The iterated structure of the all-order result for the two-loop sunrise integral

被引：97

作者：

Adams, Luise ^{[1
]}

Bogner, Christian ^{[2
]}

Weinzierl, Stefan ^{[1
]}

机构：

[1] Johannes Gutenberg Univ Mainz, Inst Phys, PRISMA Cluster Excellence, D-55099 Mainz, Germany

[2] Humboldt Univ, Inst Phys, D-10099 Berlin, Germany

来源：

JOURNAL OF MATHEMATICAL PHYSICS | 2016年 / 57卷 / 03期

关键词：

DIFFERENTIAL-EQUATIONS; TRANSCENDENTAL FUNCTIONS; MULTIPLE POLYLOGARITHMS; NUMERICAL EVALUATION; FEYNMAN-INTEGRALS; MASTER INTEGRALS; MULTILOOP INTEGRALS; ARBITRARY MASSES; MODULI SPACES; GRAPH;

D O I：

10.1063/1.4944722

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

We present a method to compute the Laurent expansion of the two-loop sunrise integral with equal non-zero masses to arbitrary order in the dimensional regularisation epsilon. This is done by introducing a class of functions (generalisations of multiple polylogarithms to include the elliptic case) and by showing that all integrations can be carried out within this class of functions. (C) 2016 AIP Publishing LLC.

引用

页数：14

共 48 条

[1] The two-loop sunrise integral around four space-time dimensions and generalisations of the Clausen and Glaisher functions towards the elliptic case [J].

Adams, Luise ;

Bogner, Christian ;

Weinzierl, Stefan .

JOURNAL OF MATHEMATICAL PHYSICS, 2015, 56 (07)

[2] The two-loop sunrise graph in two space-time dimensions with arbitrary masses in terms of elliptic dilogarithms [J].

Adams, Luise ;

Bogner, Christian ;

Weinzierl, Stefan .

JOURNAL OF MATHEMATICAL PHYSICS, 2014, 55 (10)

[3] The two-loop sunrise graph with arbitrary masses [J].

Adams, Luise ;

Bogner, Christian ;

Weinzierl, Stefan .

JOURNAL OF MATHEMATICAL PHYSICS, 2013, 54 (05)

[4]

[Anonymous], 2001, ARXIVMATHAG0103059

[5] Feynman diagrams and differential equations [J].

Argeri, Mario ;

Mastrolia, Pierpaolo .

INTERNATIONAL JOURNAL OF MODERN PHYSICS A, 2007, 22 (24) :4375-4436

[6] Elliptic integral evaluations of Bessel moments and applications [J].

Bailey, David H. ;

Borwein, Jonathan M. ;

Broadhurst, David ;

Glasser, M. L. .

JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, 2008, 41 (20)

[7] SIMPLE ONE-DIMENSIONAL INTEGRAL-REPRESENTATIONS FOR 2-LOOP SELF-ENERGIES - THE MASTER DIAGRAM [J].

BAUBERGER, S ;

BOHM, M .

NUCLEAR PHYSICS B, 1995, 445 (01) :25-46

[8] ANALYTICAL AND NUMERICAL-METHODS FOR MASSIVE 2-LOOP SELF-ENERGY DIAGRAMS [J].

BAUBERGER, S ;

BERENDS, FA ;

BOHM, M ;

BUZA, M .

NUCLEAR PHYSICS B, 1995, 434 (1-2) :383-407

[9]

BAUBERGER S, 1994, NUCL PHYS B, P95

[10] CLOSED EXPRESSIONS FOR SPECIFIC MASSIVE MULTILOOP SELF-ENERGY INTEGRALS [J].

BERENDS, FA ;

BOHM, M ;

BUZA, M ;

SCHARF, R .

ZEITSCHRIFT FUR PHYSIK C-PARTICLES AND FIELDS, 1994, 63 (02) :227-234

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