Version 3 of RunDec and CRunDec

• DOI: 10.1016/j.cpc.2017.11.014
• Publication Date: 2017-12-02T06:50:14Z
• Authors: Florian Herren; Matthias Steinhauser
• Keywords: Physics; ddc:530; 0103 physical sciences; info:eu-repo/classification/ddc/530; 530; 01 natural sciences

Abstract 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, e.g., 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.