SIDIS-RC EvGen: A Monte-Carlo event generator of semi-inclusive deep inelastic scattering with the lowest-order QED radiative corrections

Abstract

SIDIS-RC EvGen is a C++ standalone Monte-Carlo event generator for studies of semi-inclusive deep inelastic scattering (SIDIS) processes at medium to high lepton beam energies. In particular, the generator contains binary and library components for generating SIDIS events and calculating cross sections for unpolarized or longitudinally polarized beam and unpolarized, longitudinally or transversely polarized target. The structure of the generator incorporates transverse momentum-dependent parton distribution and fragmentation functions, whereby we obtain multi-dimensional binned simulation results, which will facilitate the extraction of important information about the three-dimensional nucleon structure from SIDIS measurements. In order to build this software, we have used recent elaborate QED calculations of the lowest-order radiative effects, applied to the leading order Born cross section in SIDIS. In this paper, we provide details on the theoretical formalism as well as the construction and operation of SIDIS-RC EvGen, e.g., how we handle the event generation process and perform multi-dimensional integration. We also provide example programs, flowcharts, and numerical results on azimuthal transverse single-spin asymmetries. Program summaryProgram title: SIDIS-RC EvGenCPC Library link to program files:https://doi.org/10.17632/thrkn96ydd.1Licensing provisions: GNU General Public License Version 3Developer's repository link:https://github.com/duanebyer/sidisProgramming language: C++, PythonExternal packages: FOAM, ROOT, GSL, VEGAS, Cubature, Cog, WW-SIDIS, MSTWPDFNature of problem: The task is to first create a code for calculations of the leading order Born cross section as well as radiative corrections (RCs) at the next-to-leading order (NLO) of the cross section of lepton-hadron semi-inclusive deep inelastic scattering (SIDIS) at medium to high beam energies with incident unpolarized or longitudinally polarized lepton beam and unpolarized, longitudinally or transversely polarized target, enabling to compute azimuthal single-target and double-beam-target spin asymmetries. Afterwards, a Monte-Carlo event generator based upon this code is developed, where in the coding and simulation processes multi-dimensional integrals need to be calculated precisely to obtain the exact NLO RCs to the SIDIS cross section with high precision beyond ultra-relativistic limit, which means that the lepton mass is taken into account.Solution method: The project for building the SIDIS-RC EvGen software is divided into a library component called libsidis, for the purpose of calculating the inelastic tail to the SIDIS total cross section, and a binary component called sidisgen, for generating events. The Monte-Carlo event generation is performed through the usage of the FOAM library, by applying a spatial partitioning method with hyper-cubical “foam of cells”. The multi-dimensional numerical integration is carried out by the GSL, VEGAS, and Cubature packages. The SIDIS structure functions that describe the SIDIS scattering process, and which are given in terms of transverse momentum-dependent parton distribution and fragmentation functions, are calculated in Gaussian and Wandzura–Wilczek-type approximations and implemented in the generator accordingly.Additional comments including restrictions and unusual features: The restrictions depend on the complexity of problems, limited by CPU time. As a consequence, the program running time is of order of several minutes to hours. SIDIS-RC EvGen does not comprise yet the contribution coming from the radiative tail of exclusive lepton-hadron reactions, which is a separate contribution involving exclusive structure functions that are currently not well known.Developer's repository maintained by Duane Byer; Department of Physics, Duke University.