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首页CHIRON软件包:两环ChPT数值结果的全面工具
CHIRON是一款专为手性摄动理论(Chiral Perturbation Theory, ChPT)的两个环(loop)数值结果设计的软件包。它由两个核心库组成:chiron自身和jbnumlib。chiron库提供了一套完整的工具,包括对一环和二环积分的处理程序,这些积分在ChPT中起着关键作用,如计算粒子的质量、衰减常数以及夸克-反夸克真空期望值。该软件特别关注于实现实用性和精度,以满足理论物理实验的计算需求。 版本v0.50包含了所有必要的功能,可以有效地处理低能量强相互作用中的物理量,如π介子和K介子的相关参数。其中的一项创新是,当输入的π介子和K介子质量发生变化时,软件能计算出相应的质量和衰减常数的自洽值,确保了理论预测与实验数据的一致性。 jbnumlib库则是chiron的一个补充,包含了大量用于数值计算的例程,很多源自CERNLIB数字库,但也有针对特殊功能进行了C++优化。特别是,该库中的对数和Jacobi theta函数的实现,展示了其在复杂数学运算方面的高效性能。 此外,CHIRON还包含了有限体积效应的结果,包括一环的 tadpole积分和二环的日落积分,这些都是在有限空间尺度下研究强相互作用的重要组成部分。这些结果对于理解量子场论在有限空间中的行为和修正具有重要意义。 CHIRON软件包不仅提供了实用的计算工具,而且还展示了如何将理论计算与实验数据紧密结合,为手性摄动理论的研究者和实践者提供了一个强大的工作平台。通过开放访问的方式,这一软件促进了知识的共享和科学研究的进展。
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Eur. Phys. J. C (2015) 75:27
DOI 10.1140/epjc/s10052-014-3249-9
Special Article - Tools for Experiment and Theory
CHIRON: a package for ChPT numerical results at two loops
Johan Bijnens
a
Department of Astronomy and Theoretical Physics, Lund University, Sölvegatan 14A, 223-62 Lund, Sweden
Received: 3 December 2014 / Accepted: 22 December 2014 / Published online: 24 January 2015
© The Author(s) 2015. This article is published with open access at Springerlink.com
Abstract This document describes the package CHIRON
which includes two libraries, chiron itself and jbnumlib.
chiron is a set of routines useful for two-loop numerical
results in chiral perturbation theory (ChPT). It includes pro-
grams for the needed one- and two-loop integrals as well as
routines to deal with the ChPT parameters. The present ver-
sion includes everything needed for the masses, decay con-
stants and quark-antiquark vacuum-expectation-values. An
added routine calculates consistent values for the masses and
decay constants when the pion and kaon masses are varied.
In addition a number of finite volume results are included:
one-loop tadpole integrals, two-loop sunset integrals and the
results for masses and decay constants. The numerical rou-
tine library jbnumlib contains the numerical routines used
in chiron. Many are to a large extent simple C++ ver-
sions of routines in the CERNLIB numerical library. Notable
exceptions are the dilogarithm and the Jacobi theta function
implementations. This paper describes what is included in
CHIRON v0.50.
Contents
1 Introduction ..................... 1
2 Files and setup ................... 2
3 jbnumlib ..................... 2
3.1 Special functions ............... 2
3.1.1 Dilogarithm or Li
2
(x): jbdli2(x) .2
3.1.2 Bessel functions ............ 3
3.1.3 Theta functions ............ 3
3.1.4 Higher dimensional theta functions .. 3
3.2 Integration routines .............. 3
4 ChPT notation .................... 3
5 Data structures ................... 3
5.1 physmass: Masses, F
π
, μ ........... 4
5.2 Classes for the NLO LECS: Li ........ 4
a
e-mail: bijnens@thep.lu.se
5.3 Classes for the NNLO LECS: Ci ....... 4
6 Loop integrals .................... 5
6.1 One-loop integrals ............... 5
6.1.1 Tadpoles ................ 5
6.1.2 Bubble integrals ............ 5
6.2 Sunset integrals ................ 6
6.3 One-loop finite volume integrals ....... 6
6.3.1 Tadpoles ................ 6
6.3.2 Bubble integrals ............ 6
6.4 Sunset finite volume integrals ......... 6
7 Masses, decay constants and vacuum-expectation-
values ........................ 7
7.1 Masses ..................... 7
7.2 Decay constants ................ 8
7.3 getfpimeta ................. 8
7.4 Vacuum-expectation-values .......... 8
8 Masses and decay constants at finite volume .... 9
8.1 Masses at finite volume ............ 9
8.2 Decay constants at finite volume ....... 9
9 Various comments .................. 9
9.1 Error handling ................. 9
9.2 Warnings ................... 9
9.3 Possible extensions .............. 10
10 Conclusions ..................... 10
References ........................ 10
1 Introduction
Chiral perturbation theory (ChPT) is the low-energy effec-
tive field theory of QCD. It was introduced by Weinberg,
Gasser and Leutwyler [1–3] and the present state of the art
are calculations performed at two-loop level. A review is [4]
but many more exists. The long term goal of this project is to
make available all these calculations with a consistent inter-
face in C++. Many of the original programs were written in
FORTRAN77 and are available on request from the authors,
but they are not always consistent in the interfaces and the
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