Parton distribution uncertainties using smoothness prior

A study of the parameterization uncertainty at low Bjorken x⩽0.1 for the parton distribution functions of the proton is presented. The study is based on the HERA I combined data using a flexible parameterization form based on Chebyshev polynomials with and without an additional regularization constraint. The accuracy of the data allows to determine the gluon density in the kinematic range of 0.0005⩽x⩽0.05 with a small parameterization uncertainty. An additional regularization prior leads to a significantly reduced uncertainty for x⩽0.0005.