Analytic treatment of the two loop equal mass sunrise graph

The two loop equal mass sunrise graph is considered in the continuous d-dimensional regularisation for arbitrary values of the momentum transfer. After recalling the equivalence of the expansions at d=2 and d=4, the second order differential equation for the scalar Master Integral is expanded in (d-...

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Detalles Bibliográficos
Autores principales: Laporta, S., Remiddi, E.
Lenguaje:eng
Publicado: 2004
Materias:
Particle Physics - Phenomenology
Acceso en línea:https://dx.doi.org/10.1016/j.nuclphysb.2004.10.044
http://cds.cern.ch/record/743011
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author Laporta, S.
Remiddi, E.
author_facet Laporta, S.
Remiddi, E.
author_sort Laporta, S.
collection CERN
description The two loop equal mass sunrise graph is considered in the continuous d-dimensional regularisation for arbitrary values of the momentum transfer. After recalling the equivalence of the expansions at d=2 and d=4, the second order differential equation for the scalar Master Integral is expanded in (d-2) and solved by the variation of the constants method of Euler up to first order in (d-2) included. That requires the knowledge of the two independent solutions of the associated homogeneous equation, which are found to be related to the complete elliptic integrals of the first kind of suitable arguments. The behaviour and expansions of all the solutions at all the singular points of the equation are exhaustively discussed and written down explicitly.
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spelling cern-7430112023-10-04T06:01:16Zdoi:10.1016/j.nuclphysb.2004.10.044http://cds.cern.ch/record/743011engLaporta, S.Remiddi, E.Analytic treatment of the two loop equal mass sunrise graphParticle Physics - PhenomenologyThe two loop equal mass sunrise graph is considered in the continuous d-dimensional regularisation for arbitrary values of the momentum transfer. After recalling the equivalence of the expansions at d=2 and d=4, the second order differential equation for the scalar Master Integral is expanded in (d-2) and solved by the variation of the constants method of Euler up to first order in (d-2) included. That requires the knowledge of the two independent solutions of the associated homogeneous equation, which are found to be related to the complete elliptic integrals of the first kind of suitable arguments. The behaviour and expansions of all the solutions at all the singular points of the equation are exhaustively discussed and written down explicitly.The two loop equal mass sunrise graph is considered in the continuous d-dimensional regularisation for arbitrary values of the momentum transfer. After recalling the equivalence of the expansions at d=2 and d=4, the second order differential equation for the scalar Master Integral is expanded in (d-2) and solved by the variation of the constants method of Euler up to first order in (d-2) included. That requires the knowledge of the two independent solutions of the associated homogeneous equation, which are found to be related to the complete elliptic integrals of the first kind of suitable arguments. The behaviour and expansions of all the solutions at all the singular points of the equation are exhaustively discussed and written down explicitly.The two loop equal mass sunrise graph is considered in the continuous d -dimensional regularisation for arbitrary values of the momentum transfer. After recalling the equivalence of the expansions at d = 2 and d = 4 , the second order differential equation for the scalar master integral is expanded in ( d − 2 ) and solved by the variation of the constants method of Euler up to first order in ( d − 2 ) included. That requires the knowledge of the two independent solutions of the associated homogeneous equation, which are found to be related to the complete elliptic integrals of the first kind of suitable arguments. The behaviour and expansions of all the solutions at all the singular points of the equation are exhaustively discussed and written down explicitly.hep-ph/0406160CERN-PH-TH-2004-089CERN-PH-TH-2004-089oai:cds.cern.ch:7430112004-06-15
spellingShingle Particle Physics - Phenomenology
Laporta, S.
Remiddi, E.
Analytic treatment of the two loop equal mass sunrise graph
title Analytic treatment of the two loop equal mass sunrise graph
title_full Analytic treatment of the two loop equal mass sunrise graph
title_fullStr Analytic treatment of the two loop equal mass sunrise graph
title_full_unstemmed Analytic treatment of the two loop equal mass sunrise graph
title_short Analytic treatment of the two loop equal mass sunrise graph
title_sort analytic treatment of the two loop equal mass sunrise graph
topic Particle Physics - Phenomenology
url https://dx.doi.org/10.1016/j.nuclphysb.2004.10.044
http://cds.cern.ch/record/743011
work_keys_str_mv AT laportas analytictreatmentofthetwoloopequalmasssunrisegraph
AT remiddie analytictreatmentofthetwoloopequalmasssunrisegraph

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