Automated solution of first order factorizable systems of differential equations in one variable

被引：63

作者：

Ablinger, J. ^{[1
]}

Bluemlein, J. ^{[2
]}

Marquard, P. ^{[2
]}

Rana, N. ^{[2
,3
]}

Schneider, C. ^{[1
]}

机构：

[1] Johannes Kepler Univ Linz, RISC, Altenbergerstr 69, A-4040 Linz, Austria

[2] DESY, Platanenallee 6, D-15738 Zeuthen, Germany

[3] Ist Nazl Fis Nucl, Sez Milano, Via Celoria 16, I-20133 Milan, Italy

来源：

NUCLEAR PHYSICS B | 2019年 / 939卷

基金：

奥地利科学基金会;

关键词：

QUARK FORM-FACTORS; 2-LOOP QCD CORRECTIONS; OPERATOR MATRIX-ELEMENTS; BETA-FUNCTION; NUMERICAL EVALUATION; HARMONIC SUMS; FIELD-THEORY; 6TH ROOT; FEYNMAN; SUMMATION;

D O I：

10.1016/j.nuclphysb.2018.12.010

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：

We present an algorithm which allows to solve analytically linear systems of differential equations which factorize to first order. The solution is given in terms of iterated integrals over an alphabet where its structure is implied by the coefficient matrix of the differential equations. These systems appear in a large variety of higher order calculations in perturbative Quantum Field Theories. We apply this method to calculate the master integrals of the three-loop massive form factors for different currents, as an illustration, and present the results for the vector form factors in detail. Here the solution space emerging is given by the cyclotomic harmonic polylogarithms and their associated special constants. No special basis representation of the master integrals is needed. The algorithm can be applied as well to more general cases factorizing at first order, which are based on more general alphabets, iterated integrals and associated constants. (C) 2018 Published by Elsevier B.V.

引用

页码：253 / 291

页数：39

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