Solving the Altarelli–Parisi equations with truncated moments

The technique of truncated moments of parton distributions allows us to study scaling violations without making any assumption on the shape of parton distributions. The numerical implementation of the method is, however, difficult, since the evolution equations for truncated moments are not diagonal. We present a simple way to improve the efficiency of the numerical solution of the evolution equations for truncated moments. As a result, the number of truncated moments needed to achieve the required precision in the evolution is significantly smaller than in the original formulation of the technique. The method presented here can also be used to obtain the value of parton distributions in terms of truncated moments, and, therefore, it can be viewed as a technique for the solution of the Altarelli–Parisi equations.