamsvej 17, DK-2100 Copenhagen Ø, Denmark
| | - Jaroslav Trnka
- Center for Quantum Mathematics and Physics (QMAP), Department of Physics, University of California, Davis, California 95616, USA
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Duhr C, Johansson H, Kälin G, Mogull G, Verbeek B. Full-Color Two-Loop Four-Gluon Amplitude in N=2 Supersymmetric QCD. PHYSICAL REVIEW LETTERS 2019; 123:241601. [PMID: 31922855 DOI: 10.1103/physrevlett.123.241601] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/23/2019] [Indexed: 06/10/2023]
Abstract
We present the fully integrated form of the two-loop four-gluon amplitude in N=2 supersymmetric quantum chromodynamics with gauge group SU(N_{c}) and with N_{f} massless supersymmetric quarks (hypermultiplets) in the fundamental representation. Our result maintains full dependence on N_{c} and N_{f}, and relies on the existence of a compact integrand representation that exhibits the duality between color and kinematics. Specializing to the N=2 superconformal theory, where N_{f}=2N_{c}, we obtain remarkably simple amplitudes that have an analytic structure close to that of N=4 super-Yang-Mills theory, except that now certain lower-weight terms appear. We comment on the corresponding results for other gauge groups.
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Affiliation(s)
- Claude Duhr
- Theoretical Physics Department, CERN, CH-1211 Geneva 23, Switzerland
- Center for Cosmology, Particle Physics and Phenomenology (CP3), UCLouvain, Chemin du Cyclotron 2, 1348 Louvain-La-Neuve, Belgium
| | - Henrik Johansson
- Department of Physics and Astronomy, Uppsala University, Uppsala, 75108 Sweden
- Nordita, Stockholm University and KTH Royal Institute of Technology, Roslagstullsbacken 23, Stockholm, 10691 Sweden
| | - Gregor Kälin
- Department of Physics and Astronomy, Uppsala University, Uppsala, 75108 Sweden
| | - Gustav Mogull
- Department of Physics and Astronomy, Uppsala University, Uppsala, 75108 Sweden
| | - Bram Verbeek
- Center for Cosmology, Particle Physics and Phenomenology (CP3), UCLouvain, Chemin du Cyclotron 2, 1348 Louvain-La-Neuve, Belgium
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Chicherin D, Gehrmann T, Henn JM, Wasser P, Zhang Y, Zoia S. Analytic Result for a Two-Loop Five-Particle Amplitude. PHYSICAL REVIEW LETTERS 2019; 122:121602. [PMID: 30978051 DOI: 10.1103/physrevlett.122.121602] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/28/2018] [Indexed: 06/09/2023]
Abstract
We compute the symbol of the full-color two-loop five-particle amplitude in N=4 super Yang-Mills theory, including all nonplanar subleading-color terms. The amplitude is written in terms of permutations of Parke-Taylor tree-level amplitudes and pure functions to all orders in the dimensional regularization parameter, in agreement with previous conjectures. The answer has the correct collinear limits and infrared factorization properties, allowing us to define a finite remainder function. We study the multi-Regge limit of the nonplanar terms, analyze its subleading power corrections, and analytically present the leading logarithmic terms.
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Affiliation(s)
- D Chicherin
- Max-Planck-Institut für Physik, Werner-Heisenberg-Institut, D-80805 München, Germany
| | - T Gehrmann
- Physik-Institut, Universität Zürich, Wintherturerstrasse 190, CH-8057 Zürich, Switzerland
| | - J M Henn
- Max-Planck-Institut für Physik, Werner-Heisenberg-Institut, D-80805 München, Germany
| | - P Wasser
- PRISMA Cluster of Excellence, Johannes Gutenberg University, D-55099 Mainz, Germany
| | - Y Zhang
- Max-Planck-Institut für Physik, Werner-Heisenberg-Institut, D-80805 München, Germany
| | - S Zoia
- Max-Planck-Institut für Physik, Werner-Heisenberg-Institut, D-80805 München, Germany
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Abreu S, Dixon LJ, Herrmann E, Page B, Zeng M. Two-Loop Five-Point Amplitude in N=4 Super-Yang-Mills Theory. PHYSICAL REVIEW LETTERS 2019; 122:121603. [PMID: 30978096 DOI: 10.1103/physrevlett.122.121603] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/03/2019] [Indexed: 06/09/2023]
Abstract
We compute the symbol of the two-loop five-point scattering amplitude in N=4 supersymmetric Yang-Mills theory, including its full color dependence. This requires constructing the symbol of all two-loop five-point nonplanar massless master integrals, for which we give explicit results.
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Affiliation(s)
- Samuel Abreu
- Center for Cosmology, Particle Physics and Phenomenology (CP3), Université Catholique de Louvain, 1348 Louvain-La-Neuve, Belgium
| | - Lance J Dixon
- SLAC National Accelerator Laboratory, Stanford University, Stanford, California 94039, USA
| | - Enrico Herrmann
- SLAC National Accelerator Laboratory, Stanford University, Stanford, California 94039, USA
| | - Ben Page
- Institut de Physique Théorique, CEA, CNRS, Université Paris-Saclay, F-91191 Gif-sur-Yvette cedex, France
| | - Mao Zeng
- Institut für Theoretische Physik, Eidgenössische Technische Hochschule Zürich, Wolfgang-Pauli-Strasse 27, 8093 Zürich, Switzerland
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11
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Bourjaily JL, McLeod AJ, von Hippel M, Wilhelm M. Bounded Collection of Feynman Integral Calabi-Yau Geometries. PHYSICAL REVIEW LETTERS 2019; 122:031601. [PMID: 30735423 DOI: 10.1103/physrevlett.122.031601] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/24/2018] [Indexed: 06/09/2023]
Abstract
We define the rigidity of a Feynman integral to be the smallest dimension over which it is nonpolylogarithmic. We prove that massless Feynman integrals in four dimensions have a rigidity bounded by 2(L-1) at L loops provided they are in the class that we call marginal: those with (L+1)D/2 propagators in (even) D dimensions. We show that marginal Feynman integrals in D dimensions generically involve Calabi-Yau geometries, and we give examples of finite four-dimensional Feynman integrals in massless φ^{4} theory that saturate our predicted bound in rigidity at all loop orders.
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Affiliation(s)
- Jacob L Bourjaily
- Niels Bohr International Academy and Discovery Center, Niels Bohr Institute, University of Copenhagen, Blegdamsvej 17, DK-2100, Copenhagen Ø, Denmark
| | - Andrew J McLeod
- Niels Bohr International Academy and Discovery Center, Niels Bohr Institute, University of Copenhagen, Blegdamsvej 17, DK-2100, Copenhagen Ø, Denmark
| | - Matt von Hippel
- Niels Bohr International Academy and Discovery Center, Niels Bohr Institute, University of Copenhagen, Blegdamsvej 17, DK-2100, Copenhagen Ø, Denmark
| | - Matthias Wilhelm
- Niels Bohr International Academy and Discovery Center, Niels Bohr Institute, University of Copenhagen, Blegdamsvej 17, DK-2100, Copenhagen Ø, Denmark
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Del Duca V. A tale of two Regge limits. EPJ WEB OF CONFERENCES 2018. [DOI: 10.1051/epjconf/201819200009] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
In light of the strong advances in understanding the mathematical structure of scattering amplitudes, we discuss the Regge limit of QCD and of theN= 4 Super Yang-Mills theory.
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Almelid Ø, Duhr C, Gardi E. Three-Loop Corrections to the Soft Anomalous Dimension in Multileg Scattering. PHYSICAL REVIEW LETTERS 2016; 117:172002. [PMID: 27824458 DOI: 10.1103/physrevlett.117.172002] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/26/2016] [Indexed: 06/06/2023]
Abstract
We present the three-loop result for the soft anomalous dimension governing long-distance singularities of multileg gauge-theory scattering amplitudes of massless partons. We compute all contributing webs involving semi-infinite Wilson lines at three loops and obtain the complete three-loop correction to the dipole formula. We find that nondipole corrections appear already for three colored partons, where the correction is a constant without kinematic dependence. Kinematic dependence appears only through conformally invariant cross ratios for four colored partons or more, and the result can be expressed in terms of single-valued harmonic polylogarithms of weight five. While the nondipole three-loop term does not vanish in two-particle collinear limits, its contribution to the splitting amplitude anomalous dimension reduces to a constant, and it depends only on the color charges of the collinear pair, thereby preserving strict collinear factorization properties. Finally, we verify that our result is consistent with expectations from the Regge limit.
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Affiliation(s)
- Øyvind Almelid
- Higgs Centre for Theoretical Physics, School of Physics and Astronomy, The University of Edinburgh, Edinburgh EH9 3FD, Scotland, United Kingdom
| | - Claude Duhr
- CERN Theory Division, 1211 Geneva 23, Switzerland
- Center for Cosmology, Particle Physics and Phenomenology (CP3), Université Catholique de Louvain, 1348 Louvain-La-Neuve, Belgium
| | - Einan Gardi
- Higgs Centre for Theoretical Physics, School of Physics and Astronomy, The University of Edinburgh, Edinburgh EH9 3FD, Scotland, United Kingdom
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