A semi-infinite matrix analysis of the BFKL equation

A new mapping between the BFKL equation and Beisert's representation of the XXX Heisenberg ferromagnet with spin s = - 1/2 is given. The action of the Hamiltonian operator of a spin chain with SL(2) invariance on a symmetric double copy of a harmonic oscillator excited state is shown to be iden...

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Detalles Bibliográficos
Autores principales: Bethencourt de León, N., Chachamis, G., Romagnoni, Alberto, Sabio Vera, Agustin
Lenguaje:eng
Publicado: 2011
Materias:
Particle Physics - Theory
Particle Physics - Phenomenology
hep-th
Acceso en línea:https://dx.doi.org/10.1140/epjc/s10052-020-8098-0
http://cds.cern.ch/record/1400796
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author Bethencourt de León, N.
Chachamis, G.
Romagnoni, Alberto
Sabio Vera, Agustin
author_facet Bethencourt de León, N.
Chachamis, G.
Romagnoni, Alberto
Sabio Vera, Agustin
author_sort Bethencourt de León, N.
collection CERN
description A new mapping between the BFKL equation and Beisert's representation of the XXX Heisenberg ferromagnet with spin s = - 1/2 is given. The action of the Hamiltonian operator of a spin chain with SL(2) invariance on a symmetric double copy of a harmonic oscillator excited state is shown to be identical to the action of the BFKL Hamiltonian on the gluon Green function for the azimuthal-angle averaged forward scattering case. A natural mapping between the gluon Green function, discretized in virtuality space, and the double harmonic oscillator excited state emerges.
id cern-1400796
institution Organización Europea para la Investigación Nuclear
language eng
publishDate 2011
record_format invenio
spelling cern-14007962023-03-14T19:48:21Zdoi:10.1140/epjc/s10052-020-8098-0http://cds.cern.ch/record/1400796engBethencourt de León, N.Chachamis, G.Romagnoni, AlbertoSabio Vera, AgustinA semi-infinite matrix analysis of the BFKL equationParticle Physics - TheoryParticle Physics - Phenomenologyhep-thParticle Physics - TheoryA new mapping between the BFKL equation and Beisert's representation of the XXX Heisenberg ferromagnet with spin s = - 1/2 is given. The action of the Hamiltonian operator of a spin chain with SL(2) invariance on a symmetric double copy of a harmonic oscillator excited state is shown to be identical to the action of the BFKL Hamiltonian on the gluon Green function for the azimuthal-angle averaged forward scattering case. A natural mapping between the gluon Green function, discretized in virtuality space, and the double harmonic oscillator excited state emerges.The forward BFKL equation is discretised in virtuality space and it is shown that the diffusion into infrared and ultraviolet momenta can be understood in terms of a semi-infinite matrix. The square truncation of this matrix can be exponentiated leading to asymptotic eigenstates sharing many features with the BFKL gluon Green’s function in the limit of large matrix size. This truncation is closely related to a representation of the XXX Heisenberg spin $= - \frac{1}{2}$ chain with SL(2) invariance where the Hamiltonian acts on a symmetric double copy of the harmonic oscillator. A simple modification of the BFKL matrix suppressing the infrared modes generates evolution more compatible with the Froissart bound.The forward BFKL equation is discretised in virtuality space and it is shown that the diffusion into infrared and ultraviolet momenta can be understood in terms of a semi-infinite matrix. The square truncation of this matrix can be exponentiated leading to asymptotic eigenstates sharing many features with the BFKL gluon Green's function in the limit of large matrix size. This truncation is closely related to a representation of the XXX Heisenberg spin $= - \frac{1}{2}$ chain with SL(2) invariance where the Hamiltonian acts on a symmetric double copy of the harmonic oscillator. A simple modification of the BFKL matrix suppressing the infrared modes generates evolution with energy compatible with unitarity.arXiv:1111.4553CERN-TH-2020-064oai:cds.cern.ch:14007962011-11-22
spellingShingle Particle Physics - Theory
Particle Physics - Phenomenology
hep-th
Particle Physics - Theory
Bethencourt de León, N.
Chachamis, G.
Romagnoni, Alberto
Sabio Vera, Agustin
A semi-infinite matrix analysis of the BFKL equation
title A semi-infinite matrix analysis of the BFKL equation
title_full A semi-infinite matrix analysis of the BFKL equation
title_fullStr A semi-infinite matrix analysis of the BFKL equation
title_full_unstemmed A semi-infinite matrix analysis of the BFKL equation
title_short A semi-infinite matrix analysis of the BFKL equation
title_sort semi-infinite matrix analysis of the bfkl equation
topic Particle Physics - Theory
Particle Physics - Phenomenology
hep-th
Particle Physics - Theory
url https://dx.doi.org/10.1140/epjc/s10052-020-8098-0
http://cds.cern.ch/record/1400796
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