Feynman diagrams and differential equations

被引:150
作者
Argeri, Mario [1 ]
Mastrolia, Pierpaolo [2 ]
机构
[1] Univ Naples Federico II, Dept Chem, I-80134 Naples, Italy
[2] Univ Zurich, Inst Theoret Phys, CH-8057 Zurich, Switzerland
来源
INTERNATIONAL JOURNAL OF MODERN PHYSICS A | 2007年 / 22卷 / 24期
关键词
Feynman integrals; differential equations;
D O I
10.1142/S0217751X07037147
中图分类号
O57 [原子核物理学、高能物理学];
学科分类号
070202 ;
摘要
We review in a pedagogical way the method of differential equations for the evaluation of D-dimensionally regulated Feymnan integrals. After dealing with the general features of the technique, we discuss its application in the context of one- and two-loop corrections to the photon propagator in QED, by computing the Vacuum Polarization tensor exactly in D. Finally, we treat two cases of less trivial differential equations, respectively associated to a two-loop three-point, and a four-loop two-point integral. These two examples are the playgrounds for showing more technical aspects about: Laurent expansion of the differential equations in D (around D = 4); the choice of the boundary conditions; and the link among differential and difference equations for Feymnan integrals.
引用
收藏
页码:4375 / 4436
页数:62
相关论文
共 215 条
[1]   Two-loop tensor integrals in quantum field theory [J].
Actis, S ;
Passarino, G ;
Ferroglia, A ;
Passera, M ;
Uccirati, S .
NUCLEAR PHYSICS B, 2004, 703 (1-2) :3-126
[2]   Master integrals for the two-loop light fermion contributions to gg→H and H→γγ [J].
Aglietti, U ;
Bonciani, R ;
Degrassi, G ;
Vicini, A .
PHYSICS LETTERS B, 2004, 600 (1-2) :57-64
[3]   Master integrals with 2 and 3 massive propagators for the 2-loop electroweak form factor-planar case [J].
Aglietti, U ;
Bonciani, R .
NUCLEAR PHYSICS B, 2004, 698 (1-2) :277-318
[4]   Two-loop light fermion contribution to Higgs production and decays [J].
Aglietti, U ;
Bonciani, R ;
Degrassi, G ;
Vicini, A .
PHYSICS LETTERS B, 2004, 595 :432-441
[5]   Master integrals with one massive propagator for the two-loop electroweak form factor [J].
Aglietti, U ;
Bonciani, R .
NUCLEAR PHYSICS B, 2003, 668 (1-2) :3-76
[6]  
AGLIETTI U, ARXIV07052616
[7]  
AGLIETTI U, HEPPH0111160
[8]  
AGLIETTI U, HEPPH0408014
[9]   Analytic results for virtual QCD corrections to Higgs production and decay [J].
Aglietti, Ugo ;
Bonciani, Roberto ;
Degrassi, Giuseppe ;
Vicini, Alessandro .
JOURNAL OF HIGH ENERGY PHYSICS, 2007, (01)
[10]   The tensor reduction and master integrals of the two-loop massless crossed box with light-like legs [J].
Anastasiou, C ;
Gehrmann, T ;
Oleari, C ;
Remiddi, E ;
Tausk, JB .
NUCLEAR PHYSICS B, 2000, 580 (1-2) :577-601