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 programs for the needed one- and two-loop integrals as well as routines to deal with the ChPT parameters. The present version includes everything needed for the masses, decay constants 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 routine library jbnumlib contains the numerical routines used in chiron. Many are to a large extent simple C++ versions 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.

Highlights

  • The jbnumlib routines have their output compared with the original CERNLIB routines in case they were simple translations to C++

  • This paper describes a library of useful numerical programs in C++ for chiral perturbation theory (ChPT) at upto two-loop order

  • In particular a number of numerical routines has been reimplemented in the numerical algorithm part of the library, libjbnumlib.a

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Summary

27 Page 2 of 10

The chiron routines have mainly been tested against the FORTRAN codes of the original publications. These were in turn implemented in at least two independent versions originally. 2. The numerical routines included in jbnumlib are described in Sect. 8. Some comments about errors, some warnings about the use of the routines and definitions in ChPT as well as a number of planned/possible extensions are discussed in Sect. The functions are included to make the program collection self-contained They are mainly implementations of well known programs in C++ and in particular many of the routines are a port to C++ from the CERNLIB [9] FORTRAN routines. The exact interface is best checked by looking in the include file jbnumlib.h

Files and setup
Bessel functions
Theta functions
Integration routines
ChPT notation
Data structures
27 Page 4 of 10
Classes for the NLO LECS
Classes for the NNLO LECS
Loop integrals
Tadpoles
Bubble integrals
Sunset integrals
One-loop finite volume integrals
Sunset finite volume integrals
H V λ0 16π 2
Masses
27 Page 8 of 10
Decay constants
Vacuum-expectation-values
Masses and decay constants at finite volume
Decay constants at finite volume
Masses at finite volume
Warnings
27 Page 10 of 10
Possible extensions
10 Conclusions
Full Text
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