Low-Energy Quark Mass Test for U and D Via Elastic Form Factors

Abstract

The study was aimed at providing a device to estimate the range of values of the u- and d-quark masses through the elastic ep-scattering form factors at the low energy regime. ROOT generated dcsep data sets, from theoretical and experimental form factors, were compared to modified dcseq and their intersections were determined from the average of a total of 3000 events for each dcs at various scattering angles selected randomly from 0o to 180o. The proton mass was required as a parameter used in the relativistic recoil factor of dcseq to shift its distribution closer to dcsep thereby attaining the critical intersections. For quarks carrying effective masses, the extrapolated energy intersection of dcsep generated from the average of all form factors with the modified dcseu is 226.00013MeV2 and this is lesser than that of the modified dcsed at 1093.00004MeV2 with bin size of 1MeV2 and their respective dcs intersections are 10.07049x10-4 and 0.36976x10-4, in barns. Summary of results are also given for quark masses derived from MS scheme and Lattice QCD. By considering all possible scattering angles at fixed transfer momentum, the relativistic recoil factor was treated as a constant that shifted the distribution and gave rise to a tool in estimating quark mass range.