The two-loop sunrise graph with arbitrary masses

被引：106

作者：

Adams, Luise ^{[1
]}

Bogner, Christian ^{[2
]}

Weinzierl, Stefan ^{[1
]}

机构：

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

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

来源：

JOURNAL OF MATHEMATICAL PHYSICS | 2013年 / 54卷 / 05期

关键词：

THRESHOLD EXPANSION; DIFFERENTIAL-EQUATIONS; NUMERICAL EVALUATION; MASTER INTEGRALS; FEYNMAN DIAGRAMS; SPACE; SUNSET; CONNECTION; VALUES;

D O I：

10.1063/1.4804996

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

We discuss the analytical solution of the two-loop sunrise graph with arbitrary non-zero masses in two space-time dimensions. The analytical result is obtained by solving a second-order differential equation. The solution involves elliptic integrals and in particular the solutions of the corresponding homogeneous differential equation are given by periods of an elliptic curve. (C) 2013 AIP Publishing LLC.

引用

页数：18

共 58 条

[1]

[Anonymous], 1970, SIAM Journal on Mathematical Analysis

[2] 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)

[3] 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

[4] 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

[5]

BAUBERGER S, 1994, NUCL PHYS B, P95

[6]

Bauberger S., ARXIVHEPPH9501201

[7]

Bauberger S., ARXIVHEPPH9409388

[8]

Berends F. A., ARXIVHEPPH9712209

[9] 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

[10] Threshold and pseudothreshold values of the sunset diagram [J].

Berends, FA ;

Davydychev, AI ;

Ussyukina, NI .

PHYSICS LETTERS B, 1998, 426 (1-2) :95-104

← 1 2 3 4 5 6 →