Numerical evaluation of multi-loop integrals for arbitrary kinematics with SecDec 2.0
Numerical evaluation of multi-loop integrals for arbitrary kinematics with SecDec 2.0
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DOI：
10.1016/j.cpc.2012.09.020
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发表时间：
2013-02-01
影响因子：
6.3
通讯作者：
Heinrich, Gudrun
中科院分区：
文献类型：
--
作者：
Borowka, Sophia;Carter, Jonathon;Heinrich, Gudrun
我们提出了包含各种新特性的SecDec 2.0程序。首先，它允许在不受运动学限制的情况下对多环积分进行数值计算。通过扇形分解分离出尺寸调节的紫外和红外奇点，而阈值奇点则通过复杂平面上积分轮廓的变形来处理。作为应用，我们给出了各种大规模双环四点图的数值结果。SecDec 2.0还包含了新的有用的功能，用于计算更一般的参数积分，例如与相空间积分相关。项目摘要项目名称：SecDec 2.0目录标识：aeir_v2_0项目摘要URL: http://cpc.cs.qub.ac.uk/summaries/AEIR_v2_0.htmlProgram可从：北爱尔兰贝尔法斯特女王大学CPC项目图书馆获得许可条款：标准CPC许可，http://cpc.cs.qub.ac.uk/licence/licence.htmlNo。分布式程序的行数，包括测试数据等：156829分布程序的字节数，包括测试数据等：2137907分布格式：tar。编程语言：Wolfram Mathematica， Perl, Fortran/ c++。计算机：从单个PC到集群，取决于问题。操作系统：Unix、Linux。RAM：根据问题的复杂程度分类：4.4,5,11.1。前版本目录标识符：aeir_v1_0前版本期刊编号：Comput。理论物理。Comm. 182(2011)1566新版本是否取代旧版本？问题性质：从规范理论中高阶微扰计算中出现的参数积分中提取紫外和红外奇点。存在可积奇点的数值积分（例如，运动阈值）。求解方法：利用迭代扇区分解对维数正则化中的奇异点进行代数提取。这导致维度正则化参数E中的劳伦级数，其中的系数是单位超立方体上的有限积分。这些积分用蒙特卡罗积分进行数值计算。通过在复平面上选择合适的积分轮廓，自动处理可积奇点。新版本的原因：在以前的版本中，多尺度积分的计算仅限于欧几里得区域。现在可以求任意物理运动学的多环积分。另一个主要的改进是完全并行化的可能性。修订总结：对多环积分的运动学没有限制。被积函数可以通过图的拓扑切割来构造。完全并行化的可能性。用c++而不是Fortran编写的多循环积分的数值积分。在参数范围内循环的可能性。限制：取决于问题的复杂程度，受内存和CPU时间的限制。多尺度积分只能在欧几里得点计算的限制在2.0版本中被取代。运行时间：根据问题的复杂程度，从几分钟到几天不等。提供的测试运行只需要几秒钟。(C) 2012 Elsevier B.V.版权所有
We present the program SecDec 2.0, which contains various new features. First, it allows the numerical evaluation of multi-loop integrals with no restriction on the kinematics. Dimensionally regulated ultraviolet and infrared singularities are isolated via sector decomposition, while threshold singularities are handled by a deformation of the integration contour in the complex plane. As an application, we present numerical results for various massive two-loop four-point diagrams. SecDec 2.0 also contains new useful features for the calculation of more general parameter integrals, related for example to phase space integrals.Program summaryProgram title: SecDec 2.0Catalogue identifier: AEIR_v2_0Program summary URL: http://cpc.cs.qub.ac.uk/summaries/AEIR_v2_0.htmlProgram obtainable from: CPC Program Library, Queen's University, Belfast, N. IrelandLicensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.htmlNo. of lines in distributed program, including test data, etc.: 156829No. of bytes in distributed program, including test data, etc.: 2137907Distribution format: tar.gzProgramming language: Wolfram Mathematica, Perl, Fortran/C++.Computer: From a single PC to a cluster, depending on the problem.Operating system: Unix, Linux.RAM: Depending on the complexity of the problemClassification: 4.4, 5, 11.1.Catalogue identifier of previous version: AEIR_v1_0Journal reference of previous version: Comput. Phys. Comm. 182(2011)1566Does the new version supersede the previous version?: YesNature of problem: Extraction of ultraviolet and infrared singularities from parametric integrals appearing in higher order perturbative calculations in gauge theories. Numerical integration in the presence of integrable singularities (e.g., kinematic thresholds).Solution method: Algebraic extraction of singularities in dimensional regularization using iterated sector decomposition. This leads to a Laurent series in the dimensional regularization parameter E, where the coefficients are finite integrals over the unit hypercube. Those integrals are evaluated numerically by Monte Carlo integration. The integrable singularities are handled by choosing a suitable integration contour in the complex plane, in an automated way.Reasons for new version: In the previous version the calculation of multi-scale integrals was restricted to the Euclidean region. Now multi-loop integrals with arbitrary physical kinematics can be evaluated. Another major improvement is the possibility of full parallelization.Summary of revisions:No restriction on the kinematics for multi-loop integrals.The integrand can be constructed from the topological cuts of the diagram.Possibility of full parallelization.Numerical integration of multi-loop integrals written in C++ rather than Fortran.Possibility to loop over ranges of parameters.Restrictions: Depending on the complexity of the problem, limited by memory and CPU time. The restriction that multi-scale integrals could only be evaluated at Euclidean points is superseded in version 2.0.Running time: Between a few minutes and several days, depending on the complexity of the problem. Test runs provided take only seconds. (C) 2012 Elsevier B.V. All rights reserved.