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     

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.     

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.     

HypExp 2, expanding hypergeometric functions about half-integer parameters

HypExp is a Mathematica package for expanding hypergeometric functions about integer and half-integer parameters.New version program summaryProgram title: HypExp 2Catalogue identifier: ADXF_v2_1Program summary URL: http://cpc.cs.qub.ac.uk/summaries/ADXF_v2_1.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.: 107 274No. of bytes in distributed program, including test data, etc.: 2 690 337Distribution format: tar.gzProgramming language: Mathematica 7 and 8Computer: 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, 5Catalogue identifier of previous version: ADXF_v2_0Journal reference of previous version: Comput. Phys. Comm. 178 (2008) 755Does 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: Compatibility with new versions of Mathematica.Summary of revisions: Support for versions 7 and 8 of Mathematica added. No changes in the features of the package.Restrictions: The classes of hypergeometric functions with half-integer parameters that can be expanded are listed in the long write-up.Additional comments: The package uses the package HPL included in the distribution.Running time: Depending on the expansion.     

Fast computation of the Gauss hypergeometric function with all its parameters complex with application to the Pöschl-Teller-Ginocchio potential wave functions

The fast computation of the Gauss hypergeometric function with all its parameters complex is a difficult task. Although the function verifies numerous analytical properties involving power series expansions whose implementation is apparently immediate, their use is thwarted by instabilities induced by cancellations between very large terms. Furthermore, small areas of the complex plane, in the vicinity of , are inaccessible using power series linear transformations. In order to solve these problems, a generalization of R.C. Forrey's transformation theory has been developed. The latter has been successful in treating the function with real parameters. As in real case transformation theory, the large canceling terms occurring in analytical formulas are rigorously dealt with, but by way of a new method, directly applicable to the complex plane. Taylor series expansions are employed to enter complex areas outside the domain of validity of power series analytical formulas. The proposed algorithm, however, becomes unstable in general when |a|, |b|, |c| are moderate or large. As a physical application, the calculation of the wave functions of the analytical Pöschl-Teller-Ginocchio potential involving evaluations is considered.

Program summary

Program title: hyp_2F1, PTG_wfCatalogue identifier: AEAE_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEAE_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.: 6839No. of bytes in distributed program, including test data, etc.: 63 334Distribution format: tar.gzProgramming language: C++, Fortran 90Computer: Intel i686Operating system: Linux, WindowsWord size: 64 bitsClassification: 4.7Nature of problem: The Gauss hypergeometric function , with all its parameters complex, is uniquely calculated in the frame of transformation theory with power series summations, thus providing a very fast algorithm. The evaluation of the wave functions of the analytical Pöschl-Teller-Ginocchio potential is treated as a physical application.Solution method: The Gauss hypergeometric function verifies linear transformation formulas allowing consideration of arguments of a small modulus which then can be handled by a power series. They, however, give rise to indeterminate or numerically unstable cases, when b−a and c−a−b are equal or close to integers. They are properly dealt with through analytical manipulations of the Lanczos expression providing the Gamma function. The remaining zones of the complex plane uncovered by transformation formulas are dealt with Taylor expansions of the function around complex points where linear transformations can be employed. The Pöschl-Teller-Ginocchio potential wave functions are calculated directly with evaluations.Restrictions: The algorithm provides full numerical precision in almost all cases for |a|, |b|, and |c| of the order of one or smaller, but starts to be less precise or unstable when they increase, especially through a, b, and c imaginary parts. While it is possible to run the code for moderate or large |a|, |b|, and |c| and obtain satisfactory results for some specified values, the code is very likely to be unstable in this regime.Unusual features: Two different codes, one for the hypergeometric function and one for the Pöschl-Teller-Ginocchio potential wave functions, are provided in C++ and Fortran 90 versions.Running time: 20,000 function evaluations take an average of one second.     

fgh, a code for the calculation of Coulomb radial wave functions from series expansions

The code fgh is an up-dated version of a code coulfg (see [Seaton, Comput. Phys. Comm. 25 (1982) 87]), used for the calculation of the Coulomb functions f and g, analytic in the energy, for attractive potentials. The new code works for attractive and repulsive potentials and also gives the functions h which have simple asymptotic forms. There is an option to use either the variables (?,r) customary in atomic physics, or (for positive energies) (η,ρ) customary in nuclear physics. When (η,ρ) are used, the code also gives the functions F_?(η,ρ) and G_?(η,ρ).Use of series solutions can lead to loss of accuracy due to cancellation effects. fgh provides an indication of the number of significant figures lost due to cancellations.     

Algebraic decomposition of discrete functions

Consideration was given to the functional decomposition of the discrete systems which is reducible to the functional decomposition of the discrete functions, where by the decomposition is meant the representation of a function by a formula in the basis of unary and binary operations. The algebraic decomposition in an algebra consisting of two binary operations and functions of two variables was studied. A procedure of formula design on the basis of composition of repetition-free subformulas was substantiated. Both exact and asymptotic complexity estimates of the designed formulas were given.     

Successive derivatives of Whittaker functions with respect to the first parameter

Algorithms are given for the computation of the nth derivatives of the Whittaker functions M_κ,μ(z) and W_κ,μ(z) with respect to the parameter κ. The algorithms are based on a convergent expansion, due to Buchholz, of M_κ,μ(z) in series of Bessel functions. Properties of the Buchholz polynomials and algorithms for evaluating the n-derivative of the reciprocal Gamma function are discussed in two appendices.     

Existence of states on quantum structures

Orthomodular lattices occurred as generalized event structures in the models of probability for quantum mechanics. Here we contribute to the question of existence of states (=probability measures) on orthomodular lattices. We prove that known techniques do not allow to find examples with less than 19 blocks (=maximal Boolean subalgebras). This bound is achieved by the example by Mayet [R. Mayet, Personal communication, 1993]. Although we do not finally exclude the existence of other techniques breaking this bound, existence of smaller examples is highly unexpected.     

Integrating products of Bessel functions with an additional exponential or rational factor

We provide two Matlab programs to compute integrals of the form

     

Object-oriented design patterns in Fortran 90/95: mazev1, mazev2 and mazev3

This paper discusses the concept, application, and usefulness of software design patterns for scientific programming in Fortran 90/95. An example from the discipline of object-oriented design patterns, that of a game based on navigation through a maze, is used to describe how some important patterns can be implemented in Fortran 90/95 and how the progressive introduction of design patterns can usefully restructure Fortran software as it evolves. This example is complemented by a discussion of how design patterns have been used in a real-life simulation of Particle-in-Cell plasma physics. The following patterns are mentioned in this paper: Factory, Strategy, Template, Abstract Factory and Facade.

Program summary

Program title: mazev1, mazev2, mazev3Catalogue identifier: AEAI_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEAI_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.: 1958No. of bytes in distributed program, including test data, etc.: 17 100Distribution format: tar.gzProgramming language: Fortran 95Computer: PC/MacOperating system: Unix/Linux/Mac (FreeBSD)/Windows (Cygwin)RAM: These are interactive programs with small (KB) memory requirementsClassification: 6.5, 20Nature of problem: A sequence of programs which demonstrate the use of object oriented design patterns for the restructuring of Fortran 90/95 software. The programs implement a simple maze game similar to that described in [1].Solution method: Restructuring uses versions of the Template, Strategy and Factory design patterns.Running time: Interactive.References:

[1] 

E. Gamma, R. Helm, R. Johnson, J. Vlissides, Design Patterns: Elements of Reusable Object Oriented Software, Addison-Wesley, 1995, ISBN 0201633612.

     

wannier90: A tool for obtaining maximally-localised Wannier functions

We present wannier90, a program for calculating maximally-localised Wannier functions (MLWF) from a set of Bloch energy bands that may or may not be attached to or mixed with other bands. The formalism works by minimising the total spread of the MLWF in real space. This is done in the space of unitary matrices that describe rotations of the Bloch bands at each k-point. As a result, wannier90 is independent of the basis set used in the underlying calculation to obtain the Bloch states. Therefore, it may be interfaced straightforwardly to any electronic structure code. The locality of MLWF can be exploited to compute band-structure, density of states and Fermi surfaces at modest computational cost. Furthermore, wannier90 is able to output MLWF for visualisation and other post-processing purposes. Wannier functions are already used in a wide variety of applications. These include analysis of chemical bonding in real space; calculation of dielectric properties via the modern theory of polarisation; and as an accurate and minimal basis set in the construction of model Hamiltonians for large-scale systems, in linear-scaling quantum Monte Carlo calculations, and for efficient computation of material properties, such as the anomalous Hall coefficient. wannier90 is freely available under the GNU General Public License from http://www.wannier.org/.

Program summary

Program title: wannier90Catalogue identifier: AEAK_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEAK_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.: 556 495No. of bytes in distributed program, including test data, etc.: 5 709 419Distribution format: tar.gzProgramming language: Fortran 90, perlComputer: any architecture with a Fortran 90 compilerOperating system: Linux, Windows, Solaris, AIX, Tru64 Unix, OSXRAM: 10 MBWord size: 32 or 64Classification: 7.3External routines:

•

BLAS (http://www/netlib.org/blas).

•

LAPACK (http://www.netlib.org/lapack).

Both available under open-source licenses.Nature of problem: Obtaining maximally-localised Wannier functions from a set of Bloch energy bands that may or may not be entangled.Solution method: In the case of entangled bands, the optimally-connected subspace of interest is determined by minimising a functional which measures the subspace dispersion across the Brillouin zone. The maximally-localised Wannier functions within this subspace are obtained by subsequent minimisation of a functional that represents the total spread of the Wannier functions in real space. For the case of isolated energy bands only the second step of the procedure is required.Unusual features: Simple and user-friendly input system. Wannier functions and interpolated band structure output in a variety of file formats for visualisation.Running time: Test cases take 1 minute.References:

[1] 

N. Marzari, D. Vanderbilt, Maximally localized generalized Wannier functions for composite energy bands, Phys. Rev. B 56 (1997) 12847.

[2] 

I. Souza, N. Marzari, D. Vanderbilt, Maximally localized Wannier functions for entangled energy bands, Phys. Rev. B 65 (2001) 035109.

     

Coulomb functions for attractive and repulsive potentials and for positive and negative energies

The paper gives a review of the mathematical properties of the Coulomb radial wave functions, for attractive and repulsive potentials and for positive and negative energies, together with recommendations on best methods for their computation. It includes discussions of analytic continuations (complex energies, radial co-ordinates and angular momenta) and of relativistic Coulomb functions.     

GMIC++: Grouping method in C++: an efficient method to solve large number of Master equations

In typical nucleation, growth and coarsening problems in the study of defect/adatom accumulation in crystalline solids or surfaces, a large number of Master equations are involved to describe the evolution process. As examples, defect clusters nucleate and grow from point defects in solids when subjected to particle irradiation, and atoms depositing on a substrate form clusters leading to film growth. To efficiently solve the large number of master equations, the grouping method was used, which we have coded into a standard C++ program, taking full advantage of the object-oriented programming style supported in the C++ language. Because of the generic nature of this code, it may be of interest to the modeling nucleation and growth processes. As an example to demonstrate the application of this computer code, the Ostwald ripening process of vacancy clustering during aging in metal nickel is calculated.     

Markovian Monte Carlo program EvolFMC v.2 for solving QCD evolution equations

We present the program EvolFMC v.2 that solves the evolution equations in QCD for the parton momentum distributions by means of the Monte Carlo technique based on the Markovian process. The program solves the DGLAP-type evolution as well as modified-DGLAP ones. In both cases the evolution can be performed in the LO or NLO approximation. The quarks are treated as massless. The overall technical precision of the code has been established at 5×¹⁰−4. This way, for the first time ever, we demonstrate that with the Monte Carlo method one can solve the evolution equations with precision comparable to the other numerical methods.

New version program summary

Program title: EvolFMC v.2Catalogue identifier: AEFN_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEFN_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 binary test data, etc.: 66 456 (7407 lines of C++ code)No. of bytes in distributed program, including test data, etc.: 412 752Distribution format: tar.gzProgramming language: C++Computer: PC, MacOperating system: Linux, Mac OS XRAM: Less than 256 MBClassification: 11.5External routines: ROOT (http://root.cern.ch/drupal/)Nature of problem: Solution of the QCD evolution equations for the parton momentum distributions of the DGLAP- and modified-DGLAP-type in the LO and NLO approximations.Solution method: Monte Carlo simulation of the Markovian process of a multiple emission of partons.Restrictions:

1.

Limited to the case of massless partons.

2.

Implemented in the LO and NLO approximations only.

3.

Weighted events only.

Unusual features: Modified-DGLAP evolutions included up to the NLO level.Additional comments: Technical precision established at 5×¹⁰−4.Running time: For the 10⁶ events at 100 GeV: DGLAP NLO: 27s; C^′-type modified DGLAP NLO: 150s (MacBook Pro with Mac OS X v.10.5.5, 2.4 GHz Intel Core 2 Duo, gcc 4.2.4, single thread).     

SuperIso v3.0, flavor physics observables calculations: extension to NMSSM

SuperIso v3.0 is a public program for evaluation of flavor physics observables in the minimal supersymmetric extension of the Standard Model (MSSM) and the next to minimal supersymmetric extension of the Standard Model (NMSSM). SuperIso v3.0 incorporates many flavor observables such as the inclusive branching ratio of B→Xsγ, the isospin asymmetry of B→K^∗γ, the branching ratio of Bs→μ⁺μ⁻, the branching ratio of B→τντ, the branching ratio of B→Dτντ, the branching ratio of K→μνμ and the branching ratios of Ds→τντ and Ds→μνμ. The calculation of the branching ratio of B→Xsγ includes NNLO Standard Model contributions. The program also computes the muon anomalous magnetic moment (g−2). Seven sample models are included in the package, namely mSUGRA, NUHM, AMSB and GMSB for the MSSM, and CNMSSM, NGMSB and NNUHM for the NMSSM. SuperIso uses a SUSY Les Houches Accord file (SLHA1 or SLHA2) as input, which can be either generated automatically by the program via a call to external spectrum calculators (SOFTSUSY, ISAJET or NMSSMTools), or provided by the user.

New version program summary

Program title:SuperIso v3.0Catalogue identifier: AEAN_v3_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEAN_v3_0.htmlProgram obtainable from: CPC Program Library, Queen's University, Belfast, N. IrelandLicensing provisions: GNU General Public LicenceNo. of lines in distributed program, including test data, etc.: 6869No. of bytes in distributed program, including test data, etc.: 42 627Distribution format: tar.gzProgramming language: C (C99 Standard compliant)Computer: 32- or 64-bit PC, MacOperating system: Linux, MacOSRAM: less than 1 MBClassification: 11.6External routines: ISASUGRA/ISAJET, SOFTSUSY and/or NMSSMToolsDoes the new version supersede the previous version?: YesNature of problem: Calculation of flavor physics observables as well as the muon anomalous magnetic moment in the Minimal Supersymmetric Standard Model with minimal flavor violation and in the Next to Minimal Supersymmetric Standard Model, in order to derive constraints on the supersymmetric parameter spaces.Solution method:SuperIso uses a SUSY Les Houches Accord (SLHA1 or SLHA2) file, which can be either generated automatically via a call to SOFTSUSY, ISAJET or NMSSMTools, or provided by the user. This file contains the masses, mixings and couplings of the supersymmetric particles. SuperIso then computes the most constraining flavor physics observables and the muon (g−2). SuperIso is able to perform the calculations in different supersymmetry breaking scenarios, such as mSUGRA, NUHM, AMSB and GMSB, as well as constrained NMSSM scenarios such as CNMSSM, NNUHM and NGMSB.Reasons for new version:SuperIso has been extended to the next to minimal supersymmetric extension of the Standard Model (NMSSM). The implemented routines are therefore extensively modified.Summary of revisions:

•

Improvement of the SLHA2 reader.

•

Replacement of “float” variables by “double”.

•

Implementation of an interface with NMSSMTools.

•

Extension of the calculation of flavor observables as well as the muon anomalous magnetic moment to NMSSM.

•

Addition of three different NMSSM scenarios: CNMSSM, NGMSB and NNUHM.

•

Three sample main programs have been added: cnmssm.c, ngmsb.c and nnuhm.c. Additional instructions to use them are given when running them without arguments.

Unusual features: The code is very flexible, and new observables can be added easily.Running time: Less than 1 sec     

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     

HiggsBounds 2.0.0: Confronting neutral and charged Higgs sector predictions with exclusion bounds from LEP and the Tevatron

HiggsBounds 2.0.0 is a computer code which tests both neutral and charged Higgs sectors of arbitrary models against the current exclusion bounds from the Higgs searches at LEP and the Tevatron. As input, it requires a selection of model predictions, such as Higgs masses, branching ratios, effective couplings and total decay widths. HiggsBounds 2.0.0 then uses the expected and observed topological cross section limits from the Higgs searches to determine whether a given parameter scenario of a model is excluded at the 95% C.L. by those searches. Version 2.0.0 represents a significant extension of the code since its first release (1.0.0). It includes now 28/53 LEP/Tevatron Higgs search analyses, compared to the 11/22 in the first release, of which many of the ones from the Tevatron are replaced by updates. As a major extension, the code allows now the predictions for (singly) charged Higgs bosons to be confronted with LEP and Tevatron searches. Furthermore, the newly included analyses contain LEP searches for neutral Higgs bosons (H) decaying invisibly or into (non-flavour tagged) hadrons as well as decay-mode independent searches for neutral Higgs bosons, LEP searches via the production modes τ⁺τ⁻H and , and Tevatron searches via . Also, all Tevatron results presented at the ICHEP?10 are included in version 2.0.0. As physics applications of HiggsBounds 2.0.0 we study the allowed Higgs mass range for model scenarios with invisible Higgs decays and we obtain exclusion results for the scalar sector of the Randall–Sundrum model using up-to-date LEP and Tevatron direct search results.

Program summary

Program title: HiggsBoundsCatalogue identifier: AEFF_v2_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEFF_v2_0.htmlProgram obtainable from: CPC Program Library, Queen?s University, Belfast, N. IrelandLicensing provisions: GNU General Public Licence version 3No. of lines in distributed program, including test data, etc.: 74 005No. of bytes in distributed program, including test data, etc.: 1 730 996Distribution format: tar.gzProgramming language: Fortran 77, Fortran 90 (two code versions are offered).Classification: 11.1.Catalogue identifier of previous version: AEFF_v1_0Journal reference of previous version: Comput. Phys. Comm. 181 (2010) 138External routines: HiggsBounds requires no external routines/libraries. Some sample programs in the distribution require the programs FeynHiggs 2.7.1 or CPsuperH2.2 to be installed.Does the new version supersede the previous version?: YesNature of problem: Determine whether a parameter point of a given model is excluded or allowed by LEP and Tevatron neutral and charged Higgs boson search results.Solution method: The most sensitive channel from LEP and Tevatron searches is determined and subsequently applied to test this parameter point. The test requires as input, model predictions for the Higgs boson masses, branching ratios and ratios of production cross sections with respect to reference values.Reasons for new version: This version extends the functionality of the previous version.Summary of revisions: List of included Higgs searches has been expanded, e.g. inclusion of (singly) charged Higgs boson searches. The input required from the user has been extended accordingly.Restrictions: Assumes that the narrow width approximation is applicable in the model under consideration and that the model does not predict a significant change to the signature of the background processes or the kinematical distributions of the signal cross sections.Running time: About 0.01 seconds (or less) for one parameter point using one processor of an Intel Core 2 Quad Q6600 CPU at 2.40 GHz for sample model scenarios with three Higgs bosons. It depends on the complexity of the Higgs sector (e.g. the number of Higgs bosons and the number of open decay channels) and on the code version.     

FIESTA 2: Parallelizeable multiloop numerical calculations

The program FIESTA has been completely rewritten. Now it can be used not only as a tool to evaluate Feynman integrals numerically, but also to expand Feynman integrals automatically in limits of momenta and masses with the use of sector decompositions and Mellin–Barnes representations. Other important improvements to the code are complete parallelization (even to multiple computers), high-precision arithmetics (allowing to calculate integrals which were undoable before), new integrators, Speer sectors as a strategy, the possibility to evaluate more general parametric integrals.

Program summary

Program title:FIESTA 2Catalogue identifier: AECP_v2_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AECP_v2_0.htmlProgram obtainable from: CPC Program Library, Queen's University, Belfast, N. IrelandLicensing provisions: GNU GPL version 2No. of lines in distributed program, including test data, etc.: 39 783No. of bytes in distributed program, including test data, etc.: 6 154 515Distribution format: tar.gzProgramming language: Wolfram Mathematica 6.0 (or higher) and CComputer: From a desktop PC to a supercomputerOperating system: Unix, Linux, Windows, Mac OS XHas the code been vectorised or parallelized?: Yes, the code has been parallelized for use on multi-kernel computers as well as clusters via Mathlink over the TCP/IP protocol. The program can work successfully with a single processor, however, it is ready to work in a parallel environment and the use of multi-kernel processor and multi-processor computers significantly speeds up the calculation; on clusters the calculation speed can be improved even further.RAM: Depends on the complexity of the problemClassification: 4.4, 4.12, 5, 6.5Catalogue identifier of previous version: AECP_v1_0Journal reference of previous version: Comput. Phys. Comm. 180 (2009) 735External routines: QLink [1], Cuba library [2], MPFR [3]Does the new version supersede the previous version?: YesNature of problem: The sector decomposition approach to evaluating Feynman integrals falls apart into the sector decomposition itself, where one has to minimize the number of sectors; the pole resolution and epsilon expansion; and the numerical integration of the resulting expression.Solution method: The sector decomposition is based on a new strategy as well as on classical strategies such as Speer sectors. The sector decomposition, pole resolution and epsilon-expansion are performed in Wolfram Mathematica 6.0 or, preferably, 7.0 (enabling parallelization) [4]. The data is stored on hard disk via a special program, QLink [1]. The expression for integration is passed to the C-part of the code, that parses the string and performs the integration by one of the algorithms in the Cuba library package [2]. This part of the evaluation is perfectly parallelized on multi-kernel computers.Reasons for new version:

• 1. 

  The first version of FIESTA had problems related to numerical instability, so for some classes of integrals it could not produce a result.

• 2. 

  The sector decomposition method can be applied not only for integral calculation.

Summary of revisions:

• 1. 

  New integrator library is used.

• 2. 

  New methods to deal with numerical instability (MPFR library).

• 3. 

  Parallelization in Mathematica.

• 4. 

  Parallelization on multiple computers via TCP-IP.

• 5. 

  New sector decomposition strategy (Speer sectors).

• 6. 

  Possibility of using FIESTA to for integral expansion.

• 7. 

  Possibility of using FIESTA to discover poles in d.

• 8. 

  New negative terms resolution strategies.

Restrictions: The complexity of the problem is mostly restricted by CPU time required to perform the evaluation of the integralRunning time: Depends on the complexity of the problemReferences:

• [1] 

  http://qlink08.sourceforge.net, open source.

• [2] 

  http://www.feynarts.de/cuba/, open source.

• [3] 

  http://www.mpfr.org/, open source.

• [4] 

  http://www.wolfram.com/products/mathematica/index.html.