DGLAP evolution of truncated moments of parton densities within two different approaches

Abstract

We solve the LO DGLAP QCD evolution equation for truncated Mellin moments of the nucleon nonsinglet structure function. The results are compared with those, obtained in the Chebyshev-polynomial approach for $x$-space solutions. Computations are performed for a wide range of the truncation point $10^{-5}\leq x_0\leq 0.9$ and $1\leq Q^2\leq 100 {\rm GeV}^2$. The agreement is perfect for higher moments ($n\geq 2$) and not too large $x_0$ ($x_0\leq 0.1$), even for a small number of terms in the truncated series (M=4). The accuracy of the truncated moments method increases for larger $M$ and decreases very slowly with increasing $Q^2$. For M=30 the relative error in a case of the first moment at $x_0\leq 0.1$ and $Q^2=10 {\rm GeV}^2$ doesn't exceed 5% independently on the shape of the input parametrisation. This is a quite satisfactory result. Using the truncated moments approach one can avoid uncertainties from the unmeasurable $x\to 0$ region and also study scaling violations without making any assumption on the shape of input parametrisation of parton distributions. Therefore the method of truncated moments seems to be a useful tool in further QCD analyses.