The analytic value of a 4-loop sunrise graph in a particular kinematical configuration

The 4-loop sunrise graph with two massless lines, two lines of equal mass M and a line of mass m, for external invariant timelike and equal to m^2 is considered. We write differential equations in x=m/M for the Master Integrals of the problem, which we Laurent-expand in the regularizing continuous d...

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Detalles Bibliográficos
Autores principales: Laporta, S., Mastrolia, P., Remiddi, E.
Lenguaje:eng
Publicado: 2003
Materias:
Particle Physics - Phenomenology
Acceso en línea:https://dx.doi.org/10.1016/j.nuclphysb.2004.03.029
http://cds.cern.ch/record/686278
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author Laporta, S.
Mastrolia, P.
Remiddi, E.
author_facet Laporta, S.
Mastrolia, P.
Remiddi, E.
author_sort Laporta, S.
collection CERN
description The 4-loop sunrise graph with two massless lines, two lines of equal mass M and a line of mass m, for external invariant timelike and equal to m^2 is considered. We write differential equations in x=m/M for the Master Integrals of the problem, which we Laurent-expand in the regularizing continuous dimension d around d=4, and then solve exactly in x up to order (d-4)^3 included; the result is expressed in terms of Harmonic PolyLogarithms of argument x and maximum weight 7. As a by product, we obtain the x=1 value, expected to be relevant in QED 4-loop static quantities like the electron (g-2). The analytic results were checked by an independent precise numerical calculation
id cern-686278
institution Organización Europea para la Investigación Nuclear
language eng
publishDate 2003
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spelling cern-6862782023-03-14T19:12:07Zdoi:10.1016/j.nuclphysb.2004.03.029http://cds.cern.ch/record/686278engLaporta, S.Mastrolia, P.Remiddi, E.The analytic value of a 4-loop sunrise graph in a particular kinematical configurationParticle Physics - PhenomenologyThe 4-loop sunrise graph with two massless lines, two lines of equal mass M and a line of mass m, for external invariant timelike and equal to m^2 is considered. We write differential equations in x=m/M for the Master Integrals of the problem, which we Laurent-expand in the regularizing continuous dimension d around d=4, and then solve exactly in x up to order (d-4)^3 included; the result is expressed in terms of Harmonic PolyLogarithms of argument x and maximum weight 7. As a by product, we obtain the x=1 value, expected to be relevant in QED 4-loop static quantities like the electron (g-2). The analytic results were checked by an independent precise numerical calculationThe 4-loop sunrise graph with two massless lines, two lines of equal mass M and a line of mass m, for external invariant timelike and equal to m^2 is considered. We write differential equations in x=m/M for the Master Integrals of the problem, which we Laurent-expand in the regularizing continuous dimension d around d=4, and then solve exactly in x up to order (d-4)^3 included: the result is expressed in terms of Harmonic PolyLogarithms of argument x and maximum weight 7. As a by product, we obtain the x=1 value, expected to be relevant in QED 4-loop static quantities like the electron (g-2). The analytic results were checked by an independent precise numerical calculationThe 4-loop sunrise graph with two massless lines, two lines of equal mass  M and a line of mass  m , for external invariant timelike and equal to m 2 is considered. We write differential equations in x = m / M for the Master Integrals of the problem, which we Laurent-expand in the regularizing continuous dimension d around d =4, and then solve exactly in x up to order ( d −4) 3 included; the result is expressed in terms of harmonic polylogarithms of argument x and maximum weight 7. As a by product, we obtain the x =1 value, expected to be relevant in QED 4-loop static quantities like the electron ( g −2). The analytic results were checked by an independent precise numerical calculation.hep-ph/0311255CERN-TH-2003-277TTP03-36CERN-TH-2003-277TTP-2003-36oai:cds.cern.ch:6862782003-11-20
spellingShingle Particle Physics - Phenomenology
Laporta, S.
Mastrolia, P.
Remiddi, E.
The analytic value of a 4-loop sunrise graph in a particular kinematical configuration
title The analytic value of a 4-loop sunrise graph in a particular kinematical configuration
title_full The analytic value of a 4-loop sunrise graph in a particular kinematical configuration
title_fullStr The analytic value of a 4-loop sunrise graph in a particular kinematical configuration
title_full_unstemmed The analytic value of a 4-loop sunrise graph in a particular kinematical configuration
title_short The analytic value of a 4-loop sunrise graph in a particular kinematical configuration
title_sort analytic value of a 4-loop sunrise graph in a particular kinematical configuration
topic Particle Physics - Phenomenology
url https://dx.doi.org/10.1016/j.nuclphysb.2004.03.029
http://cds.cern.ch/record/686278
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