Analyzing the parton densities and constructing the xF3 structure function, using the Laguerre polynomials expansion and Monte Carlo calculations

Abstract

We consider the neutrino-nucleon scattering to analyse the xF3 structure function. We solve first numerically the DGLAP evolution equation, using the Laguerre polynomials expansion and Monte Carlo calculations. What we get for the evolved parton densities is in good agreement with the fitting GRSV and CETQ parameterizations. We then construct the xF3 structure function in the Bjorken x-space using the Laguerre polynomials expansion while we achieve this structure function initially in the Mellin moment space. The relations which convert the structure function from the Mellin moment space to the Bjorken x-space, using the Laguerre polynomials, are introduced for the first time in this article. These relations enable us to do the fitting and extract the QCD cut-off parameter which is in good agreement with what is expected. To confirm the calculation we reconstruct the xF3 structure function directly in Bjorken x-space using the evolved parton densities which are obtained, themselves, based on the Laguerre expansion. At this stage, to get the evolved parton densities, we employ the QCD cut-off parameter which we get from the fitting. The results for the xF3 structure function, using the two different described methods, are in good agreement with each other and also with the available experimental data which confirms the validity of our calculations.