RacoonWW1.3: A Monte Carlo program for four-fermion production at ee colliders

We present the Monte Carlo generator RacoonWW that computes cross sections to all processes e⁺e⁻→4f and e⁺e⁻→4fγ and calculates the complete electroweak radiative corrections to e⁺e⁻→WW→4f in the electroweak Standard Model in double-pole approximation. The calculation of the tree-level processes e⁺e⁻→4f and e⁺e⁻→4fγ is based on the full matrix elements for massless (polarized) fermions. When calculating radiative corrections to e⁺e⁻→WW→4f, the complete virtual doubly-resonant electroweak corrections are included, i.e. the factorizable and non-factorizable virtual corrections in double-pole approximation, and the real corrections are based on the full matrix elements for e⁺e⁻→4fγ. The matching of soft and collinear singularities between virtual and real corrections is done alternatively in two different ways, namely by using a subtraction method or by applying phase-space slicing. Higher-order initial-state photon radiation and naive QCD corrections are taken into account. RacoonWW also provides anomalous triple gauge-boson couplings for all processes e⁺e⁻→4f and anomalous quartic gauge-boson couplings for all processes e⁺e⁻→4fγ.     

PHANTOM: A Monte Carlo event generator for six parton final states at high energy colliders

PHANTOM is a tree level Monte Carlo for six parton final states at proton-proton, proton-antiproton and electron-positron colliders at and including possible interferences between the two sets of diagrams. This comprehends all purely electroweak contributions as well as all contributions with one virtual or two external gluons. It can generate unweighted events for any set of processes and it is interfaced to parton shower and hadronization packages via the latest Les Houches Accord protocol. It can be used to analyze the physics of boson-boson scattering, Higgs boson production in boson-boson fusion, and three boson production.

Program summary

Program title:PHANTOM (V. 1.0)Catalogue identifier: AECE_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AECE_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.: 175 787No. of bytes in distributed program, including test data, etc.: 965 898Distribution format: tar.gzProgramming language: Fortran 77Computer: Any with a UNIX, LINUX compatible Fortran compilerOperating system: UNIX, LINUXRAM: 500 MBClassification: 11.1External routines: LHAPDF (Les Houches Accord PDF Interface, http://projects.hepforge.org/lhapdf/), CIRCE (beamstrahlung for e⁺e⁻ ILC collider).Nature of problem: Six fermion final state processes have become important with the increase of collider energies and are essential for the study of top, Higgs and electroweak symmetry breaking physics at high energy colliders. Since thousands of Feynman diagrams contribute in a single process and events corresponding to hundreds of different final states need to be generated, a fast and stable calculation is needed.Solution method:PHANTOM is a tree level Monte Carlo for six parton final states at proton-proton, proton-antiproton and electron-positron colliders. It computes all amplitudes at and including possible interferences between the two sets of diagrams. The matrix elements are computed with the helicity formalism implemented in the program PHACT [1]. The integration makes use of an iterative-adaptive multichannel method which, relying on adaptivity, allows the use of only a few channels per process. Unweighted event generation can be performed for any set of processes and it is interfaced to parton shower and hadronization packages via the latest Les Houches Accord protocol.Restrictions: All Feynman diagrams are computed al LO.Unusual features: Phantom is written in Fortran 77 but it makes use of structures. The g77 compiler cannot compile it as it does not recognize the structures. The Intel, Portland Group, True64 HP Fortran 77 or Fortran 90 compilers have been tested and can be used.Running time: A few hours for a cross section integration of one process at per mille accuracy. One hour for one thousand unweighted events.References:

[1]

A. Ballestrero, E. Maina, Phys. Lett. B 350 (1995) 225, hep-ph/9403244; A. Ballestrero, PHACT 1.0, Program for helicity amplitudes Calculations with Tau matrices, hep-ph/9911318, in: B.B. Levchenko, V.I. Savrin (Eds.), Proceedings of the 14th International Workshop on High Energy Physics and Quantum Field Theory (QFTHEP 99), SINP MSU, Moscow, p. 303.

     

eett6f v. 1.0: A program for top quark pair production and decay into 6 fermions at linear colliders

The first version of a computer program eett6f for calculating cross sections of e⁺e⁻→6 fermions processes relevant for a -pair production and decay at centre of mass energies typical for linear colliders is presented. eett6f v. 1.0 allows for calculating both the total and differential cross sections at tree level of the Standard Model (SM). The program can be used as the Monte Carlo generator of unweighted events as well.     

WPHACT 2.0: A fully massive Monte Carlo generator for four fermion physics at ee colliders

WPHACT 2.0 is the new fully massive version of a MC program and unweighted event generator which computes all Standard Model processes with four fermions in the final state at e⁺e⁻ colliders. The program can now generate unweighted events for any subset of all four fermion final states in a single run, by making use of dedicated pre-samples which can cover the entire phase space. Improvements with respect to WPHACT 1.0 include the Imaginary Fermion Loop gauge restoring scheme, new phase space mappings, a new input system, the possibility to compute subsets of Feynman diagrams and options for including ISR via QEDPS, running α_QED, CKM mixing, resonances in channels.     

The Monte Carlo Event Generator AcerMC version 1.0 with interfaces to PYTHIA 6.2 and HERWIG 6.3

The AcerMC Monte Carlo Event Generator is dedicated for the generation of Standard Model background processes at pp LHC collisions. The program itself provides a library of the massive matrix elements and phase space modules for generation of a set of selected processes: , , , , and complete electroweak process. The hard process event, generated with one of these modules, can be completed by the initial and final state radiation, hadronization and decays, simulated with either PYTHIA or HERWIG Monte Carlo event generator. Interfaces to both of these generators are provided in the distribution version. The matrix element codes have been derived with the help of the MADGRAPH package. The phase-space generation is based on the multi-channel self-optimizing approach as proposed in NEXTCALIBUR event generator. Eventually, additional smoothing of the phase space was obtained by using a modified ac-VEGAS routine in order to improve the generation efficiency.     

Development of a Geant4 solid for stereo mini-jet cells in a cylindrical drift chamber

Stereo mini-jet cells will be indispensable components of a future e⁺e⁻ linear collider central tracker such as JLC-CDC. There is, however, no official Geant4 solid available at present to describe such geometrical objects, which had been a major obstacle for us to develop a full Geant4-based simulator with stereo cells built in. We have thus extended Geant4 to include a new solid (TwistedTubs), which consists of three kinds of surfaces: two end planes, inner and outer hyperboloidal surfaces, and two so-called twisted surfaces that make slant and twisted φ-boundaries. Design philosophy and its realization in the Geant4 framework are described together with algorithmic details. We have implemented stereo cells with the new solid, and tested them using geantinos and Pythia events (e⁺e⁻→ZH at  GeV). The performance was found reasonable: the stereo cells consumed only 25% more CPU time than ordinary axial cells.     

TaylUR 3, a multivariate arbitrary-order automatic differentiation package for Fortran 95

This new version of TaylUR is based on a completely new core, which now is able to compute the numerical values of all of a complex-valued function's partial derivatives up to an arbitrary order, including mixed partial derivatives.

New version program summary

Program title: TaylURCatalogue identifier: ADXR_v3_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADXR_v3_0.htmlProgram obtainable from: CPC Program Library, Queen's University, Belfast, N. IrelandLicensing provisions: GPLv2No. of lines in distributed program, including test data, etc.: 6750No. of bytes in distributed program, including test data, etc.: 19 162Distribution format: tar.gzProgramming language: Fortran 95Computer: Any computer with a conforming Fortran 95 compilerOperating system: Any system with a conforming Fortran 95 compilerClassification: 4.12, 4.14Catalogue identifier of previous version: ADXR_v2_0Journal reference of previous version: Comput. Phys. Comm. 176 (2007) 710Does the new version supersede the previous version?: YesNature of problem: Problems that require potentially high orders of partial derivatives with respect to several variables or derivatives of complex-valued functions, such as e.g. momentum or mass expansions of Feynman diagrams in perturbative QFT, and which previous versions of this TaylUR [1,2] cannot handle due to their lack of support for mixed partial derivatives.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 partial derivatives with respect to the user-defined independent variables. Derivatives of products and composite functions are computed using multivariate forms [3] of Leibniz's rule where ν=(ν₁,…,νd), , , Dνf=^∂|ν|f/(ν₁^∂x₁?νd^∂xd), and μ<ν iff either |μ|<|ν| or |μ|=|ν|,μ₁=ν₁,…,μk=νk,μk+1<νk+1 for some k∈{0,…,d−1}, and of Fàa di Bruno's formula where the sum is over , . An indexed storage system is used to store the higher-order derivative tensors in a one-dimensional array. The relevant indices (k₁,…,ks;λ₁,…,λs) and the weights occurring in the sums in Leibniz's and Fàa di Bruno's formula are precomputed at startup and stored in static arrays for later use.Reasons for new version: The earlier version lacked support for mixed partial derivatives, but a number of projects of interest required them.Summary of revisions: The internal representation of a taylor object has changed to a one-dimensional array which contains the partial derivatives in ascending order, and in lexicographic order of the corresponding multiindex within the same order. The necessary mappings between multiindices and indices into the taylor objects' internal array are computed at startup. To support the change to a genuinely multivariate taylor type, the DERIVATIVE function is now implemented via an interface that accepts both the older format derivative(f,mu,n) and also a new format derivative(f,mu(:))=Dμf that allows access to mixed partial derivatives. Another related extension to the functionality of the module is the HESSIAN function that returns the Hessian matrix of second derivatives of its argument. Since the calculation of all mixed partial derivatives can be very costly, and in many cases only some subset is actually needed, a masking facility has been added. Calling the subroutine DEACTIVATE_DERIVATIVE with a multiindex as an argument will deactivate the calculation of the partial derivative belonging to that multiindex, and of all partial derivatives it can feed into. Similarly, calling the subroutine ACTIVATE_DERIVATIVE will activate the calculation of the partial derivative belonging to its argument, and of all partial derivatives that can feed into it. Moreover, it is possible to turn off the computation of mixed derivatives altogether by setting Diagonal_taylors to .TRUE.. It should be noted that any change of Diagonal_taylors or Taylor_order invalidates all existing taylor objects. To aid the better integration of TaylUR into the HPSrc library [4], routines SET_DERIVATIVE and SET_ALL_DERIVATIVES are provided as a means of manually constructing a taylor object with given derivatives.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: These are the same as in previous versions, but are enumerated again here for clarity. The complex conjugation operation assumes all independent variables to be real. The functions REAL and AIMAG do not convert to real type, but return a result of type taylor (with the real/imaginary part of each derivative taken) instead. The user-defined functions VALUE, REALVALUE and IMAGVALUE, which return the value of a taylor object as a complex number, and the real and imaginary part of this value, respectively, as a real number are also provided. Fortran 95 intrinsics that are defined only for arguments of real type (ACOS, AINT, ANINT, ASIN, ATAN, ATAN2, CEILING, DIM, FLOOR, INT, LOG10, MAX, MAXLOC, MAXVAL, MIN, MINLOC, MINVAL, MOD, MODULO, NINT, SIGN) will silently take the real part of taylor-valued arguments unless the module variable Real_args_warn is set to .TRUE., in which case they will return a quiet NaN value (if supported by the compiler) when called with a taylor argument whose imaginary part exceeds the module variable Real_args_tol. In those cases where the derivative of a function becomes undefined at certain points (as for ABS, AINT, ANINT, MAX, MIN, MOD, and MODULO), while the value is well defined, the derivative fields will be filled with quiet NaN values (if supported by the compiler).Additional comments: This version of TaylUR is released under the second version of the GNU General Public License (GPLv2). Therefore anyone is free to use or modify the code for their own calculations. As part of the licensing, it is requested that any publications including results from the use of TaylUR or any modification derived from it cite Refs. [1,2] as well as this paper. Finally, users are also requested to communicate to the author details of such publications, as well as of any bugs found or of required or useful modifications made or desired by them.Running time: The running time of TaylUR operations grows rapidly with both the number of variables and the Taylor expansion order. Judicious use of the masking facility to drop unneeded higher derivatives can lead to significant accelerations, as can activation of the Diagonal_taylors variable whenever mixed partial derivatives are not needed.Acknowledgments: The author thanks Alistair Hart for helpful comments and suggestions. This work is supported by the Deutsche Forschungsgemeinschaft in the SFB/TR 09.References:

[1]

G.M. von Hippel, TaylUR, an arbitrary-order diagonal automatic differentiation package for Fortran 95, Comput. Phys. Comm. 174 (2006) 569.

[2]

G.M. von Hippel, New version announcement for TaylUR, an arbitrary-order diagonal automatic differentiation package for Fortran 95, Comput. Phys. Comm. 176 (2007) 710.

[3]

G.M. Constantine, T.H. Savits, A multivariate Faa di Bruno formula with applications, Trans. Amer. Math. Soc. 348 (2) (1996) 503.

[4]

A. Hart, G.M. von Hippel, R.R. Horgan, E.H. Müller, Automated generation of lattice QCD Feynman rules, Comput. Phys. Comm. 180 (2009) 2698, doi:10.1016/j.cpc.2009.04.021, arXiv:0904.0375.

     

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.     

How strong is Nisan?s pseudo-random generator?

We study the resilience of the classical pseudo-random generator (PRG) of Nisan (1992) [6] against space-bounded machines that make multiple passes over the input. Nisan?s PRG is known to fool log-space machines that read the input once. We ask what are the limits of this PRG regarding log-space machines that make multiple passes over the input. We show that for every constant k Nisan?s PRG fools log-space machines that make passes over the input, using a seed of length , for some k^′>k. We complement this result by showing that in general Nisan?s PRG cannot fool log-space machines that make nO(1) passes even for a seed of length . The observations made in this note outline a more general approach in understanding the difficulty of derandomizing BPNC¹.