Using differential equations to compute two-loop box integrals

被引:46
作者
Gehrmann, T
Remiddi, E
机构
[1] Univ Karlsruhe, Inst Theoret Teilchenphys, D-76128 Karlsruhe, Germany
[2] Univ Bologna, Dipartmento Fis, I-40126 Bologna, Italy
[3] Ist Nazl Fis Nucl, Sez Bologna, I-40126 Bologna, Italy
关键词
D O I
10.1016/S0920-5632(00)00851-3
中图分类号
O412 [相对论、场论]; O572.2 [粒子物理学];
学科分类号
摘要
The calculation of exclusive observables beyond the one-loop level requires elaborate techniques for the computation of multi-leg two-loop integrals. We discuss how the large number of different integrals appearing in actual two-loop calculations can be reduced to a small number of master integrals. An efficient method to compute these master integrals is to derive and solve differential equations in the external invariants for them. As an application of the differential equation method, we compute the O(epsilon)-term of a particular combination of on-shell massless planar double box integrals, which appears in the tensor reduction of 2 --> 2 scattering amplitudes at two loops.
引用
收藏
页码:251 / 255
页数:5
相关论文
共 19 条
[1]  
ANASTASIOU C, IN PRESS NUCL PHYS B
[2]  
BINOTH T, HEPPH0004013
[3]  
BOLLINI CG, 1972, NUOV CIMEN S I FIS B, VB 12, P20
[4]  
Caffo M, 1998, ACTA PHYS POL B, V29, P2627
[5]  
Caffo M, 1998, NUOVO CIMENTO A, V111, P365
[6]   INTEGRATION BY PARTS - THE ALGORITHM TO CALCULATE BETA-FUNCTIONS IN 4-LOOPS [J].
CHETYRKIN, KG ;
TKACHOV, FV .
NUCLEAR PHYSICS B, 1981, 192 (01) :159-204
[7]   ANALYTIC RENORMALIZATION VIA CONTINUOUS SPACE DIMENSION [J].
CICUTA, GM ;
MONTALDI, E .
LETTERE AL NUOVO CIMENTO, 1972, 4 (09) :329-&
[8]  
GEHRMANN T, IN PRESS NUCL PHYS B
[9]   DIMENSIONALLY REGULARIZED 2-LOOP ON-SHELL QUARK FORM-FACTOR [J].
GONSALVES, RJ .
PHYSICAL REVIEW D, 1983, 28 (06) :1542-1549
[10]   DIFFERENTIAL-EQUATIONS METHOD - NEW TECHNIQUE FOR MASSIVE FEYNMAN DIAGRAM CALCULATION [J].
KOTIKOV, AV .
PHYSICS LETTERS B, 1991, 254 (1-2) :158-164