Multi-loop Integrand Reduction with Computational Algebraic Geometry

We discuss recent progress in multi-loop integrand reduction methods. Motivated by the possibility of an automated construction of multi-loop amplitudes via generalized unitarity cuts we describe a procedure to obtain a general parameterisation of any multi-loop integrand in a renormalizable gauge t...

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Detalles Bibliográficos
Autores principales: Badger, Simon, Frellesvig, Hjalte, Zhang, Yang
Lenguaje:eng
Publicado: 2013
Materias:
Particle Physics - Phenomenology
Acceso en línea:https://dx.doi.org/10.1088/1742-6596/523/1/012061
http://cds.cern.ch/record/1611006
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author Badger, Simon
Frellesvig, Hjalte
Zhang, Yang
author_facet Badger, Simon
Frellesvig, Hjalte
Zhang, Yang
author_sort Badger, Simon
collection CERN
description We discuss recent progress in multi-loop integrand reduction methods. Motivated by the possibility of an automated construction of multi-loop amplitudes via generalized unitarity cuts we describe a procedure to obtain a general parameterisation of any multi-loop integrand in a renormalizable gauge theory. The method relies on computational algebraic geometry techniques such as Gr\"obner bases and primary decomposition of ideals. We present some results for two and three loop amplitudes obtained with the help of the Macaulay2 computer algebra system and the Mathematica package BasisDet.
id cern-1611006
institution Organización Europea para la Investigación Nuclear
language eng
publishDate 2013
record_format invenio
spelling cern-16110062021-10-20T02:15:33Zdoi:10.1088/1742-6596/523/1/012061http://cds.cern.ch/record/1611006engBadger, SimonFrellesvig, HjalteZhang, YangMulti-loop Integrand Reduction with Computational Algebraic GeometryParticle Physics - PhenomenologyWe discuss recent progress in multi-loop integrand reduction methods. Motivated by the possibility of an automated construction of multi-loop amplitudes via generalized unitarity cuts we describe a procedure to obtain a general parameterisation of any multi-loop integrand in a renormalizable gauge theory. The method relies on computational algebraic geometry techniques such as Gr\"obner bases and primary decomposition of ideals. We present some results for two and three loop amplitudes obtained with the help of the Macaulay2 computer algebra system and the Mathematica package BasisDet.We discuss recent progress in multi-loop integrand reduction methods. Motivated by the possibility of an automated construction of multi-loop amplitudes via generalized unitarity cuts we describe a procedure to obtain a general parameterisation of any multi-loop integrand in a renormalizable gauge theory. The method relies on computational algebraic geometry techniques such as Gr\"obner bases and primary decomposition of ideals. We present some results for two and three loop amplitudes obtained with the help of the Macaulay2 computer algebra system and the Mathematica package BasisDet.arXiv:1310.4445CERN-PH-TH-2013-246CERN-PH-TH-2013-246oai:cds.cern.ch:16110062013-10-16
spellingShingle Particle Physics - Phenomenology
Badger, Simon
Frellesvig, Hjalte
Zhang, Yang
Multi-loop Integrand Reduction with Computational Algebraic Geometry
title Multi-loop Integrand Reduction with Computational Algebraic Geometry
title_full Multi-loop Integrand Reduction with Computational Algebraic Geometry
title_fullStr Multi-loop Integrand Reduction with Computational Algebraic Geometry
title_full_unstemmed Multi-loop Integrand Reduction with Computational Algebraic Geometry
title_short Multi-loop Integrand Reduction with Computational Algebraic Geometry
title_sort multi-loop integrand reduction with computational algebraic geometry
topic Particle Physics - Phenomenology
url https://dx.doi.org/10.1088/1742-6596/523/1/012061
http://cds.cern.ch/record/1611006
work_keys_str_mv AT badgersimon multiloopintegrandreductionwithcomputationalalgebraicgeometry
AT frellesvighjalte multiloopintegrandreductionwithcomputationalalgebraicgeometry
AT zhangyang multiloopintegrandreductionwithcomputationalalgebraicgeometry

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