BOKASUN: A fast and precise numerical program to calculate the Master Integrals of the two-loop sunrise diagrams

We present the program BOKASUN for fast and precise evaluation of the Master Integrals of the two-loop self-mass sunrise diagram for arbitrary values of the internal masses and the external four-momentum. We use a combination of two methods: a Bernoulli accelerated series expansion and a Runge-Kutta numerical solution of a system of linear differential equations.

Program summary

Program title: BOKASUNCatalogue identifier: AECG_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AECG_v1_0.htmlProgram obtainable from: CPC Program Library, Queen's University, Belfast, N. IrelandLicensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.htmlNo. of lines in distributed program, including test data, etc.: 9404No. of bytes in distributed program, including test data, etc.: 104 123Distribution format: tar.gzProgramming language: FORTRAN77Computer: Any computer with a Fortran compiler accepting FORTRAN77 standard. Tested on various PC's with LINUXOperating system: LINUXRAM: 120 kbytesClassification: 4.4Nature of problem: Any integral arising in the evaluation of the two-loop sunrise Feynman diagram can be expressed in terms of a given set of Master Integrals, which should be calculated numerically. The program provides a fast and precise evaluation method of the Master Integrals for arbitrary (but not vanishing) masses and arbitrary value of the external momentum.Solution method: The integrals depend on three internal masses and the external momentum squared p². The method is a combination of an accelerated expansion in 1/p² in its (pretty large!) region of fast convergence and of a Runge-Kutta numerical solution of a system of linear differential equations.Running time: To obtain 4 Master Integrals on PC with 2 GHz processor it takes 3 μs for series expansion with pre-calculated coefficients, 80 μs for series expansion without pre-calculated coefficients, from a few seconds up to a few minutes for Runge-Kutta method (depending on the required accuracy and the values of the physical parameters).     

TSIL: a program for the calculation of two-loop self-energy integrals

TSIL is a library of utilities for the numerical calculation of dimensionally regularized two-loop self-energy integrals. A convenient basis for these functions is given by the integrals obtained at the end of O.V. Tarasov's recurrence relation algorithm. The program computes the values of all of these basis functions, for arbitrary input masses and external momentum. When analytical expressions in terms of polylogarithms are available, they are used. Otherwise, the evaluation proceeds by a Runge-Kutta integration of the coupled first-order differential equations for the basis integrals, using the external momentum invariant as the independent variable. The starting point of the integration is provided by known analytic expressions at (or near) zero external momentum. The code is written in C, and may be linked from C/C++ or Fortran. A Fortran interface is provided. We describe the structure and usage of the program, and provide a simple example application. We also compute two new cases analytically, and compare all of our notations and conventions for the two-loop self-energy integrals to those used by several other groups.

Program summary

Title of program:TSILVersion number: 1.0Catalogue identifier: ADWSProgram summary URL:http://cpc.cs.qub.ac.uk/summaries/ADWSProgram obtainable from: CPC Program Library, Queen's University of Belfast, N. IrelandProgramming language: CPlatform: Any platform supporting the GNU Compiler Collection (gcc), the Intel C compiler (icc), or a similar C compiler with support for complex mathematicsNo. of lines in distributed program, including test data, etc.: 42 730No. of bytes in distributed program, including test data, etc.: 297 101Distribution format: tar.gzNature of physical problem: Numerical evaluation of dimensionally regulated Feynman integrals needed in two-loop self-energy calculations in relativistic quantum field theory in four dimensions.Method of solution: Analytical evaluation in terms of polylogarithms when possible, otherwise through Runge-Kutta solution of differential equations.Limitations: Loss of accuracy in some unnatural threshold cases that do not have vanishing masses.Typical running time: Less than a second.     

TaylUR, an arbitrary-order diagonal automatic differentiation package for Fortran 95

We present TaylUR, a Fortran 95 module to automatically compute the numerical values of a complex-valued function's derivatives with respect to several variables up to an arbitrary order in each variable, but excluding mixed derivatives. Arithmetic operators and Fortran intrinsics are overloaded to act correctly on objects of a defined type taylor, which encodes a function along with its first few derivatives with respect to the user-defined independent variables. Derivatives of products and composite functions are computed using Leibniz's rule and Faà di Bruno's formula. TaylUR makes heavy use of operator overloading and other Fortran 95 features such as elemental functions.

Program summary

Program title: TaylURCatalogue identifier:ADXR_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADXR_v1_0Program obtainable from: CPC Program Library, Queen's University of Belfast, N. IrelandLicensing provisions:noneProgramming language:Fortran 95Computer:Any computer with a conforming Fortran 95 compilerOperating system:Any system with a conforming Fortran 95 compilerNo. of lines in distributed program, including test data, etc.:6286No. of bytes in distributed program, including test data, etc:14 994Distribution format:tar.gzNature of problem:Problems that require potentially high orders of derivatives with respect to some variables, such as e.g. expansions of Feynman diagrams in particle masses in perturbative Quantum Field Theory, and which cannot be treated using existing Fortran modules for automatic differentiation [C.W. Straka, ADF95: Tool for automatic differentiation of a FORTRAN code designed for large numbers of independent variables, Comput. Phys. Comm. 168 (2005) 123-139, arXiv:cs.MS/0503014; S. Stamatiadis, R. Prosmiti, S.C. Farantos, auto_deriv: Tool for automatic differentiation of a FORTRAN code, Comput. Phys. Comm. 127 (2000) 343-355].Solution method:Arithmetic operators and Fortran intrinsics are overloaded to act correctly on objects of a defined type taylor, which encodes a function along with its first few derivatives with respect to the user-defined independent variables. Derivatives of products and composite functions are computed using Leibniz's rule and Faà di Bruno's formula.Restrictions:Memory and CPU time constraints may restrict the number of variables and Taylor expansion order that can be achieved. Loss of numerical accuracy due to cancellation may become an issue at very high orders.Unusual features:No mixed higher-order derivatives are computed. The complex conjugation operation assumes all independent variables to be real.Running time:The running time of TaylUR operations depends linearly on the number of variables. Its dependence on the Taylor expansion order varies from linear (for linear operations) through quadratic (for multiplication) to exponential (for elementary function calls).     

HypExp, a Mathematica package for expanding hypergeometric functions around integer-valued parameters

We present the Mathematica package HypExp which allows to expand hypergeometric functions around integer parameters to arbitrary order. At this, we apply two methods, the first one being based on an integral representation, the second one on the nested sums approach. The expansion works for both symbolic argument z and unit argument. We also implemented new classes of integrals that appear in the first method and that are, in part, yet unknown to Mathematica.

Program summary

Title of program:HypExpCatalogue identifier:ADXF_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADXF_v1_0Program obtainable from: CPC Program Library, Queen's University of Belfast, N. IrelandLicence:noneComputers:Computers running Mathematica under Linux or WindowsOperating system:Linux, WindowsProgram language:MathematicaNo. of bytes in distributed program, including test data, etc.:739 410No. of lines in distributed program, including test data, etc.:89 747Distribution format:tar.gzOther package needed:the package HPL, included in the distributionExternal file required:noneNature of the physical problem:Expansion of hypergeometric functions around integer-valued parameters. These are needed in the context of dimensional regularization for loop and phase space integrals.Method of solution:Algebraic manipulation of nested sums and integral representation.Restrictions on complexity of the problem:Limited by the memory availableTypical running time:Strongly depending on the problem and the availability of libraries.     

GeM software package for computation of symmetries and conservation laws of differential equations

We present a recently developed Maple-based “GeM” software package for automated symmetry and conservation law analysis of systems of partial and ordinary differential equations (DE). The package contains a collection of powerful easy-to-use routines for mathematicians and applied researchers. A standard program that employs “GeM” routines for symmetry, adjoint symmetry or conservation law analysis of any given DE system occupies several lines of Maple code, and produces output in the canonical form. Classification of symmetries and conservation laws with respect to constitutive functions and parameters present in the given DE system is implemented. The “GeM” package is being successfully used in ongoing research. Run examples include classical and new results.

Program summary

Title of program: GeMCatalogue identifier: ADYK_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADYK_v1_0Program obtainable from: CPC Program Library, Queen's University of Belfast, N. IrelandLicensing provisions: noneComputers: PC-compatible running Maple on MS Windows or Linux; SUN systems running Maple for Unix on OS SolarisOperating systems under which the program has been tested: Windows 2000, Windows XP, Linux, SolarisProgramming language used: Maple 9.5Memory required to execute with typical data: below 100 MegabytesNo. of lines in distributed program, including test data, etc.: 4939No. of bytes in distributed program, including test data, etc.: 166 906Distribution format: tar.gzNature of physical problem: Any physical model containing linear or nonlinear partial or ordinary differential equations.Method of solution: Symbolic computation of Lie, higher and approximate symmetries by Lie's algorithm. Symbolic computation of conservation laws and adjoint symmetries by using multipliers and Euler operator properties. High performance is achieved by using an efficient representation of the system under consideration and resulting symmetry/conservation law determining equations: all dependent variables and derivatives are represented as symbols rather than functions or expressions.Restrictions on the complexity of the problem: The GeM module routines are normally able to handle ODE/PDE systems of high orders (up to order seven and possibly higher), depending on the nature of the problem. Classification of symmetries/conservation laws with respect to one or more arbitrary constitutive functions of one or two arguments is normally accomplished successfully.Typical running time: 1-20 seconds for problems that do not involve classification; 5-1000 seconds for problems that involve classification, depending on complexity.     

MERADGEN 1.0: Monte Carlo generator for the simulation of radiative events in parity conserving doubly-polarized Møller scattering

The Monte Carlo generator MERADGEN 1.0 for the simulation of radiative events in parity conserving doubly-polarized Møller scattering has been developed. Analytical integration wherever it is possible provides rather fast and accurate generation. Some numerical tests and histograms are presented.

Program summary

Program title: MERADGEN 1.0Catalogue identifier:ADYM_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADYM_v1_0Program obtainable from: CPC Program Library, Queen's University of Belfast, N. IrelandLicensing provisions: noneProgramming language: FORTRAN 77Computer(s) for which the program has been designed: allOperating system(s) for which the program has been designed: LinuxRAM required to execute with typical data: 1 MBNo. of lines in distributed program, including test data, etc.:2196No. of bytes in distributed program, including test data, etc.:23 501Distribution format:tar.gzHas the code been vectorized or parallelized?: noNumber of processors used: 1Supplementary material: noneExternal routines/libraries used: noneCPC Program Library subprograms used: noneNature of problem: Simulation of radiative events in parity conserving doubly-polarized Møller scattering.Solution method: Monte Carlo method for simulation within QED, analytical integration wherever it is possible that provides rather fast and accurate generation.Restrictions: noneUnusual features: noneAdditional comments: noneRunning time: The simulation of 10⁸ radiative events for itest:=1 takes up to 45 seconds on AMD Athlon 2.80 GHz processor.     

SuSpect: A Fortran code for the Supersymmetric and Higgs particle spectrum in the MSSM

We present the Fortran code SuSpect version 2.3, which calculates the Supersymmetric and Higgs particle spectrum in the Minimal Supersymmetric Standard Model (MSSM). The calculation can be performed in constrained models with universal boundary conditions at high scales such as the gravity (mSUGRA), anomaly (AMSB) or gauge (GMSB) mediated supersymmetry breaking models, but also in the non-universal MSSM case with R-parity and CP conservation. Care has been taken to treat important features such as the renormalization group evolution of parameters between low and high energy scales, the consistent implementation of radiative electroweak symmetry breaking and the calculation of the physical masses of the Higgs bosons and supersymmetric particles taking into account the dominant radiative corrections. Some checks of important theoretical and experimental features, such as the absence of non-desired minima, large fine-tuning in the electroweak symmetry breaking condition, as well as agreement with precision measurements can be performed. The program is simple to use, self-contained and can easily be linked to other codes; it is rather fast and flexible, thus allowing scans of the parameter space with several possible options and choices for model assumptions and approximations.

Program summary

Title of program:SuSpectCatalogue identifier:ADYR_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADYR_v1_0Program obtainable from: CPC Program Library, Queen's University of Belfast, N. IrelandLicensing provisions:noneProgramming language used:FORTRAN 77Computer:Unix machines, PCNo. of lines in distributed program, including test data, etc.:21 821No. of bytes in distributed program, including test data, etc.:249 657Distribution format:tar.gzOperating system:Unix (or Linux)RAM:approximately 2500 KbytesNumber of processors used:1 processorNature of problem:SuSpect calculates the supersymmetric and Higgs particle spectrum (masses and some other relevant parameters) in the unconstrained Minimal Supersymmetric Standard Model (MSSM), as well as in constrained models (cMSSMs) such as the minimal Supergravity (mSUGRA), the gauge mediated (GMSB) and anomaly mediated (AMSB) Supersymmetry breaking scenarii. The following features and ingredients are included: renormalization group evolution between low and high energy scales, consistent implementation of radiative electroweak symmetry breaking, calculation of the physical particle masses with radiative corrections at the one- and two-loop level.Solution method:The main methods used in the code are: (1) an (adaptative fourth-order) Runge-Kutta type algorithm (following a standard algorithm described in “Numerical Recipes”), used to solve numerically a set of coupled differential equations resulting from the renormalization group equations at the two-loop level of the perturbative expansions; (2) diagonalizations of mass matrices; (3) some mathematical (Spence, etc) functions resulting from the evaluation of one and two-loop integrals using the Feynman graphs techniques for radiative corrections to the particle masses; (4) finally, some fixed-point iterative algorithms to solve non-linear equations for some of the relevant output parameters.Restrictions:(1) The code is limited at the moment to real input parameters. (2) It also does not include flavor non-diagonal terms which are possible in the most general soft supersymmetry breaking Lagrangian. (3) There are some (mild) limitations on the possible range of values of input parameter, i.e. not any arbitrary values of some input parameters are allowed: these limitations are essentially based on physical rather than algorithmic issues, and warning flags and other protections are installed to avoid as much as possible execution failure if unappropriate input values are used.Running time:between 1 and 3 seconds depending on options, with a 1 GHz processor.     

HypExp 2, Expanding hypergeometric functions about half-integer parameters

In this article, we describe a new algorithm for the expansion of hypergeometric functions about half-integer parameters. The implementation of this algorithm for certain classes of hypergeometric functions in the already existing Mathematica package HypExp is described. Examples of applications in Feynman diagrams with up to four loops are given.

New version program summary

Program title:HypExp 2Catalogue identifier:ADXF_v2_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADXF_v2_0.htmlProgram obtainable from:CPC Program Library, Queen's University, Belfast, N. IrelandLicensing provisions:Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.htmlNo. of lines in distributed program, including test data, etc.:106 401No. of bytes in distributed program, including test data, etc.:2 668 729Distribution format:tar.gzProgramming language:MathematicaComputer:Computers running MathematicaOperating system:Linux, Windows, MacRAM:Depending on the complexity of the problemSupplementary material:Library files which contain the expansion of certain hypergeometric functions around their parameters are availableClassification:4.7, 5Does the new version supersede the previous version?:YesNature of problem:Expansion of hypergeometric functions about parameters that are integer and/or half-integer valued.Solution method:New algorithm implemented in Mathematica.Reasons for new version:Expansion about half-integer parameters.Summary of revisions:Ability to expand about half-integer valued parameters added.Restrictions:The classes of hypergeometric functions with half-integer parameters that can be expanded are listed below.Additional comments:The package uses the package HPL included in the distribution.Running time:Depending on the expansion.     

CPsuperH2.0: An improved computational tool for Higgs phenomenology in the MSSM with explicit CP violation

We describe the Fortran code CPsuperH2.0, which contains several improvements and extensions of its predecessor CPsuperH. It implements improved calculations of the Higgs-boson pole masses, notably a full treatment of the 4×4 neutral Higgs propagator matrix including the Goldstone boson and a more complete treatment of threshold effects in self-energies and Yukawa couplings, improved treatments of two-body Higgs decays, some important three-body decays, and two-loop Higgs-mediated contributions to electric dipole moments. CPsuperH2.0 also implements an integrated treatment of several B-meson observables, including the branching ratios of Bs→μ⁺μ⁻, Bd→τ⁺τ⁻, Bu→τν, B→Xsγ and the latter's CP-violating asymmetry ACP, and the supersymmetric contributions to the mass differences. These additions make CPsuperH2.0 an attractive integrated tool for analyzing supersymmetric CP and flavour physics as well as searches for new physics at high-energy colliders such as the Tevatron, LHC and linear colliders.¹

Program summary

Program title: CPsuperH2.0Catalogue identifier: ADSR_v2_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADSR_v2_0.htmlProgram obtainable from: CPC Program Library, Queen's University, Belfast, N. IrelandLicensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.htmlNo. of lines in distributed program, including test data, etc.: 13 290No. of bytes in distributed program, including test data, etc.: 89 540Distribution format: tar.gzProgramming language: Fortran 77Computer: PC running under Linux and computers in Unix environmentOperating system: LinuxRAM: 32 MbytesClassification: 11.1Catalogue identifier of the previous version: ADSR_v1_0Journal reference of the previous version: CPC 156 (2004) 283Does the new version supersede the previous version?: YesNature of problem: The calculations of mass spectrum, decay widths and branching ratios of the neutral and charged Higgs bosons in the Minimal Supersymmetric Standard Model with explicit CP violation have been improved. The program is based on recent renormalization-group-improved diagrammatic calculations that include dominant higher-order logarithmic and threshold corrections, b-quark Yukawa-coupling resummation effects and improved treatment of Higgs-boson pole-mass shifts. The couplings of the Higgs bosons to the Standard Model gauge bosons and fermions, to their supersymmetric partners and all the trilinear and quartic Higgs-boson self-couplings are also calculated. The new implementations include a full treatment of the 4×4(2×2) neutral (charged) Higgs propagator matrix together with the center-of-mass dependent Higgs-boson couplings to gluons and photons, two-loop Higgs-mediated contributions to electric dipole moments, and an integrated treatment of several B-meson observables.Solution method: One-dimensional numerical integration for several Higgs-decay modes, iterative treatment of the threshold corrections and Higgs-boson pole masses, and the numerical diagonalization of the neutralino mass matrix.Reasons for new version: Mainly to provide a coherent numerical framework which calculates consistently observables for both low- and high-energy experiments.Summary of revisions: Improved treatment of Higgs-boson masses and propagators. Improved treatment of Higgs-boson couplings and decays. Higgs-mediated two-loop electric dipole moments. B-meson observables.Running time: Less than 0.1 seconds.     

f1: a code to compute Appell's F1 hypergeometric function

In this work we present the FORTRAN code to compute the hypergeometric function F₁(α,β₁,β₂,γ,x,y) of Appell. The program can compute the F₁ function for real values of the variables {x,y}, and complex values of the parameters {α,β₁,β₂,γ}. The code uses different strategies to calculate the function according to the ideas outlined in [F.D. Colavecchia et al., Comput. Phys. Comm. 138 (1) (2001) 29].

Program summary

Title of the program: f1Catalogue identifier: ADSJProgram summary URL:http://cpc.cs.qub.ac.uk/summaries/ADSJProgram obtainable from: CPC Program Library, Queen's University of Belfast, N. IrelandLicensing provisions: noneComputers: PC compatibles, SGI Origin2∗Operating system under which the program has been tested: Linux, IRIXProgramming language used: Fortran 90Memory required to execute with typical data: 4 kbytesNo. of bits in a word: 32No. of bytes in distributed program, including test data, etc.: 52 325Distribution format: tar gzip fileExternal subprograms used: Numerical Recipes hypgeo [W.H. Press et al., Numerical Recipes in Fortran 77, Cambridge Univ. Press, 1996] or chyp routine of R.C. Forrey [J. Comput. Phys. 137 (1997) 79], rkf45 [L.F. Shampine and H.H. Watts, Rep. SAND76-0585, 1976].Keywords: Numerical methods, special functions, hypergeometric functions, Appell functions, Gauss functionNature of the physical problem: Computing the Appell F₁ function is relevant in atomic collisions and elementary particle physics. It is usually the result of multidimensional integrals involving Coulomb continuum states.Method of solution: The F₁ function has a convergent-series definition for |x|<1 and |y|<1, and several analytic continuations for other regions of the variable space. The code tests the values of the variables and selects one of the precedent cases. In the convergence region the program uses the series definition near the origin of coordinates, and a numerical integration of the third-order differential parametric equation for the F₁ function. Also detects several special cases according to the values of the parameters.Restrictions on the complexity of the problem: The code is restricted to real values of the variables {x,y}. Also, there are some parameter domains that are not covered. These usually imply differences between integer parameters that lead to negative integer arguments of Gamma functions.Typical running time: Depends basically on the variables. The computation of Table 4 of [F.D. Colavecchia et al., Comput. Phys. Comm. 138 (1) (2001) 29] (64 functions) requires approximately 0.33 s in a Athlon 900 MHz processor.     

HPL, a Mathematica implementation of the harmonic polylogarithms

In this paper, we present an implementation of the harmonic polylogarithm of Remiddi and Vermaseren [E. Remiddi, J.A.M. Vermaseren, Int. J. Modern Phys. A 15 (2000) 725, hep-ph/9905237] for Mathematica. It contains an implementation of the product algebra, the derivative properties, series expansion and numerical evaluation. The analytic continuation has been treated carefully, allowing the user to keep the control over the definition of the sign of the imaginary parts. Many options enables the user to adapt the behavior of the package to his specific problem.

Program summary

Program title: HPLCatalogue identifier:ADWXProgram summary URL:http://cpc.cs.qub.ac.uk/summaries/ADWXProgram obtained from: CPC Program Library, Queen's University of Belfast, N. IrelandLicensing provisions:noneProgramming language: MathematicaNo. of lines in distributed program, including test data, etc.:13 310No. of bytes in distributed program, including test data, etc.: 1 990 584Distribution format: tar.gzComputer:all computers running MathematicaOperating systems:operating systems running MathematicaNature of problem: Computer algebraic treatment of the harmonic polylogarithms which appear in the evaluation of Feynman diagramsSolution method: Mathematica implementation     

USFKAD: An expert system for partial differential equations

The computation of the solution, by the separation of variables process, of the Poisson, diffusion, and wave equations in rectangular, cylindrical, or spherical coordinate systems, with Dirichlet, Neumann, or Robin boundary conditions, can be carried out in the time, Laplace, or frequency domains by a decision-tree process, using a library of eigenfunctions. We describe an expert system, USFKAD, that has been constructed for this purpose.

Program summary

Title of program:USFKADCatalogue identifier:ADYN_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADYN_v1_0Program obtainable from: CPC Program Library, Queen's University of Belfast, N. IrelandLicensing provisions:noneOperating systems under which the program has been tested: Windows, UNIXProgramming language used:C++, LaTeXNo. of lines in distributed program, including test data, etc.: 11 699No. of bytes in distributed program, including test data, etc.: 537 744Memory required to execute with typical data: 1.3 MegabytesDistribution format: tar.gzNature of mathematical problem: Analytic solution of Poisson, diffusion, and wave equationsMethod of solution: Eigenfunction expansionsRestrictions concerning the complexity of the problem: A few rarely-occurring singular boundary conditions are unavailable, but they can be approximated by regular boundary value problems to arbitrary accuracy.Typical running time:1 secondUnusual features of the program: Solutions are obtained for Poisson, diffusion, or wave PDEs; homogeneous or nonhomogeneous equations and/or boundary conditions; rectangular, cylindrical, or spherical coordinates; time, Laplace, or frequency domains; Dirichlet, Neumann, Robin, singular, periodic, or incoming/outgoing boundary conditions. Output is suitable for pasting into LaTeX documents.     

-XSummer- Transcendental functions and symbolic summation in Form

Harmonic sums and their generalizations are extremely useful in the evaluation of higher-order perturbative corrections in quantum field theory. Of particular interest have been the so-called nested sums, where the harmonic sums and their generalizations appear as building blocks, originating for example, from the expansion of generalized hypergeometric functions around integer values of the parameters. In this paper we discuss the implementation of several algorithms to solve these sums by algebraic means, using the computer algebra system Form.

Program summary

Title of program:XSummerCatalogue identifier:ADXQ_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADXQ_v1_0Program obtainable from:CPC Program Library, Queen's University of Belfast, N. IrelandLicense:GNU Public License and Form LicenseComputers:allOperating system:allProgram language:FormMemory required to execute:Depending on the complexity of the problem, recommended at least 64 MB RAMNo. of lines in distributed program, including test data, etc.:9854No. of bytes in distributed program, including test data, etc.:126 551Distribution format:tar.gzOther programs called:noneExternal files needed:noneNature of the physical problem:Systematic expansion of higher transcendental functions in a small parameter. The expansions arise in the calculation of loop integrals in perturbative quantum field theory.Method of solution:Algebraic manipulations of nested sums.Restrictions on complexity of the problem:Usually limited only by the available disk space.Typical running time:Dependent on the complexity of the problem.     

Automatic calculation of supersymmetric renormalization group equations and loop corrections

SARAH is a Mathematica package for studying supersymmetric models. It calculates for a given model the masses, tadpole equations and all vertices at tree-level. This information can be used by SARAH to write model files for CalcHep/CompHep or FeynArts/FormCalc. In addition, the second version of SARAH can derive the renormalization group equations for the gauge couplings, parameters of the superpotential and soft-breaking parameters at one- and two-loop level. Furthermore, it calculates the one-loop self-energies and the one-loop corrections to the tadpoles. SARAH can handle all N=1 SUSY models whose gauge sector is a direct product of SU(N) and U(1) gauge groups. The particle content of the model can be an arbitrary number of chiral superfields transforming as any irreducible representation with respect to the gauge groups. To implement a new model, the user has just to define the gauge sector, the particle, the superpotential and the field rotations to mass eigenstates.

Program summary

Program title: SARAHCatalogue identifier: AEIB_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEIB_v1_0.htmlProgram obtainable from: CPC Program Library, Queen's University, Belfast, N. IrelandLicensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.htmlNo. of lines in distributed program, including test data, etc.: 97 577No. of bytes in distributed program, including test data, etc.: 2 009 769Distribution format: tar.gzProgramming language: MathematicaComputer: All systems that Mathematica is available forOperating system: All systems that Mathematica is available forClassification: 11.1, 11.6Nature of problem: A supersymmetric model is usually characterized by the particle content, the gauge sector and the superpotential. It is a time consuming process to obtain all necessary information for phenomenological studies from these basic ingredients.Solution method: SARAH calculates the complete Lagrangian for a given model whose gauge sector can be any direct product of SU(N) gauge groups. The chiral superfields can transform as any, irreducible representation with respect to these gauge groups and it is possible to handle an arbitrary number of symmetry breakings or particle rotations. Also the gauge fixing terms can be specified. Using this information, SARAH derives the mass matrices and Feynman rules at tree-level and generates model files for CalcHep/CompHep and FeynArts/FormCalc. In addition, it can calculate the renormalization group equations at one- and two-loop level and the one-loop corrections to the one- and two-point functions.Unusual features: SARAH just needs the superpotential and gauge sector as input and not the complete Lagrangian. Therefore, the complete implementation of new models is done in some minutes.Running time: Measured CPU time for the evaluation of the MSSM on an Intel Q8200 with 2.33 GHz. Calculating the complete Lagrangian: 12 seconds. Calculating all vertices: 75 seconds. Calculating the one- and two-loop RGEs: 50 seconds. Calculating the one-loop corrections: 7 seconds. Writing a FeynArts file: 1 second. Writing a CalcHep/CompHep file: 6 seconds. Writing the LaTeX output: 1 second.     

2HDMC - two-Higgs-doublet model calculator

We describe the public C++ code 2HDMC which can be used to perform calculations in a general, CP-conserving, two-Higgs-doublet model (2HDM). The program features simple conversion between different parametrizations of the 2HDM potential, a flexible Yukawa sector specification with choices of different Z₂-symmetries or more general couplings, a decay library including all two-body - and some three-body - decay modes for the Higgs bosons, and the possibility to calculate observables of interest for constraining the 2HDM parameter space, as well as theoretical constraints from positivity and unitarity. The latest version of the 2HDMC code and full documentation is available from: http://www.isv.uu.se/thep/MC/2HDMC.

Program summary

Program title:2HDMCCatalogue identifier: AEFI_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEFI_v1_0.htmlProgram obtainable from: CPC Program Library, Queen's University, Belfast, N. IrelandLicensing provisions: GNU GPLNo. of lines in distributed program, including test data, etc.: 12 032No. of bytes in distributed program, including test data, etc.: 90 699Distribution format: tar.gzProgramming language: C++Computer: Any computer running LinuxOperating system: LinuxRAM: 5 MbClassification: 11.1External routines: GNU Scientific Library (http://www.gnu.org/software/gsl/)Nature of problem: Determining properties of the potential, calculation of mass spectrum, couplings, decay widths, oblique parameters, muon g−2, and collider constraints in a general two-Higgs-doublet model.Solution method: From arbitrary potential and Yukawa sector, tree-level relations are used to determine Higgs masses and couplings. Decay widths are calculated at leading order, including FCNC decays when applicable. Decays to off-shell vector bosons are obtained by numerical integration. Observables are computed (analytically or numerically) as function of the input parameters.Restrictions: CP-violation is not treated.Running time: Less than 0.1 s on a standard PC     

GYutsis: heuristic based calculation of general recoupling coefficients

General angular momentum recoupling coefficients can be expressed as a summation formula over products of 6-j coefficients. Yutsis, Levinson and Vanagas developed graphical techniques for representing the general recoupling coefficient as a cubic graph and they describe a set of reduction rules allowing a stepwise generation of the corresponding summation formula. This paper is a follow up to [Van Dyck and Fack, Comput. Phys. Comm. 151 (2003) 353-368] where we described a heuristic algorithm based on these techniques. In this article we separate the heuristic from the algorithm and describe some new heuristic approaches which can be plugged into the generic algorithm. We show that these new heuristics lead to good results: in many cases we get a more efficient summation formula than our previous approach, in particular for problems of higher order. In addition the new features and the use of our program GYutsis, which implements these techniques, is described both for end users and application programmers.

Program summary

Title of program: CycleCostAlgorithm, GYutsisCatalogue number: ADSAProgram Summary URL:http://cpc.cs.qub.ac.uk/summaries/ADSAProgram obtainable from: CPC Program Library, Queen's University of Belfast, N. Ireland. Users may obtain the program also by downloading either the compressed tar file gyutsis.tgz (for Unix and Linux) or the zip file gyutsis.zip (for Windows) from our website (http://caagt.rug.ac.be/yutsis/). An applet version of the program is also available on our website and can be run in a web browser from the URL http://caagt.rug.ac.be/yutsis/GYutsisApplet.html.Licensing provisions: noneComputers for which the program is designed: any computer with Sun's Java Runtime Environment 1.4 or higher installed.Programming language used: Java 1.2 (Compiler: Sun's SDK 1.4.0)No. of lines in program: approximately 9400No. of bytes in distributed program, including test data, etc.: 544 117Distribution format: tar gzip fileNature of physical problem: A general recoupling coefficient for an arbitrary number of (integer or half-integer) angular momenta can be expressed as a formula consisting of products of 6-j coefficients summed over a certain number of variables. Such a formula can be generated using the program GYutsis (with a graphical user front end) or CycleCostAlgorithm (with a text-mode user front end).Method of solution: Using the graphical techniques of Yutsis, Levinson and Vanagas (1962) a summation formula for a general recoupling coefficient is obtained by representing the coefficient as a Yutsis graph and by performing a selection of reduction rules valid for such graphs. Each reduction rule contributes to the final summation formula by a numerical factor or by an additional summation variable. Whereas an optimal summation formula (i.e. with a minimum number of summation variables) is hard to obtain, we present here some new heuristic approaches for selecting an edge from a k-cycle in order to transform it into an (k−1)-cycle (k>3) in such a way that a ‘good’ summation formula is obtained.Typical running time: From instantaneously for the typical problems to 30 s for the heaviest problems on a Pentium II-350 Linux-system with 256 MB RAM.     

PLNoise: a package for exact numerical simulation of power-law noises

Many simulations of stochastic processes require colored noises: here I describe a small program library that generates samples with a tunable power-law spectral density: the algorithm can be modified to generate more general colored noises, and is exact for all time steps, even when they are unevenly spaced (as may often happen in the case of astronomical data, see e.g. [N.R. Lomb, Astrophys. Space Sci. 39 (1976) 447]. The method is exact in the sense that it reproduces a process that is theoretically guaranteed to produce a range-limited power-law spectrum 1/f1+β with −1<β?1. The algorithm has a well-behaved computational complexity, it produces a nearly perfect Gaussian noise, and its computational efficiency depends on the required degree of noise Gaussianity.

Program summary

Title of program: PLNoiseCatalogue identifier:ADXV_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADXV_v1_0.htmlProgram obtainable from: CPC Program Library, Queen's University of Belfast, N. IrelandLicensing provisions: noneProgramming language used: ANSI CComputer: Any computer with an ANSI C compiler: the package has been tested with gcc version 3.2.3 on Red Hat Linux 3.2.3-52 and gcc version 4.0.0 and 4.0.1 on Apple Mac OS X-10.4Operating system: All operating systems capable of running an ANSI C compilerNo. of lines in distributed program, including test data, etc.:6238No. of bytes in distributed program, including test data, etc.:52 387Distribution format:tar.gzRAM: The code of the test program is very compact (about 50 Kbytes), but the program works with list management and allocates memory dynamically; in a typical run (like the one discussed in Section 4 in the long write-up) with average list length 2⋅¹⁰⁴, the RAM taken by the list is 200 Kbytes.External routines: The package needs external routines to generate uniform and exponential deviates. The implementation described here uses the random number generation library ranlib freely available from Netlib [B.W. Brown, J. Lovato, K. Russell, ranlib, available from Netlib, http://www.netlib.org/random/index.html, select the C version ranlib.c], but it has also been successfully tested with the random number routines in Numerical Recipes [W.H. Press, S.A. Teulkolsky, W.T. Vetterling, B.P. Flannery, Numerical Recipes in C: The Art of Scientific Computing, second ed., Cambridge Univ. Press, Cambridge, 1992, pp. 274-290]. Notice that ranlib requires a pair of routines from the linear algebra package LINPACK, and that the distribution of ranlib includes the C source of these routines, in case LINPACK is not installed on the target machine.Nature of problem: Exact generation of different types of Gaussian colored noise.Solution method: Random superposition of relaxation processes [E. Milotti, Phys. Rev. E 72 (2005) 056701].Unusual features: The algorithm is theoretically guaranteed to be exact, and unlike all other existing generators it can generate samples with uneven spacing.Additional comments: The program requires an initialization step; for some parameter sets this may become rather heavy.Running time: Running time varies widely with different input parameters, however in a test run like the one in Section 4 in this work, the generation routine took on average about 7 ms for each sample.     

The tauola-photos-F environment for the TAUOLA and PHOTOS packages, release II

We present the system for maintaining the versions of two packages: the TAUOLA of τ-lepton decay and PHOTOS for radiative corrections in decays. The following features can be chosen in an automatic or semi-automatic way: (1) format of the common block HEPEVT; (2) version of the physics input (for TAUOLA): as published, as initialized by the CLEO collaboration, as initialized by the ALEPH collaboration (it is suggested to use this version only with the help of the collaboration advice), new optional parametrization of matrix elements in 4π decay channels; (3) type of application: stand-alone, universal interface based on the information stored in the HEPEVT common block including longitudinal spin effects in the elementary Z/γ^∗→τ⁺τ⁻ process, extended version of the standard universal interface including full spin effects in the H/A→τ⁺τ⁻ decay, interface for KKMC Monte Carlo, (4) random number generators; (5) compiler options. The last section of the paper contains documentation of the programs updates introduced over the last two years.

Program summary

Title of program:tauola-photos-F, release IICatalogue identifier:ADXO_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADXO_v1_0Programs obtainable from: CPC Program Library, Queen's University of Belfast, N. IrelandComputer: PC running GNU/Linux operating systemProgramming languages and tools used:CPP: standard C-language preprocessor, GNU Make builder tool, also FORTRAN compilerNo. of lines in distributed program, including test data, etc.: 194 118No. of bytes in distributed program, including test data, etc.:2 481 234Distribution format: tar.gzCatalogue identifier:ADXO_v2_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADXO_v2_0No. of lines in distributed program, including test data, etc.:308 235No. of bytes in distributed program, including test data, etc.:2 988 363Distribution format:tar.gzDoes the new version supersede the previous version:YesNature of the physical problem: The code of Monte Carlo generators often has to be tuned to the needs of large HEP Collaborations and experiments. Usually, these modifications do not introduce important changes in the algorithm, but rather modify the initialization and form of the hadronic current in τ decays. The format of the event record (HEPEVT common block) used to exchange information between building blocks of Monte Carlo systems often needs modification. Thus, there is a need to maintain various, slightly modified versions of the same code. The package presented here allows the production of ready-to-compile versions of TAUOLA [S. Jadach, Z. Wa?s, R. Decker, J.H. Kühn, Comput. Phys. Comm. 76 (1993) 361; A.E. Bondar, et al., Comput. Phys. Comm. 146 (2002) 139] and PHOTOS [E. Barberio, Z. Wa?s, Comput. Phys. Comm. 79 (1994) 291] Monte Carlo generators with appropriate demonstration programs. The new algorithm, universal interface of TAUOLA to work with the HEPEVT common block, is also documented here. Finally, minor technical improvements of TAUOLA and PHOTOS are also listed.Method of solution: The standard UNIX tool: the C-language preprocessor is used to produce a ready-to-distribute version of TAUOLA and PHOTOS code. The final FORTRAN code is produced from the library of ‘pre-code’ that is included in the package.Reasons for new version: The functionality of the version of TAUOLA and PHOTOS changed over the last two years. The changes, and their reasons, are documented in Section 9, and our new papers cited in this section.Additional comments: The updated version includes new features described in Section 9 of the paper. PHOTOS and TAUOLA were first submitted to the library as separate programs. Summary details of these previous programs are obtainable from the CPC Program Library.Typical running time: Depends on the speed of the computer used and the demonstration program chosen. Typically a few seconds.