CHIRON: a package for ChPT numerical results at two loops

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.

arXiv comment19 pages

References in corpus (9)

• The Mesonic Chiral Lagrangian of Order $p^6$
• Mesonic low-energy constants
• Pion and Kaon Electromagnetic Form Factors
• Two-point Functions at Two Loops in Three Flavour Chiral Perturbation Theory
• A new global fit of the $L_i^r$ at next-to-next-to-leading order in Chiral Perturbation Theory
• Two-loop Analysis of Axialvector Current Propagators in Chiral Perturbation Theory
• Finite Volume at Two-loops in Chiral Perturbation Theory
• Two-loop Sunset Integrals at Finite Volume
• Finite Volume Dependence of the Quark-Antiquark Vacuum Expectation Value

Cited by in corpus (11)

• $F_K/F_{\pi }$ from Möbius domain-wall fermions solved on gradient-flowed HISQ ensembles
• Vector two-point functions in finite volume using partially quenched chiral perturbation theory
• The isospin-3 three-particle $K$-matrix at NLO in ChPT
• Analytic representation of $F_K/F_{\pi }$ in two loop chiral perturbation theory
• Meson-baryon effective chiral Lagrangians at order $p^4$
• An Analytic Analysis of the Pion Decay Constant in Three-Flavoured Chiral Perturbation Theory
• Analytic representations of $m_K$, $F_K$, $m_{\eta }$ and $F_{\eta }$ in two loop $SU(3)$ chiral perturbation theory
• An Analytic Approach to Sunset Diagrams in Chiral Perturbation Theory: Theory and Practice
• Finite Volume for Three-Flavour Partially Quenched Chiral Perturbation Theory through NNLO in the Meson Sector
• A unified formulation of one-loop tensor integrals for finite volume effects
• Three-pion scattering: From the chiral Lagrangian to the lattice