Abstract
In this article we present REvolver, a C++ library for renormalization group evolution and automatic flavor matching of the QCD coupling and quark masses, as well as precise conversion between various quark mass renormalization schemes. The library systematically accounts for the renormalization group evolution of low-scale short-distance masses which depend linearly on the renormalization scale and sums logarithmic terms of high and low scales that are missed by the common logarithmic renormalization scale evolution. The library can also be accessed through Mathematica and Python interfaces and provides renormalization group evolution for complex renormalization scales as well. Program summaryProgram Title:REvolverCPC Library link to program files:https://doi.org/10.17632/m6cjfmzsxb.1Developer's repository link:https://gitlab.com/REvolver-hep/REvolverCode Ocean capsule:https://codeocean.com/capsule/6150064Licensing provisions: GPLv3 or laterProgramming language:C++, Python, Wolfram LanguageNature of problem: The strong coupling and the quark masses are fundamental parameters of QCD that are scheme and renormalization-scale dependent. The choice of scheme depends on the active number of flavors and the range of scales, and is dictated by the requirements to minimize the size of corrections and to sum large logarithmic corrections to all orders. For the strong coupling and the quark masses at high scales, the MS‾ scheme with logarithmic scale dependence is used. For quark masses at low scales, short-distance mass schemes with linear scale-dependence are used. The REvolver library provides conversions for the strong coupling and the most common quark mass schemes, with renormalization scale evolution implemented such that all types of large logarithmic terms are summed to all orders, accounting for flavor threshold effects and state-or-the-art correction terms. The pole mass, which is not a short-distance mass and contains a sizable renormalon ambiguity, is treated as a derived quantity.Solution method: Renormalization group equations are solved for complex-valued scales to machine precision based on fast-converging iterative algorithms and analytic all-order expressions. Matching relations for the strong coupling at flavor thresholds are computed in a way that gives equal results for upward and downward evolution. Core objects allow to define an arbitrary number of physical scenarios for strong coupling values and quark mass spectra, where options for precision and matching scales can be set freely, and values for quark masses in all common schemes including the pole mass can be extracted. All REvolver routines are implemented entirely in C++ and can be accessed through Mathematica and Python interfaces.
Highlights
Quark masses are fundamental parameters of quantum chromodynamics (QCD) and their precise determination in adequate schemes and at appropriate renormalization scales is of high interest for theoretical as well as experimental studies of many processes
Asymptotic pole and low-scale mass and the running (MSR) mass To demonstrate the REvolver functionalities related to mass conversions accounting for flavor threshold effects, we investigate how much the asymptotic top quark pole mass mpt ole as well as the top MSR mass at 2 GeV mMt SR(2 GeV) would change if the strong coupling value quoted in Ref. [24] αs(1508.04 GeV) = 0.0822+−00..00003341 would be interpreted as a 6-flavor compared to a 5-flavor result
In this article we have presented REvolver, a C++ library for carrying out state-of-the-art renormalization group evolution and flavor matching for the QCD coupling and quark masses, and conversion between the most common quark mass renormalization schemes
Summary
Quark masses are fundamental parameters of quantum chromodynamics (QCD) and their precise determination in adequate schemes and at appropriate renormalization scales is of high interest for theoretical as well as experimental studies of many processes. The REvolver library, exceeds CRunDec/RunDec (i) by providing the Core concept that allows to automatically create, extend and manage an arbitrary number of scenarios for strong coupling values, mass spectra and theory settings, and to extract quark masses and the QCD coupling in all flavor number schemes and at all scales,. (iii) by giving access to machine-precision numerical routines that provide quasi-exact solutions of the renormalization group equations for the running masses and the strong coupling at complex scales, and (iv) by providing routines to determine the asymptotic series for the pole mass to an arbitrary order that allow to extract different pole mass definitions and to quantify the pole mass renormalon ambiguity with various methods. A number of essential formulae for implementation-dependent quantities are provided which cannot be found in the literature in the form used in REvolver
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