Multiparton webs beyond three loops
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Springer
Received: April 1, 2020 Accepted: May 4, 2020 Published: May 26, 2020
Multiparton webs beyond three loops
a
Department of Physics, Chaitanya Bharathi Institute of Technology, Gandipet, Hyderabad, Telangana State 500075, India b Department of Physics, Indian Institute of Technology Hyderabad, Kandi, Sangareddy, Telangana State 502285, India c Dipartimento di Fisica and Arnold-Regge Center, Universit` a di Torino, and INFN, Sezione di Torino, Via Pietro Giuria 1, I-10125 Torino, Italy
E-mail: neelimaagarwal [email protected], [email protected], [email protected], [email protected], [email protected] Abstract: Correlators of Wilson-line operators are fundamental ingredients for the study of the infrared properties of non-abelian gauge theories. In perturbation theory, they are known to exponentiate, and their logarithm can be organised in terms of collections of Feynman diagrams called webs. We study the classification of webs to high perturbative orders, proposing a set of tools to generate them recursively: in particular, we introduce the concept of Cweb, or correlator web, which is a set of skeleton diagrams built with connected gluon correlators, instead of individual Feynman diagrams. As an application, we enumerate all Cwebs entering the soft anomalous dimension matrix for multi-parton scattering amplitudes at four loops, and we compute the mixing matrices for all Cwebs connecting four or five Wilson lines at that loop order, verifying that they obey sum rules that were derived or conjectured in the literature. Our results provide the colour building blocks for the calculation of the soft anomalous dimension matrix at four-loop order. Keywords: NLO Computations, QCD Phenomenology ArXiv ePrint: 2003.09714
c The Authors. Open Access, Article funded by SCOAP3 .
https://doi.org/10.1007/JHEP05(2020)128
JHEP05(2020)128
Neelima Agarwal,a Abhinava Danish,b Lorenzo Magnea,c Sourav Palb and Anurag Tripathib
Contents 1 Introduction
1
2 Diagrammatic exponentiation for multiple Wilson-line correlators
4
3 From gluon webs to correlator webs
8 13
5 A selection of four-loop Cwebs 5.1 A four-loop, four-line Cweb 5.2 A four-loop, five-line Cweb 5.3 A note on colour structures at four loops
16 16 18 19
6 Summary and outlook
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A Mixing matrices and exponentiated colour factors A.1 Cwebs connecting four Wilson lines A.2 Cwebs connecting five Wilson lines
22 22 41
1
Introduction
Studies of the structure of infrared (IR) singularities that appear in scattering amplitudes in gauge field theories have a long and rich history, and have led to remarkable all-order insights into the organisation of the perturbative expansion [1–16]. In the computation of loop corrections to scattering amplitudes, IR singularities arise when a virtual particle flowing in a loop becomes soft or collinear to one of the external particles. Upon constructing, from amplitudes, a well-defined physical observable, these singularities are cancelled by the contribution of real emission diagrams, which must be integrat
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