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On the kinematic algebra for BCJ numerators beyond the MHV sector
Uppsala University, Disciplinary Domain of Science and Technology, Physics, Department of Physics and Astronomy, Theoretical Physics. Zhejiang Normal Univ, Dept Phys, Jinhua, Zhejiang, Peoples R China;Queen Mary Univ London, Sch Phys & Astron, Ctr Res String Theory, Mile End Rd, London E1 4NS, England.
Uppsala University, Disciplinary Domain of Science and Technology, Physics, Department of Physics and Astronomy, Theoretical Physics. Stockholm Univ, NORDITA, Roslagstullsbacken 23, S-10691 Stockholm, Sweden;KTH Royal Inst Technol, Roslagstullsbacken 23, S-10691 Stockholm, Sweden.
Uppsala University, Disciplinary Domain of Science and Technology, Physics, Department of Physics and Astronomy, Theoretical Physics.ORCID iD: 0000-0002-7044-8375
Uppsala University, Disciplinary Domain of Science and Technology, Physics, Department of Physics and Astronomy, Theoretical Physics. Nanjing Univ, Dept Phys, Nanjing, Jiangsu, Peoples R China;Humboldt Univ, Inst Phys, Zum Grossen Windkanal 6, D-12489 Berlin, Germany;Humboldt Univ, IRIS Adlershof, Zum Grossen Windkanal 6, D-12489 Berlin, Germany.
2019 (English)In: Journal of High Energy Physics (JHEP), ISSN 1126-6708, E-ISSN 1029-8479, no 11, article id 55Article in journal (Refereed) Published
Abstract [en]

The duality between color and kinematics present in scattering amplitudes of Yang-Mills theory strongly suggests the existence of a hidden kinematic Lie algebra that controls the gauge theory. While associated BCJ numerators are known on closed forms to any multiplicity at tree level, the kinematic algebra has only been partially explored for the simplest of four-dimensional amplitudes: up to the MHV sector. In this paper we introduce a framework that allows us to characterize the algebra beyond the MHV sector. This allows us to both constrain some of the ambiguities of the kinematic algebra, and better control the generalized gauge freedom that is associated with the BCJ numerators. Specifically, in this paper, we work in dimension-agnostic notation and determine the kinematic algebra valid up to certain ? ((epsilon i .epsilon j )(2)) terms that in four dimensions compute the next-to-MHV sector involving two scalars. The kinematic algebra in this sector is simple, given that we introduce tensor currents that generalize standard Yang-Mills vector currents. These tensor currents control the generalized gauge freedom, allowing us to generate multiple different versions of BCJ numerators from the same kinematic algebra. The framework should generalize to other sectors in Yang-Mills theory.

Place, publisher, year, edition, pages
Springer, 2019. no 11, article id 55
Keywords [en]
Scattering Amplitudes, Gauge Symmetry
National Category
Algebra and Logic Subatomic Physics
Identifiers
URN: urn:nbn:se:uu:diva-400094DOI: 10.1007/JHEP11(2019)055ISI: 000499490200001OAI: oai:DiVA.org:uu-400094DiVA, id: diva2:1383281
Funder
Swedish Research Council, 621-2014-5722Knut and Alice Wallenberg Foundation, KAW 2013.0235Ragnar Söderbergs stiftelseGerman Research Foundation (DFG), PL457/3-1Available from: 2020-01-07 Created: 2020-01-07 Last updated: 2020-01-07Bibliographically approved

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