Version 3 of RunDec and CRunDec
Version 3 of RunDec and CRunDec
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DOI：
10.1016/j.cpc.2017.11.014
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发表时间：
2017-03
期刊：
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通讯作者：
Florian Herren;M. Steinhauser
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作者：
Florian Herren;M. Steinhauser
我们推出了 RunDec 和 CRunDec 包的新版本，可用于强耦合常数和夸克质量的运行和解耦。此外，还实现了几个重夸克质量的转换公式。新版本包括 QCD beta 函数的五环校正和四环解耦效应。此外，MS 中定义的重夸克质量与其他短距离方案之间的各种关系都实现为下一个到下一个到下一个前导顺序。我们详细讨论了这些改进，并提供了几个示例，展示了如何在频繁发生的情况下使用 RunDec 和 CRunDec。程序摘要 程序标题：RunDec、CRunDec Program Files doi：http://dx。土井。 org/10.17632/4gsm8tmjtj。 1 许可条款：GPLv3 编程语言：程序在 Mathematica (RunDec) 和 C++ 11 (CRundec) 中实现。问题的性质：量子色动力学耦合常数 α s (n f)(μ) 的值取决于所考虑的能量尺度 μ 和活跃夸克味的数量 n f。这同样适用于轻夸克质量 m q (n f)(μ)，如果它们例如在 MS 方案中评估的话。在 RunDec 和 CRunDec 程序中，收集了所有相关公式并提供了各种程序，可以使用最先进的校正项方便地评估 α s (n f)(μ) 和 m q (n f)(μ)。此外，程序包含几个转换公式，可以将重夸克的 MS 值转换为其他短距离值或壳上定义。解决方法：CRunDec是用C++实现的。为了求解微分方程，采用了自适应龙格-库塔程序。 Mathematica版本的RunDec使用Mathematica提供的函数来求解微分方程。包括限制在内的附加注释：对于输入参数的非物理选择，结果可能是无意义的。
We present new versions of the packages RunDec and CRunDec which can be used for the running and decoupling of the strong coupling constant and quark masses. Furthermore several conversion formulae for heavy quark masses are implemented. The new versions include five-loop corrections of the QCD beta function and four-loop decoupling effects. Furthermore, various relations between the heavy quark mass defined in the MS¯ and other short-distance schemes are implemented to next-to-next-to-next-to-leading order. We discuss in detail the improvements and provide several examples which show how RunDec and CRunDec can be used in frequently occurring situations. Program summary Program title: RunDec, CRunDec Program Files doi: http://dx. doi. org/10.17632/4gsm8tmjtj. 1 Licensing provisions: GPLv3 Programming language: The procedures are implemented both in Mathematica (RunDec) and in C++ 11 (CRundec). Nature of problem: The value for the coupling constant of Quantum Chromodynamics, α s (n f)(μ), depends on the considered energy scale, μ, and the number of active quark flavours, n f. The same applies to light quark masses, m q (n f)(μ), if they are, eg, evaluated in the MS¯ scheme. In the programs RunDec and CRunDec all relevant formulae are collected and various procedures are provided which allow for a convenient evaluation of α s (n f)(μ) and m q (n f)(μ) using the state-of-the-art correction terms. Furthermore, the programs contain several conversion formulae which allow to transform the MS¯ value of a heavy quark into other short-distance values or the on-shell definition. Solution method: CRunDec is implemented in C++. For the solution of the differential equations an adaptive Runge–Kutta procedure has been implemented. The Mathematica version RunDec uses function provided by Mathematica to solve the differential equations. Additional comments including restrictions: It could be that for an unphysical choice of the input parameters the results are nonsensical.