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Athron, P., Park, J. H., Stockinger, D., & Voigt, A. (2015). FlexibleSUSY-A spectrum generator generator for supersymmetric models. Comput. Phys. Commun., 190, 139–172.
Abstract: We introduce FlexibleSUSY, a Mathematica and C++ package, which generates a fast, precise C++ spectrum generator for any SUSY model specified by the user. The generated code is designed with both speed and modularity in mind, making it easy to adapt and extend with new features. The model is specified by supplying the superpotential, gauge structure and particle content in a SARAH model file; specific boundary conditions e.g. at the GUT, weak or intermediate scales are defined in a separate FlexibleSUSY model file. From these model files, FlexibleSUSY generates C++ code for self-energies, tadpole corrections, renormalization group equations (RGEs) and electroweak symmetry breaking (EWSB) conditions and combines them with numerical routines for solving the RGEs and EWSB conditions simultaneously. The resulting spectrum generator is then able to solve for the spectrum of the model, including loop-corrected pole masses, consistent with user specified boundary conditions. The modular structure of the generated code allows for individual components to be replaced with an alternative if available. FlexibleSUSY has been carefully designed to grow as alternative solvers and calculators are added. Predefined models include the MSSM, NMSSM, E6SSM, USSM, R-symmetric models and models with right-handed neutrinos. Program Summary Program title: FlexibleSUSY Catalogue identifier: AEVIv10 Program summary URL: http://cpc.cs.qub.ac.uk/summaries/AEVIv10.html obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: GNU General Public License, version 3 No. of lines in distributed program, including test data, etc.: 129406 No. of bytes in distributed program, including test data, etc.: 854831 Distribution format: tar.gz Programming language: C++, Wolfram/Mathematica, FORTRAN, Bourne shell. Computer: Personal computer. Operating system: Tested on Linux 3.x, Mac OS X. Classification: 11.1, 11.6, 6.5. External routines: SARAH 4.0.4, Boost library, Eigen, LAPACK Nature of problem: Determining the mass spectrum and mixings for any supersymmetric model. The generated code must find simultaneous solutions to constraints which are specified at two or more different renormalization scales, which are connected by renormalization group equations forming a large set of coupled first-order differential equations. Solution method: Nested iterative algorithm and numerical minimization of the Higgs potential. Restrictions: The couplings must remain perturbative at all scales between the highest and the lowest boundary condition. FlexibleSUSY assumes that all couplings of the model are real (i.e. CP-conserving). Due to the modular nature of the generated code, adaption and extension to overcome restrictions in scope is quite straightforward. Running time: 0.06-0.2 seconds per parameter point.
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Sanchis-Lozano, M. A., Barbero, J. F., & Navarro-Salas, J. (2012). Prime Numbers, Quantum Field Theory and the Goldbach Conjecture. Int. J. Mod. Phys. A, 27(23), 1250136–24pp.
Abstract: Motivated by the Goldbach conjecture in number theory and the Abelian bosonization mechanism on a cylindrical two-dimensional space-time, we study the reconstruction of a real scalar field as a product of two real fermion (so-called prime) fields whose Fourier expansion exclusively contains prime modes. We undertake the canonical quantization of such prime fields and construct the corresponding Fock space by introducing creation operators b(p)(dagger) – labeled by prime numbers p – acting on the vacuum. The analysis of our model, based on the standard rules of quantum field theory and the assumption of the Riemann hypothesis, allows us to prove that the theory is not renormalizable. We also comment on the potential consequences of this result concerning the validity or breakdown of the Goldbach conjecture for large integer numbers.
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